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7 Day Prayer Miracle

7 Day Prayer Miracles is products which depict the life of Amanda Rose, who is living testimony of what the miracle can do in your life. She went through a difficult time in her life but eventually, it came to pass. The most troubling challenges which she went through was the tragic accident which saw her husband bedridden for some time. In addition to that, she had a lot of debts, which was bringing a lot of embarrassment to other people in life. However, after meeting Michael, who shared with her about the prayers, she decided to try the power of the prayer. On the first day when she prayed, she received a call from the landlord who apologized. She received some more miracles in life, and she was a witness what God could do with your life. The product is available on e-Book and comes with a bonus More here...

7 Day Prayer Miracle Summary


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Milestones in the History of Celestial Mechanics of the Planetary System

The history of Celestial Mechanics should start with the first attempts to observe and predict the apparent motions of the Moon, the Sun, and the planets w.r.t. the celestial sphere of fixed stars. Our story, however, begins in the 16th century with the epoch of Tycho Brahe (1546-1601) and Johannes Kepler (1571-1630). Towards the end of the 16th century Brahe had set new standards in astronomical observation techniques. First in Denmark (1576-1597), then in Prague (1599-1601), he and his collaborators observed the positions of the planets and the Sun w.r.t. the zodiacal stars with an accuracy of about 1-2 arcminutes ('). Loosely speaking, the position of a celestial body is the direction from the observer to the observed object at a certain observation epoch. The astronomical position is characterized by a unit vector (which in turn may be specified by two angles) and the corresponding observation time. The accuracy achieved by Brahe was one of the best in the pre-telescope era, close...

Laplaces Response and Implications for Celestial Mechanics

Pierre-Simon Laplace (1749-1827) was the foremost mathematical physicist of his generation. He is best known for his Celestial Mechanics, which appeared in five volumes between 1799 and 1825 and which put this science on a new and more systematic foundation. Although Laplace never gave Le Sage's theory serious consideration, he was influenced by it to explore two effects that Other philosophers, on the contrary, admit their ignorance on the nature of matter, of space, of force and of extension, and trouble themselves little about first causes, seeing in attraction only a general phenomenon which, being subjectable to a rigorous calculation, gives the complete explanation of all the celestial phenomena and the means of perfecting the tables and the theory of the motion of the stars. It is uniquely under this point of view that I have envisaged attraction in my work. Perhaps I have not had enough consideration for the first philosophers of whom I have just spoken, in not presenting to...

Anaxagoras Makes the Celestial Bodies Mundane

Anaxagoras still held the view, as did Anaximenes of Miletus, that the Earth is flat and floats in the air. This did not hinder him from making important observations about celestial matters. He suggested that the Moon receives its light from the Sun and he correctly explained solar and lunar eclipses. He taught that celestial phenomena could be understood in terms of the same materials as those down here. So he regarded the Sun as a hot glowing mass or a rock on fire, and the Moon with plains and ravines similar to the Earth. He was impressed by the fall of a meteorite and explained it as a result of an earthquake occurring on some celestial body. Ideas like these were not well received by many, as stars and planets were generally viewed as gods. Anaxagoras was accused of impiety. Pericles helped him to escape

Celestial Coordinates

In astronomy, many different coordinate systems are commonly used. To enjoy the night sky it is not necessary to tangle with the mathematics of coordinates. However, it is quite useful to become familiar with the most important coordinate system, the celestial equatorial system. One can imagine the equatorial system as a projection of the earth's longitude and latitude circles from the center of the earth onto the celestial sphere. Right ascension corresponds to geographical longitude declination corresponds to geographical latitude. In the same way that Greenwich marks the zero meridian on earth, the first point of Aries serves as the zero point for the right ascension it is the location of the sun on March 20 21. From there, right ascension is measured towards the east from 0 to 360 , or, more often, from 0h to 24h (hours) with 1h 15 . Declination increases as geographical latitude from 0 at the equator to 90 at the poles. Northern declinations are positive, southern ones negative....

Stars And Celestial Coordinates

Celestial pole and extending to the Red Road, what in modern terms would be called the celestial equator. In terms of the concept of the celestial sphere, as it later became known, each lodge is analogous to an orange slice, in which the orange, or celestial sphere, is cut into 28 slices. The width of the mansions varied considerably, from 1.5 degrees to 30 degrees. The primary concept in describing the motion of a planet was the time at which it reached the meridian. Thus time rather than angular measure was the fundamental conceptual parameter of interest in astronomy. The coordinates of a celestial object were specified by the lodge in which it was located, its distance from the edge of the lodge, and the distance from the celestial pole. Distances were expressed in terms of a unit called a du, there being 365 1 4 dus in a whole circle. The du was the distance traveled by the Sun on the celestial sphere in one day and was therefore a temporal unit of measurement. With the advent of...

Hipparchus Discovers the Slow Wobbling of the Celestial Sphere

Catalogs of stars and other celestial bodies have been and continue to be very important for our knowledge of the universe. In fact, comparing his stellar catalog with the measurements by two Alexandrian astronomers one and half centuries earlier, Hipparchus discovered a slow motion of the sky. He used coordinates to give the location of a star on the sky. These are similar to latitude and longitude on the spherical Earth. To define these two coordinates, one needs a fundamental circle dividing the sphere into halves and on it a fixed zero-point. For the Earth, these are the equator and its intersection with the north-south line (meridian) passing through Greenwich Observatory near London. The longitude of, say, a ship on Earth is the number of degrees from Greenwich along the equator to where a north-south line through the ship crosses the equator. The latitude of the ship is the number of degrees along this circle north or south of the Earth's equator. In the course of a year, the...

Southern hemisphere celestial spheres

To clarify the ideas introduced in the previous sections, we consider the celestial sphere for an observer in the southern hemisphere. Let the latitude be S. Then the celestial pole above the horizon is the south celestial pole Q. We proceed as follows Figure 8.4. A southern hemisphere celestial sphere. Figure 8.4. A southern hemisphere celestial sphere. 4. Insert Q, the south celestial pole, between the south point S and the zenith Z and such that the altitude SQ of the pole is the latitude of the observer. We can then insert the north celestial pole P directly opposite. 5. Put the celestial equator in the diagram, remembering that P and Q are its poles.

Introduction to Geometry on the Celestial Sphere

The celestial sphere is an imaginary sphere of unit radius centered on the observer, used to represent directions in space. It comes from classical observational astronomy and is far older than almost any other modern astronomical concept The compelling image of the bowl of the sky at night makes it easy to think of stars and planets moving on a fixed, distant sphere. We now know, of course, that their distances from us are vastly different But the concept of watching and computing the position and motion of things on the unit celestial sphere remains a very valuable contribution of classical astronomy to modem spaceflight analysis. Unfortunately, relatively few modern references are available. By far, the most detailed treatment is provided by Wertz 2001 . Green 1985 , and Smart 1977 provide information on spherical astronomy. Figure 5-3 illustrates the use of the celestial sphere to represent directions to objects in space. These objects may be very close, such as other components...

Finding Celestial Objects

Three essentials for CCD imaging are finding, focusing, and following you can't make images if you can't find celestial objects images have little value if they are not in focus and your telescope must follow an object for a reasonable length of time for a high-quality image. Equipment that makes these tasks easy is fundamental to long-exposure imaging. Many observers report some degree of difficulty finding celestial objects when they begin using an astronomical CCD or DSLR camera. The skills needed to find objects for imaging are no different than those needed for visual finding the difference lies entirely in the accuracy required. While pointing within V20 is adequate for most visual observers, digital imaging is most efficient when you can accurately point the telescope within a few minutes of arc pointing errors of V20 are frustrating, if not unacceptable. Unity-Power Finders. Although Telrad-type finders offer neither magnification nor added light grasp, many observers swear by...

Location On The Celestial Sphere

Every star has a location on the celestial sphere, where it appears to be when sighted from Earth. The right ascension and declination of stars for a standard epoch, or point of time selected as a fixed reference, change little over a period of many years. They can be read from a celestial globe, star atlas, or computer software. (See Table 1.1, for example. You'll be referring to this table when the information it contains is discussed in later chapters.) The locations of the Sun, Moon, and planets on the celestial sphere change regularly. You can find their monthly positions, rise and set times, and other practical data in current astronomical publications, computer software (see Useful Resources and Web Sites) and at the U.S. Naval Observatory Web site. http aa.usno.navy.mil Explain why in any given era the stars may be found at practically the same coordinates on the celestial sphere, while the Sun, Moon, and planets change their locations regularly._

Guides to the South Celestial Pole SCP Fig 23 not to scale

* The closest constellation to the South Celestial Pole is the dim constellation Octans. It is too dim to be of much value in locating the SCP. * The South Celestial Pole lies midway between Acrux (Star 1 of Crux) and Achernar of Eridanus, but 4.5 degrees to the side of that line. * Moving along the line from Star 3 of Crux through Acrux, approximately 472 times the length of Crux leads to the South Celestial Pole. * The South Celestial Pole is on a line perpendicular to the midpoint of a line between Rigil Kentaurus (Star 1) and Hadar (Star 2) of Centaurus. The distance to the SCP is approximately six times the distance between Rigil Kentaurus and Hadar. * If you flip the triangle of Hydrus over, Star 1 of Hydrus, which is closest to Achernar, will lay near the South Celestial Pole. * Star 2 of Hydrus is 13 degrees from the South Celestial Pole. * A line from Sirius to Canopus leads to the South Celestial Pole. The distance between Sirius and Canopus is 36 degrees, between Canopus...

Rotational Kinematics and Celestial Sphere

Figure 7.7 depicts a celestial sphere centered in the origin of a coordinate frame. As we have discussed, length scales do not influence attitude determination and control, and so we may consider the sphere to be of unit radius. Fig. 7.7 Attitude measurements on the unit celestial sphere. Fig. 7.7 Attitude measurements on the unit celestial sphere. Directions may be specified in several ways on the celestial sphere. Possibly the most obvious is to use the Cartesian (x, y, z) coordinates of a particular point. Since

Properties and distances of celestial objects

The information content in the radiation recorded in observations allows astronomers to derive the properties of celestial objects. The ranges of the values of these properties are found to be astronomically large. Luminosities are derived from measured fluxes and distances. The solar luminosity, 3.8 x 1026 W, is a benchmark reference that of a bright quasar is 1013 times larger. The mass of the moon, earth, or of a galaxy can be determined by tracking the motion of one or more orbiting objects. The sun's mass, 1.99 x 1030 kg, is also a standard reference the (Milky Way) Galaxy is 1011 times more massive. The virial theorem is used to obtain the masses of clusters of galaxies. Temperatures can be defined for thermal sources, wherein the matter and radiation are in, or approximately in, thermal equilibrium. The temperatures of a hot gas may be determined in a variety of ways that may yield different values. Thus astronomers refer to kinetic, color, effective, excitation, and ionization...

The Celestial Coordinate System

One of the things that you will absolutely need is a star chart or atlas. Before we actually look at a star chart or atlas, there is one thing that you must understand the celestial coordinate system. This is an imaginary projection of the Earth's geographical coordinate system onto the celestial sphere that seems to turn overhead at night. This celestial grid is complete with equator, latitudes, longitudes and poles. As you know, the Earth is in constant motion as it rotates on its axis. As a result, the celestial coordinate system is being displaced very slowly with respect to the stars. The celestial equator is a 360-degree circle bisecting the celestial sphere into the northern celestial hemisphere and the southern celestial hemisphere. Like the Earth's equator, it is the prime parallel of latitude and is designated 0 degrees. The celestial parallels of latitude are called coordinates of declination (Dec) and much like the Earth's latitudes they are named for their angular...

Bl The International Celestial Reference Frame

Quite capable of making measurements at that level of accuracy. Professional astro-metry is now at the milli-arc-second level, thanks to very-long-baseline interferometry (VLBI) radio telescopes, and the Hipparcos astrometry satellite. The ICRF provides a celestial reference frame that meets the accuracy needs of modern astrometry. It is consistent with the simple picture of Figure B.1 but adds a variety of detailed prescriptions. For example, it is one thing to glibly say that the celestial equator is the projection of Earth's equator onto the sky'', and quite another to deal with the complexities of the real, moving Earth. The orientation of the Earth's equator wanders due to precession, by a few milli-arc-seconds per year. In order to be precise, you need to specify the date on which you set the orientation of the Equator when you projected it into the sky. Similarly, the position of the origin of Right Ascension isn't a fixed position in space the Earth's orbit around the Sun...

Solid angle on the celestial sphere

Solid Angle

The concept of solid angle Q is fundamental to all of astronomy. It is simply an angular area on the sky, or equivalently, on the celestial sphere. This area can be expressed as square degrees or square radians the latter unit is called the We refrain from saying that a region of 1 rad x 1 rad on the celestial sphere has a solid angle of 1.0 sr. Such a statement is incorrect because the celestial sphere is not a flat surface. Integration to find a solid angle that is a substantial portion of the celestial sphere makes use of the differential increment of solid angle d shown in Fig. 7 as a small shaded rectangular area. The solid angle is simply the product of two angular displacements each of which is a linear displacement on a sphere of unit radius. From Fig. 7, The solid angle of the entire celestial sphere can be calculated as follows. Apply the definition of the element of solid angle (14), Thus, the solid angle of the entire celestial sphere is 4 sr in agreement with (13). In...

Galaxies Near the Celestial Poles

There are two special areas in the sky that are not emphasized by star patterns the celestial poles 139 . Sweeping around them is perhaps the easiest with an altazimuth-mounted telescope. You will find a lot of galaxies within 5 of either pole (Tables 7.8 and 7.9). The most prominent northern object is NGC 3172, better known as Polarissima Borealis (Fig. 7.13). It is visible in a 12'', whereas its small companion MCG 15-1-10 needs at least 16'' aperture. The southern counterpart, NGC 2573 in Octans ( Polarissima Australis Fig. 7.14), is a bit brighter. Visual descriptions are given in Table 7.10. of the northern celestial pole (sorted by decreasing declination) Galaxies within 5 of the southern celestial pole (sorted by increasing declination) Table 7.10. Observations of galaxies near the celestial poles (sorted by designation)

The Perseids celestial fireworks

Greatest Eclipse

Apparently, the practice lasted for centuries. Today few people would profess belief in the divinatory power of shooting stars. For those that do, however, the sky this week will be crisscrossed with celestial portents in the form of the Perseid meteor shower. This is probably not a good week to be king.

Measuring the Motion of Celestial Bodies

North Celestial Pole Altitude

If we extend the plane on which the earth moves around the sun, imagining we are cutting the celestial sphere, we can define a circle known as the ecliptic. The earth's axis is not perpendicular to the plane of the ecliptic, but is inclined about 23 degrees with respect to it. This is thus the angle that the ecliptic forms with the celestial equator, that is, with the projection into the sky of the terrestrial equator. The inclination, or obliquity, of the ecliptic gives us the alternating seasons and is thus essential for life itself. (Over thousands of years it undergoes only slight variations). For us earthlings the ecliptic also represents the path of the sun in the course of the year in relation to the stars dotted around in the background. If we imagine prolonging the terrestrial axis onto the celestial sphere, a point in the sky is identified that we call the celestial pole (north or south depending on the hemisphere of the observer but to simplify matters, I shall refer only...

The Ecliptic and Celestial Equatorial Planes

The ecliptic (the path of the earth about the sun) is said to be in the ecliptic plane, which therefore contains the sun's and the earth's mass centers (Fig. 1.1). One also speaks of the celestial equatorial plane, which is the plane parallel to the earth's equatorial plane and through the sun's mass center. The ecliptic and celestial equatorial planes intersect, as illustrated in the figure, in a line referred to as the equinox line (because, when the earth on its annual path crosses this line, day and night have equal length). The crossing points are called the vernal equinox (the earth is at this point on about the 21st of March) and the autumnal equinox (about the 22nd of September). As discussed in Chapter 7, the vernal and autumnal equinox points play an important role in the operation of geosynchronous and other spacecraft. During two periods each year, centered around these points, and centered around local midnight, the sun will be eclipsed for these satellites. Special...

Celestial Showtime

When it comes to celestial displays, Eclipse first, and the rest nowhere also represents a succinct summary of the opinion of the eclipse enthusiast. Many people routinely book flights and accommodation a year ahead to ensure they are in the right place at the right time to experience a total solar eclipse, then feverishly check the next scheduled performance in this free-to-view continuing astronomical extravaganza to begin planning their next trip. Solar eclipses have been interpreted as evil omens by many civilizations because the life-giving sunlight is obscured for a few minutes, producing a profound effect upon all under the celestial shadow. Lunar eclipses, although they last far longer, are not so

Celestial Portraits

You now have some rough tools for measuring separations and sizes in the sky, but you still need a way to anchor your measurements, which, remember, are relative to where you happen to be standing on Earth. We need the celestial equivalent of landmarks. divided into constellations. The stars thus grouped generally have no physical relationship to one another. Nor do they necessarily even lie at the same distance from Earth some are much farther from us than others. So, remember, we simply imagine, for the sake of convenience, that they are embedded in the celestial sphere. The answer is that they are convenient (not to mention poetic) celestial landmarks. Take a right at Hank's gas station, you might tell a friend. What's so special about that particular gas station Nothing until you endow it with significance as a landmark. Nor was there anything special about a group of physically unrelated stars until someone endowed them with significance. Now these constellations can help us find...

The Celestial Sphere

The ancient universe was confined within a finite spherical shell. The stars were fixed to this shell and thus were all equidistant from the Earth, which was at the centre of the spherical universe. This simple model is still in many ways as useful as it was in antiquity it helps us to easily understand the diurnal and annual motions of stars, and, more important, to predict these motions in a relatively simple way. Therefore we will assume for the time being that all the stars are located on the surface of an enormous sphere and that we are at its centre. Because the radius of this celestial sphere is practically infinite, we can neglect the effects due to the changing position of the observer, caused by the rotation and orbital motion of the Earth. These effects will be considered later in Sects. 2.9 and 2.10. Since the distances of the stars are ignored, we need only two coordinates to specify their directions. Each coordinate frame has some fixed reference plane passing through...

Celestial Sphere

The earth is surrounded by stars at various distances, but when the night sky is viewed on a clear night from anywhere on the earth, it appears that all the stars (and other celestial objects) are fixed onto a huge sphere surrounding the observer. From any given place at any given time, roughly half of the sphere is visible above the horizon, provided that there are clear views unobscured by things like trees or buildings. The other half is below the horizon and invisible. The earth rotates in space once a day, and the stars are effectively motionless. (They are actually in motion with respect to one another, but generally the effects of these proper motions are so negligible that they will not affect the configurations of the stars in a way detectable with the naked eye over many tens of thousands of years or more.) This means that from the viewpoint of an observer on the earth, the celestial sphere appears to rotate around him or her once a day, with all the stars affixed to it....

Celestial Meridian

Go outside and trace out your zenith, celestial horizon, and celestial meridian by imagining yourself, like that stargazer, at the center of the huge celestial sphere. If possible, try this on a clear, dark, starry night. Face south. Observe the stars near your celestial meridian several times during the night. Describe what you observe._ Answer The stars move from east to west and transit, or cross, your celestial meridian. This is because of the Earth's rotation from west to east. A star culminates, or reaches its highest altitude, when it is on the celestial meridian.

Celestial Globe

The celestial globe records the figures and stars of all the constellations against a grid of lines representing longitude and latitude. During the 17th and 18th centuries, all ships of the Dutch East India Company were given a matching pair of globes terrestrial (p.10) and celestial. Calculations could be made by comparing the coordinates on the two different globes. In practice, however, most navigators seemed to use flat sea-charts to plot their journeys. Hydra, the water snake Celestial globe 1618

Celestial Mechanics

Celestial mechanics, the study of motions of celestial bodies, together with spherical astronomy, was the main branch of astronomy until the end of the 19th century, when astrophysics began to evolve rapidly. The primary task of classical celestial mechanics was to explain and predict the motions of planets and their satellites. Several empirical models, like epicycles and Kepler's laws, were employed to describe these motions. But none of these models explained why the planets moved the way they did. It was only in the 1680's that a simple explanation was found for all these mo

Celestial Brightness

Comets vary in luminosity, or brightness, just as much as do the stars. To define how bright a celestial object appears, astronomers use a numerical It turns out that according to the modern definitions of magnitude, certain celestial objects have numbers less than 1 or even less than 0. Fractional numbers are the rule, not the exception, and they are usually expressed in decimal form. The dog star, Sirius, has magnitude -1.43. Venus, the Moon, and the Sun have even lower magnitudes.

Celestial Tourism

This type of astronomy program allows the user to move around a virtual 3D space environment to view objects from different angles. Some programs, such as RITI's Celestial Explorer Mars, enable planetary surfaces to be mapped, zoomed-in upon, and viewed in 3D 'flyaround' mode, while other programs take the user further afield, into roamable stellar and intergalactic realms, notable among these being Deep Space Explorer by Space.com.

The Celestial Empire

These shells were used for divinations a question was written on them and then the inner part was punctured and placed over a heat source. According to the cracks produced on the outer part of the shell, the diviner made his predictions, which were later recorded on the same shell, together with the date. Often, the success or failure of the prediction was also recorded, together with important celestial events that happened in the meanwhile, such as eclipses. The Shang were followed by the Zhou (1000-221 BC). Under the Zhou dynasty the imperial domain expanded toward the north, beyond the Yangtze River, and the celestial foundation of the emperor's power acquired its definitive form. The emperor, the son of the sky,'' was considered responsible for the cosmic order, while the temporal power was in the hands of a feudal bureaucratic structure, and the effective control of the territory was ceded to local families. Due to fragmentation and internal fights, however, the imperial power...

Basic astronomical phenomena

A great deal of human effort has been expended over the past 4000 years or so in trying to predict and explain the motions of the Sun, Moon, planets and stars. Since Babylonian times, this quest has relied heavily on mathematics, and the developments in man's understanding of the heavens have been inextricably linked to progress in the mathematical sciences. As far as the Sun, Moon and planets are concerned, attempts at an explanation of their motion using mathematical techniques began in ancient Greece and the first mathematical model of the heavens was constructed by Eudoxus in the fourth century BC. The final piece of the celestial jigsaw was supplied by Einstein's theory of general relativity in the twentieth century and, since 1915, all major phenomena associated with planetary motion have possessed theoretical explanations. This should not be taken to imply that we know everything about the future positions of the bodies in our Solar System. Indeed, the researches of Poincare in...

Another kind of sailing

The techniques that once made piloting, dead reckoning and celestial navigation separate skills, are history. Nowadays navigation depends on accessing detailed and accurate data provided by an array of electronic devices that do not care if you are inshore, offshore, or in the middle of nowhere. But take these clever instruments away and the flow of data dries up, and we are lost unless we find some other way of acquiring the information that will allow us to continue on our way.

Right Ascension and Declination

One of these time points, the vernal equinox, occurs on March 21, give or take about a day the other, the autumnal equinox, occurs on September 22, give or take about a day. At the equinoxes, the Sun is exactly at the celestial equator it rises exactly in the east and sets exactly in the west, assuming that the observer is not at either of the geographic poles. The crude celestial maps of Fig. 1-7 show the situation at either of the equinoxes. That is, the date is on or around March 21 or September 22. You can deduce this because the Sun rises exactly in the east and sets exactly in the west, so it must be exactly at the celestial equator. At the latitude of Lake Tahoe, the Sun is 39 degrees away from the zenith (51 degrees above the southern horizon) at high noon on these days. Polaris is 39 degrees above the northern horizon all the time. The entire heavens seem to rotate counterclockwise around Polaris.

Circumpolar Constellations

Imagine that you're stargazing on a clear night from some location in the mid-northern latitudes, such as southern Europe, Japan, or the central United States. Suppose that you sit down and examine the constellations on every clear evening, a couple of hours after sunset, for an entire year. Sometimes the Moon is up, and sometimes it isn't. Its phase and brightness affect the number of stars you see even on the most cloud-free, haze-free nights. But some constellations stand out enough to be seen on any evening when the weather permits. The constellations near the north celestial pole are visible all year long. The following subsections describe these primary constellations.

What we learn in this chapter

Celestial measurements reaching back 3000 years or more were carried out in many cultures worldwide. Early astronomers in Greece deduced important conclusions about the nature of the earth and the solar system. Modern astronomy began in the renaissance with the observations of Tycho Brahe and Galileo and the theoretical work of Kepler and Newton. The progress of our knowledge of the sky may be traced through a series of major discoveries which often follow the development of new technologies such as the telescope, computers, and space observatories. Astronomy is now carried out across the entire electromagnetic spectrum from the radio to the gamma ray (see cover illustrations) as well as with cosmic rays, neutrinos, and gravitational waves. The mutual dependence of theory and observation has led to major advances in the understanding of a wide diversity of celestial objects such as stars, supernova remnants, galaxies, and the universe itself. Current observations reveal important...

Ophiuchus And Serpens

In the southern sky, centered at the celestial equator, is the constellation Ophiuchus, the snake bearer. This poor soul holds a snake, the constellation Serpens, that stretches well to either side. You might imagine that Ophiuchus has a meaningless job, but nothing could be further from the truth. Ophiuchus must keep a tight hold on Serpens (Fig. 2-21), for if that

The distances of the Sun and Moon

Just like the stellar parallax in a heliocentric universe (see Figure 2.6, p. 40), the diurnal parallax is the change in the apparent position of an object (in this case the Sun) as a result of the position of the observer. With stellar parallax it is the position of the Earth in its orbit that causes the difference, whereas for diurnal parallax it is the position of the observer on the Earth that is the cause. Thus, the longitude of the object O in Figure 3.1 (which can be thought of as a view from the celestial north pole) differs depending upon whether it is viewed from P1 or P2, two points at different positions on the Earth. Two observers are not required to determine this difference, however, since the object O takes part in the daily rotation of the heavens and its longitude will thus be affected by the time of day at which measurements are taken. Thus, if one makes observations of the sun 6 h apart, for example, the longitudes will not differ by the amount due to the motion of...

Photon and nonphoton astronomy

Information about the cosmos can also be gleaned from the detection and measurement of particulate matter. Cosmic rays are bits of matter (protons and heavier atomic nuclei) that travel with high energies, arriving at the earth from distant celestial regions (e.g., the sun, a supernova, an active galactic nucleus). Since most cosmic ray particles are charged, the weak and irregular magnetic fields that lie between the stars will change their directions of travel through the action of the magnetic F q (v X B) force. The particles from a given source will spiral around the magnetic fields in the Galaxy for millions of years, circulating in the company of particles from many other sources.

There Is No Southern Polaris

We need a time of reference for our circumpolar observations, and mid-April is as good a time as any. Imagine that you are in the countryside near Sydney or Cape Town or Buenos Aires and that you go outdoors to stargaze at around 10 00 p.m. Assume that the sky is clear, there is no haze, and the Moon is below the horizon so that its light does not interfere with stargazing. You know that the south celestial pole is 35 degrees above the southern horizon. You search for a significant star, or at least a constellation, to mark the spot using the fist rule. (Hold your right arm out straight and make a tight fist. Point the knuckles toward your right. The top of your fist is about 10 angular degrees from the bottom.) You find the southern horizon using a compass or your knowledge of the area and proceed three and a half fists up into the sky. There is nothing significant. The south polar region is devoid of bright or even moderately bright stars. This caused some trouble for mariners who...

Constellations of the Southern Autumn

Imagine that it is still the same night and still the same time (10 00 p.m.), and you turn your attention toward the east, north, and west, that part of the sky not confined to the vicinity of the celestial pole. Constellations in this part of the sky rise and set they are not always above the horizon. As is the case in the northern hemisphere, the farther from the pole a constellation is located, the more time it spends each day below the horizon. A star at the equator spends exactly half the sidereal day, or about 11 hours and 58 minutes, above the horizon and half the time out of sight beneath Earth. Ultimately, for observers at 35 degrees south latitude, constellations with declinations of more than +55 degrees (within 35 degrees of the north celestial pole) never make it above the northern horizon.

Mathematical sphere atinfinity

It is convenient to imagine a sphere at great distance ( infinity ) upon which all stars lie. This is called the celestial sphere (Fig. 1). The positions of stars on this sphere may be specified with two angles, analogous to the way latitude and longitude specify a position on the earth's surface. This celestial sphere is an artificial construction stars are not all at the same distance. Stars in the (MW) Galaxy range in distance from 4 LY to more than 50 000 LY from the earth while the farthest quasars may be as distant as 1010 LY. Nevertheless, the concept of celestial sphere is useful for charting the sky as one sees it. Motions of stars on the celestial sphere arise from their intrinsic motion relative to each other in three-dimensional space. The motion on the celestial sphere (i.e., normal to the line of sight) is called proper motion, which is typically less than 1 year. Catalogs quote the position of the star at a fixed time (epoch), e.g., 1950 or 2000, and also give the rate...

Surveys charts and catalogs

Astronomers must be able to refer to a given star or other celestial object after studying it. This can be done with the star coordinates or with a name. Our knowledge of the existence of the fainter stars in the optical sky derives from surveys of the sky, such as a series of large-area photographs or the counting rate data from an x-ray detector that scans the entire sky. Such surveys typically yield the celestial coordinate of each located object. Interesting objects of a given type that are found in such surveys can be plotted on maps of the sky (charts) or listed with positions and other information in printed catalogs.

Introduction to Drawings and Real Time Video

Because of the problems of being sure of the actual true orientations of new and unfamiliar objects with the rotating-eyepiece positions of many Newtonian reflectors, lateral reversals of star diagonals, etc., I will not confuse things further by indicating on the deep space illustrations the positions on the celestial sphere. Remember image intensifiers also project an upright image, so this adds an additional complication be aware of this when consulting star charts. I have decided simply to present the deep space images as they appeared to me at the time of viewing. This should be simple enough to interact with your own viewing, and known images.

Criticisms of Ptolemy

Space in the Universe, and celestial bodies move with uniform circular motion. He thought there had to be a unique spherical body corresponding to each motion that Ptolemy had introduced in the Almagest. In a later work, Doubts Concerning Ptolemy, Ibn al-Haitham noted that Ptolemy had set himself the task of accounting for the phenomena using uniform circular motions and that, since he had introduced the equant mechanism, he could not be considered to have succeeded. He objected to Ptolemy's lunar theory because it involved an imaginary point opposite the centre of the deferent controlling the motion of the lunar apogee, and this seemed physically impossible. Above all, Ibnal-Haitham argued, astronomy should deal with real bodies and not imaginary ones.

Universal and atomic times

Formally, UT is defined in terms of the sidereal time at Greenwich. Specifically, 0 h UT (midnight in Greenwich) on Jan. 1 is defined to occur at Greenwich mean sidereal time (GMST) 6.7 h. Examine Fig. 3.1 and note that on Jan. 1, which is 285 d after Mar. 21, the sun is about 18.7 h east of the equinox (285 d 365 d) x 24 h 18.7 h , that is, a0 18.7 h. At midnight in Greenwich on this date, the zenith will be on the side of the celestial sphere exactly opposite (in RA) to the sun, i.e., at 18.7 - 12 6.7 h. The sidereal time at Greenwich will thus be about 6.7 h at 0 h UT on Jan. 1, in accord with the definition. As stated above, one can set a UT clock by observing the stars passing over Greenwich at midnight on Jan. 1. When the appropriate meridian of the celestial sphere (sidereal time 6 h 42 m 6.7 h on Jan. 1) transits the zenith, it is exactly 0 h UT. The current relation used to set UT in terms of the star transits at Greenwich gives Greenwich mean sidereal time at 0 h UT in terms...

Eudoxus system of concentric spheres

The Babylonians were concerned with predicting the time at which a particular phenomenon (e.g. a planetary opposition) would occur, since it was the date that was ominous. Their astronomy was thus concerned with the analysis of discrete processes. On the other hand, as we shall see, the Greeks in their astronomy focused on predicting where a celestial body would be at a given time, and they were thus concerned with modelling a continuous process, which naturally leads to the use of geometrical methods. The first person to produce a geometrical model of celestial motions was Eudoxus, who was born in Cnidus on the western coast of Asia Minor in about 400 BC. According to Diogenes Laertius' Lives of Philosophers (written in AD third century) he was taught geometry by Archytas of Tarentum, one of the leading Pythagorean philosophers, and studied with Plato, who was about 30 years older than him. None of Eudoxus' works have survived. Most of the information we have about his system of...

How Bright Are Comets

When you hear or read about the discovery of a new comet or about the apparition of a known one, you should be equipped with a good pair of binoculars because it will have a relatively high visual magnitude (low brightness). The best binoculars are the wide-angle types with large-diameter objective lenses. The sort used by military commanders are ideal. This will let you scan the sky with ease, and the stereoscopic viewing will help to enhance the contrast between the comet and other celestial objects. Once you have found a comet using binoculars, then a telescope, using an eyepiece having a long focal length for low magnification, can be employed to look at it in more detail. Schmidt-Cassegrain telescopes, popular among amateur astronomers and casual observers, are available in hobby stores and are good for comet watching.

Dead reckoning and estimated positions

In the 15th century the pioneers of the great European age of exploration made long ocean voyages using nothing but dead reckoning. Columbus relied on it for his 1492 voyage and reconstructions from his logs (he kept two) showed he managed an accuracy of well over 90 . If they practised the new art of celestial navigation they usually did this ashore, with the aim of obtaining positions to support claims of sovereignty and to update their charts.

Pointlike and extended sources

Celestial objects with measurable angular sizes are called resolved or diffuse sources. The flux is described completely with specific intensity I(v,0,0,t) (W m-2 Hz-1 sr-1) which describes the variation of flux with position 0,0 on the sky. Integration of I over the solid angle of a source yields the above-mentioned spectral flux density S. Surface brightness B(v,0,0,t) (W m-2 Hz-1 sr-1) describes the radiation leaving the surface of a celestial body. It can be shown to be identically equal to the detected specific intensity, B I, a general relation that follows from Liouville's theorem. Looking into the source itself, the power generated per cubic meter is the volume emissivity j (W m-3 Hz-1). For an optically thin source of known thickness along the line of sight, it is quite simply related to the specific intensity a distant observer would measure.

Problems And Challenges

First, only a tiny part of the sky can be scanned at any given time. A narrow field of reception is necessary because celestial objects generate a lot of radio noise, and this can be minimized only by focusing in on very small regions of the sky. Also, in order to get a signal to travel through the vast depths of interstellar space, it must be focused in a narrow beam. We cannot spray a signal all over the whole sky it will become too diluted by the time it reaches the stars.

Development Of Life f

If a planet is ideal for the development of life, there is no guarantee that life arises and evolves. A large asteroid or comet impact would cut evolution short if it were violent enough. An unfavorable change in the behavior of the parent star also would snuff out life. A close call with a passing celestial object, such as a neutron star or a black hole, would disrupt the orderly nature of the planetary orbits of the star system. The big question is this Was life created, and did it get going on its evolutionary way on Earth because of a series of flukes so rare as to have a combined probability of almost zero Scientists have created complex molecules thought to be the precursors of living matter in a laboratory, but this is not the same thing as synthesizing life and demonstrating that its formation is a common thing.

Where Is All The Antimatter

Why don't we see antimatter floating around in the Universe Why, for example, are Earth, Moon, Venus, and Mars all made of matter, not antimatter (If any celestial object were made of antimatter, then as soon as a spacecraft landed on it, the ship would vanish in a fantastic burst of energy.) This is an interesting question. We are not absolutely certain that all the distant stars and galaxies we see out there consist of matter. We do know, however, that if there were any antimatter in our immediate vicinity, it would have long ago combined with matter and been annihilated. If there were both matter and antimatter in the primordial Solar System, the mass of the matter was greater, for it prevailed after the contest.

The motion of the lunar apogee

The Achilles heel of Newtonian celestial dynamics appeared to be the lunar theory. The larger of the lunar inequalities depends to some extent on the motion of the lunar apogee, the magnitude of which still lacked a theoretical explanation. The Moon was seen as the best test of the theory of gravitation, and in the 1740s this led Euler, Clairaut and d'Alembert to try and determine if the Sun's influence on the Earth-Moon system could explain the apsidal motion. All three used analytical approaches to the problem based around approximate methods of solution for Eqn (9.3), and all three were led to the conclusion Newton had reached, i.e. that the predicted motion of the lunar apogee was only half the

Chargecoupled Device

A charge-coupled device (CCD) is a camera that converts visible-light images into digital signals. Some CCDs also work with IR or UV. Astronomers use CCDs to record and enhance images of all kinds of celestial objects. Common digital cameras work on a principle similar to that of the CCD.

Emission Reflection and Dark Nebulae

NGC 2070 angular size 20 , celestial coordinates (0538s690), constellation Dorado. Tarantula Nebula extraordinary object within the Large Magellanic Cloud rivals the great M42. NGC 3372 angular size 80' x 85' , celestial coordinates (1044s595), constellation Carina. Keyhole Nebula magnificent sight, with numerous dark lanes crossing, much in the manner of the Trifid Nebula contains the famous variable star Eta Carinae. NGC 5189 angular size 185' x 130', celestial coordinates (1333s655), constellation Musca. Because of the whims of my local climate, it is often impractical for me to attempt much in the way of galactic and certain other deep space observing during late spring, a good portion of the summer and early fall. At the coast in Southern California we are frequently plagued with a night-time marine layer and haze during these times. In order to see all that the sky has to offer, I frequently spend long sessions at the telescope whenever the air is as good as it can be, enough so...

Observational Equipment

Stars, galaxies, planets, and other things in the Cosmos radiate at all wavelengths, not only at wavelengths convenient for humans to observe. In some portions of the IR spectrum, the atmosphere of our planet is opaque. Between about 770 nm (the longest visible red wavelength) and 2 micrometers ( m), our atmosphere is reasonably clear, and it is possible to observe IR energy in this wavelength range from surface-based locations. To see celestial images at longer IR wavelengths, the observations must be made from high in the atmosphere or from space.

Location Location Location

As our cities swell, good places for astronomical viewing are becoming hard to find. We light up the darkness so that our streets are safe for driving powered vehicles, even as the exhaust from those machines thickens the veil between us and the Sun, Moon, planets, stars, nebulae, and galaxies. Tall buildings turn fields into canyons. Some children grow up without learning to recognize any celestial objects other than the Sun and Moon. It doesn't have to be this way.

German Equatorial Mount

One of the best-known sets of telescope bearings is found in the German equatorial mount. It can be recognized by its unique configuration and counterweight (Fig. 20-13). It, like the fork mount wedge, moves along RA and declination coordinates. The RA axis is adjustable and must be aimed at the north celestial pole. The most sophisticated German equatorial mounts are equipped with sighting scopes that make them fairly easy to align. Once the mount is adjusted properly and the telescope is aimed at an object in the sky, the object can be followed by moving only the RA bearing. To north celestial pole To north celestial pole

NGC 6853 M27 The Dumbbell Nebula

With or without a narrowband filter, the Dumbbell Nebula makes its presence known immediately, even in our compromised skies. This is not one of those sights that you suspect you can see It appears as a bright white egg-shape in the field of view, quite luminous and striking (Figure 7.55). Sufficient aperture will resolve its famous outline easily, and shadings of brightness become obvious. The subtle extensions on either side may be seen with larger scopes, and give the nebula a somewhat different overall outline, much more elongated (as in my drawing in Figure 7.55a). The illuminating star is a hard catch, though in good viewing conditions, you may possibly succeed. It just shows on the video frame (Figure 7.55b) at the center of the bar . An image intensifier works in an interesting way the nebula fades substantially, but many stars within and around it, unseen without intensification, become obvious to the point that perceptions of the internal structure of the nebula itself seem...

Epochs for coordinate systems

The equatorial coordinate system used for celestial measurements depends on the orientation of the earth, and this is a continuously changing function of time (Section 3.2). The time chosen during some period (usually decades) for the specification of celestial coordinates in catalogs and communications between astronomers is called the standard epoch, traditionally expressed in years.

Part Five Space Observation and Travel

In this book, we'll go on a few mind journeys. For example, we'll take a tour of the entire Solar System, riding hybrid space aircraft into the atmospheres and, in some cases, to the surfaces of celestial bodies other than Earth. Some of the details of this trip constitute fiction, but the space vehicles and navigational mechanics are based on realistic technology and astronomical facts.

Greater than the Whole

Around 150 BCE the Greeks had a mechanical computer capable of predicting the movement of the sun, the moon, and some planets, as well as being able to add, subtract, multiply, and divide. Its remains were found in 1901 aboard a shipwreck. It took over a century to work out what it was. The Greeks also knew about the astrolabe and had star catalogues. The Pharaohs used sundials and knew the earth was spherical. They even measured its diameter pretty accurately. Devices for measuring the altitude of celestial bodies have been around for thousands of years. It is presumptuous to assume this knowledge was not used at sea. Different early cultures, separated by time and geography, all mastered the science of navigation. They did not rely on celestial benevolence, a sixth sense, charms, incantations, or sacrifices, human or otherwise, but skills and knowledge based on the close observation of natural phenomena, the meticulous construction of mental maps, simple instruments, and detailed...

Time from the Sun The Equation of Time

Solar time is based upon the apparent solar day, which is the time between two successive local noons at the same longitude. The length of the solar day varies, partly because the earth's orbit is an ellipse, and also because the earth's axis is tilted to the celestial equator.

Distances and sizes Distance ladder

266 9 Properties and distances of celestial objects Table 9.2. Size (radius) and distance examples The distance to a celestial object is difficult to obtain, in principle, because the sky appears two-dimensional to us. The angular position of a star on the celestial sphere requires only the two angular coordinates. Indirect means must be used to obtain the

Interplay of observation and theory

The objective of astronomical studies is to learn about the nature of the celestial objects, including their sizes, masses, constituents, and the basic physical processes that take place within or near them. Progress is made through an interplay of observational data and theoretical insight. Observations guide the theorist and theories suggest observations. The pace of this interplay greatly accelerated in the late nineteenth and twentieth centuries due to the rapid increase in technical capability described above. The recent history of astronomy is replete with examples of this symbiosis of observation and theory.

The revival of learning in Western Europe

Trade routes between Western Christendom and the Arab world had been established by the ninth century, but the transmission of scientific knowledge to the West did not really begin until contact with Islamic scholarship was made when European scholars started visiting Spanish monasteries in the eleventh century. Latin translations of previously unknown works began to be made from about 1000, the rate at which they appeared reaching a peak in the twelfth century - often referred to as the 'century of translation'. The Spanish city of Toledo was conquered by Alfonso VI in 1085 and, in the twelfth century, became the main centre for translation from Arabic into Latin. Many of the works that were translated were highly technical, and specialized words which were not understood were often simply transliterated. Some of these words now form part of our technical vocabulary, such as 'zenith' and 'nadir' (the nadir is the point on the celestial sphere diametrically opposed to the zenith)....

Horizon coordinate system

An observer on the earth's surface at low latitudes notes that the sun rises in the east and sets in the west. During the night, the same observer would note that the stars and planets also rise in the east, move across the sky, and set in the west. These motions are simply an effect of the earth's daily rotation about its axis. For an observer at the earth's north pole, the north celestial pole (NCP) of the celestial sphere is directly overhead (at the zenith). For this same observer, the stars just above the horizon move all around the horizon at a fixed elevation once per day, never dipping below it. At other northern latitudes, the pole is not directly overhead, but stars sufficiently near the NCP will still appear to rotate around the NCP without setting. Stars further south do rise and set (e.g., the sun), and stars even farther south are never seen by the northern observer. The motion of stars in an earth-based horizon system is illustrated in Fig. 1. The view is from the west...

Crosscorrelation or shading method

Shading method of creating a sky map from interferometry data. For each time interval, each bin on the sky is assigned a value which is the product of the instantaneous value of the fringe pattern at the bin position and the instantaneous value of the actual response. (a) Sinusoidal shading pattern for one instant of time. Its amplitude will be large if a celestial source is on a visibility line. (b) Shading pattern for a single point source near the north celestial pole for a continuous 12-h observation as in Fig. 3. The central peak is located at the source position cf. Fig. 4c. The random noise in a real observation would add irregularities to the map. The Bessel-function profile is sketched qualitatively. Figure 7.8. Shading method of creating a sky map from interferometry data. For each time interval, each bin on the sky is assigned a value which is the product of the instantaneous value of the fringe pattern at the bin position and the instantaneous value of the...

Early Greek astronomy

Up until about 300 BC, Greek astronomy was almost entirely qualitative. Indeed, there is no evidence that the accurate prediction of heavenly phenomena was even thought of as a desirable goal. This situation changed when the Greeks came into contact with the quantitative methods of Babylonian astronomers during the expansion of their empire under Alexander the Great. Before then, however, celestial phenomena were the subject of a great deal of philosophical debate that provided the basis on which later astronomers could build. Four major schools of philosophical thought existed during the 300 or so years prior to the construction of the first mathematical model of the Universe by Eudoxus.13 There were the Ionians, a group founded by Thales of Miletus (in Asia Minor, modern-day Turkey) in about 600 BC. During the sixth century BC the region of Asia Minor went through a considerable upheaval due to the expansion of the Persian empire and many philosophers travelled to other parts of the...

Lunar and planet motions eclipses

Moldes Bonecas Pano Articuladas

The bodies in the solar system are quite close to us compared to the stars thus they have substantial angular velocities relative to the earth. Their apparent positions on the celestial sphere change radically on an annual scale and by significant amounts day by day. The celestial motions of these bright objects have long fascinated humankind. The motions of the sun and moon on the celestial sphere lead to solar and lunar eclipses. The former occurs when the moon comes between the earth and sun and blocks, at least partially, the observer's view of the sun. The latter occurs when the moon is on the far side of the earth from the sun and enters the shadow of the earth. The moon orbits the earth every 27.32 d (the tropical month, the time it takes between south-to-north crossings of the celestial equator, i.e., equinox to equinox. The sidereal period (relative to the stars) is nearly identical to this, within 10-4 d. Thus the moon changes its position on the celestial sphere a great...

What Is Galactic Coordinate

Double Stars Coordinate Transform

The celestial positions of several important objects at the two standard epochs are shown in Table 1. The indicator for the other axis reads the pointing angle relative to the earth's spin axis, or equivalently relative to the earth's equator. This is the declination of the pointing direction for the epoch of the observation, e.g., epoch 2002.50 for the 2002 July 1. Conversely, if one wishes to use the mechanical indicators to point a telescope toward a given (faint) star on this date, one must know or calculate its epoch 2002.5 celestial coordinates and take into account the time of day. Galactic coordinates Another coordinate system in common use is the galactic coordinate system. In this system, the equator on the celestial sphere is defined to be a great circle that runs along the Milky Way. A schematic of the Galaxy is shown in Fig. 3. It is a disk-shaped cluster of some 1011 stars. The visible stars tend to cluster in spiral arms, and the sun is one unimportant star well removed...

Early development of astronomy First astronomers

The periodic motions of the sun and moon were noted and described with calendars as early as the thirteenth century BCE in China. Surviving physical structures appear to be related to the motions of celestial bodies. Notable are an eighth century BCE sundial in Egypt and the assemblage of large stones at Stonehenge in England dating from about 2000 BCE (Fig. 1)1. The Babylonians and Assyrians in the Middle East are known to have been active astronomers in the several centuries BCE (The designations BCE before common era and CE common era are equivalent to BC and AD respectively.) where r is the unit vector along the line connecting the two bodies. Such a force leads directly to the elliptical orbits, to the speeds of motion in the planetary orbit, and to the variation of period with semimajor axis described by Kepler's three laws. Thus, all the celestial motions of the earth, moon, and sun could be explained with a single underlying force. This understanding of the role of gravity...

Ptolemy and the Almagest

In the Almagest, the motion of each celestial body is considered in turn and, if all the models are put together, we get the world system sketched in Figure 3.5. The diagram illustrates the epicyclic nature of the planetary models, but not the many other elements used by Ptolemy to reflect more accurately the observational evidence. An important thing to note is the fact that, for Mercury and Venus, the line joining the Earth to the centre of their epicycles is the same as that joining the Earth to the Sun, whereas for the outer planets, which may appear anywhere with respect to the Sun, the radius connecting the planet to the centre of its epicycle is parallel to the Earth-Sun line. Thus, it is evident that the Sun does not simply orbit the Earth like the other planets, but has a much more significant role. The motion of the Sun also plays a role in the lunar theory. As the Sun has an important function in the theories of all the heavenly bodies, it is logical to begin with a solar...

Universal gravitation

A number of phenomena had caused Newton to consider that gravity was a property of all celestial bodies. In order to make the leap to universal gravitation, an understanding was required of how a large body like the Earth would attract an external object if its pull was the result of attractions from all its constituent parts. Newton answered these questions by proving some results concerning the attraction of thin spherical shells. His approach was hard-going the description below is a modern adaptation.

Energy and number spectra

This quantity is appropriate for a diffuse (resolved) celestial source, one larger in angular size than the telescope resolution. It is often rewritten in terms of other combinations of units. For example, one could choose, The jansky was named after Karl Jansky, the discoverer of celestial radio waves (in 1932). This unit is used in Table 8.2.

Eudoxus Planetary Model

Pressure Vessel Thick Walled

In Eudoxus' theory for the Moon (see Figure 2.1, in which AB represents the celestial equator and CD the ecliptic), the outermost of the three spheres completes 1 revolution from east to west in 1 day, thus accounting for the diurnal rotation of the Moon. In order to account for the motion of the Moon around the ecliptic, Eudoxus introduced a second sphere attached to the first through an axis passing through the poles of the ecliptic and rotating from west to east. Eudoxus also knew that the Moon did not follow exactly the ecliptic, but deviated a little above and below it, and accounted for this by including a

Technology revolution

Photography was an epochal development for astronomy in the nineteenth century. Before this, the faintest object detectable was limited by the number of photons (the quanta of light) that could be collected in the integration time of the eye, 30 ms (millisecond) to 250 ms if dark adapted. If a piece of film is placed at the focus of a telescope, the photons can be collected for periods up to and exceeding 1 hour. This allowed the detection of objects many orders of magnitude fainter than could be seen by eye. A photograph could record not only an image of the sky, but also the spectrum of a celestial object. The latter shows the distribution of energy as a function of wavelength or frequency. The light from the object is dispersed into its constituent colors with a prism or grating before being imaged onto the film. Large telescopes together with photography and spectroscopy greatly enlarge the domains of quantitative measurements available to astronomers. A given celestial object can...

The Stars

Suppose that a star is at x degrees north celestial latitude and y degrees west celestial longitude. If you stand at the point on the surface corresponding to x N and y W, then a straight, infinitely long geometric ray originating at the center of Earth and passing right between your eyes will shoot up into space in the direction of the star (Fig. 1-3). Celestial latitude x Celestial longitude y Earth's center Figure 1-3. Celestial latitude and longitude. The next time you get a chance, set up a telescope and point it at some star that is overhead. Use the shortest focal-length eyepiece that the telescope has so that the magnification is high. Center the star in the field of view. If that star is exactly overhead, then its celestial latitude and longitude correspond to yours. For example, if you're on the shore of Lake Tahoe, your approximate latitude is 39 N and your approximate longitude is 120 W. If you have a telescope pointing straight up and a star is centered in the field of...

Compass Bearing

The azimuth of a celestial object is the compass bearing, in degrees, of the point on the horizon directly below that object in the sky. Imagine drawing a line in the sky downward from some object until it intersects the horizon at a right angle. The point at which this intersection occurs is the azimuth of the object. If an object is straight overhead, its azimuth is undefined.

The Vernal Equinox

The answer is that the Sun crosses the sky a little more slowly than the stars. Every day, the Sun moves slightly toward the east with respect to the background of stars. On March 21, the Sun is at the celestial equator and is located in a certain position with respect to the stars. This point among the stars is called, naturally enough, the vernal equinox (just as the date is called). It represents an important reference point in the system of celestial coordinates most often used by astronomers right ascension (RA) and declination (dec). As time passes, the Sun rises about 4 minutes later each day relative to the background of stars. The sidereal (star-based) day is about 23 hours and 56 minutes long the synodic (sun-based) day is precisely 24 hours long. We measure time with respect to the Sun, not the stars. Declination is the same as celestial latitude, except that north is replaced by positive and south is replaced by negative. The south celestial pole is at dec -90 degrees the...

The Ecliptic

The path that the Sun follows against the background of stars during the year is a slanted celestial circle called the ecliptic. Imagine Earth's orbit around the Sun it is an ellipse (not quite a perfect circle, as we will later learn), and it lies in a flat geometric plane. This plane, called the plane of the ecliptic, is tilted by 23.5 degrees relative to the plane defined by Earth's equator. If the plane of the ecliptic were made visible somehow, it would look like a thin gray line through the heavens that passes through the celestial equator at the equinoxes, reaching a northerly peak at the June solstice and a southerly peak at the December solstice. If you've ever been in a planetarium, you've seen the ecliptic projected in that artificial sky, complete with RA numbers proceeding from right to left from the vernal equinox. Suppose that you convert the celestial latitude and longitude coordinate system to a Mercator projection, similar to those distorted maps of the world in...

Illusions and Myths

We know that the constellations are not true groups of stars but only appear that way from our Solar System. The stars within a constellation are at greatly varying distances. Two stars that look like they are next to each other really may be light-years apart (a light-year is the distance light travels in a year) but nearly along the same line of sight. As seen from some other star in this part of the galaxy, those two stars may appear far from each other in the sky, maybe even at celestial antipodes (points 180 degrees apart on the celestial sphere). Familiar constellations

Southern Coordinates

Southern celestial coordinates are similar to northern celestial coordinates. They operate according to the same mathematics. The main difference is that the two coordinate hemispheres are mirror images of one another. While the northern heavens seem to rotate counterclockwise around the north celestial pole, the southern Sun, Moon, planets, and stars seem to rotate clockwise around the south celestial pole.

Southern Radec

Give or take about a day the other occurs on September 22, give or take about a day. At the equinoxes, the Sun is exactly at the celestial equator it rises exactly in the east and sets exactly in the west, assuming that the observer is not at either of the geographic poles. The names vernal and autumnal, as used in the northern hemisphere, are not really correct in the southern hemisphere because the seasons are reversed compared with those in the north. Thus it is best to speak of the March equinox and the September equinox. The crude celestial maps of Fig. 3-2 show the situation at either equinox. That is, the date is on or around March 21 or September 22. You can deduce this because the Sun rises exactly in the east and sets exactly in the west, so it must be at the celestial equator. At the latitude of Sydney, the Sun is 35 degrees away from the zenith (55 degrees above the northern horizon) at high noon on either of these days. The south celestial pole, which unfortunately has no...

Crux And Musca

As you stand facing toward the south, you will see, high in the sky, a group of four stars forming a kitelike shape. This is Crux, more commonly called the southern cross. Just below it, somewhat dimmer, is a star group shaped somewhat like a ladle. This is Musca or Musca Australis, the southern fly. Look at these two constellations carefully, and make educated guesses as to their centers (Fig. 3-5). The center of Crux is easy to decide on, but the center of Musca is a little tougher. Pick a point on the handle of the ladle, just above the scoop. These two constellation-center points are separated by about 10 degrees of arc, a fact that you can verify by the fist rule. Now go two fists down toward the southern horizon from the center point of Musca. This will give you a point close to the south celestial pole.

Volans And Carina

Above and to the right of the celestial pole are Volans, the flying fish, and Carina, the keel or ship (Fig. 3-10). Carina is noteworthy because it contains the yellowish white star Canopus, which is the second brightest nighttime star after Sirius. The two constellations closest to the south celestial pole are Chameleon, the lizard, and Octans, the octant. The stars in these groups are so dim that unless you are out in the country away from city lights, you will not see them. Also, if the Moon is near full phase and is above the horizon, its scattered light might wash these constellations out. At this time of the year, Octans in the evening sky appears as a tall, slender triangle immediately to the east of the celestial pole, and Chameleon is near and above it (Fig. 3-11). Apus, the bird of paradise, appears in this group too, centered about 12 degrees (a little more than one fist) above and to the left of the pole.


3.2 Coordinates on a celestial sphere Problem 3.21. (a) What are the approximate equatorial coordinates of the north celestial pole, of the sun on March 21, the star shown in Fig. 1, and the nominal galactic center at l b 0 In each case, specify the epoch of your answer. What are the J2000 coordinates of the Crab nebula (b) Locate Norton's 2000.0 Star Atlas in the library and find the J2000.0 coordinates (to the nearest arcminute) of the variable and bright star 7 Cassiopeiae, the Seyfert galaxy NGC 1068, the variable star Carinae, and the globular cluster M 30 You can measure from the charts or use the 2000 coordinates listed in the several tables of the Atlas the Atlas suppresses the J prefix. Ans. (a) galactic center a 18 h, 8 -30 Problem 3.22. (a) Plot the following objects on a copy of Fig. 5 and determine by inspection the galactic coordinates of the objects as best you can (e.g., to about 20 precision, though in some instances one can do better) the Crab nebula at a (B1950) 5 h...

The Planets

Today, amateur astronomers, using CCD imaging and modest apertures, are capturing detail and resolution thought to be impossible even by the world's largest telescopes of the most recent past. Often they succeed astoundingly in brightly lit suburban areas, on balconies, rooftops and the like, which in the past would have been considered totally unsuitable, even for live viewing. Visually though, there is nothing quite like the experience of actually observing a planet such as Mars. It remains one of the most exciting celestial sights directly accessible from our city locations. When conditions are favorable, the variety and wealth of detail discernable may astound you, assuming you have reasonably good equipment. With a little persistence, the God of War will provide some spectacular viewing. As with all suburban planetary viewing, just keep bright lights shielded from your line of sight.


Before the publication of the researches of Copernicus, the orthodox scientific creed averred that the earth was stationary, and that the apparent movements of the heavenly bodies were indeed real movements. Ptolemy had laid down this doctrine 1,400 years before. In his theory this huge error was associated with so much important truth, and the whole presented such a coherent scheme for the explanation of the heavenly movements, that the Ptolemaic theory was not seriously questioned until the great work of Copernicus appeared. No doubt others, before Copernicus, had from time to time in some vague fashion surmised, with more or less plausibility, that the sun, and not the earth, was the centre about which the system really revolved. It is, however, one thing to state a scientific fact it is quite another thing to be in possession of the train of reasoning, founded on observation or experiment, by which that fact may be established. Pythagoras, it appears, had indeed told his disciples...

Tycho Brahe

On the 21st October, 1560, an eclipse of the sun occurred, which was partially visible at Copenhagen. Tycho, boy though he was, took the utmost interest in this event. His ardour and astonishment in connection with the circumstance were chiefly excited by the fact that the time of the occurrence of the phenomenon could be predicted with so much accuracy. Urged by his desire to understand the matter thoroughly, Tycho sought to procure some book which might explain what he so greatly wanted to know. In those days books of any kind were but few and scarce, and scientific books were especially unattainable. It so happened, however, that a Latin version of Ptolemy's astronomical works had appeared a few years before the eclipse took place, and Tycho managed to buy a copy of this book, which was then the chief authority on celestial matters. Young as the boy astronomer was, he studied hard, although perhaps not always successfully, to understand Ptolemy, and to this day his copy of the...

Lifetime On Uranus

At the Uranian vernal equinox, when you were 21 Earth years old, the Sun would travel in an Earthlike way across the sky, behaving like it does in Minneapolis around the end of March or September, but with daylight lasting only 9 Earth hours and darkness another 9 Earth hours. Perhaps you would read in books (or on computer screens) about the changes of seasons in places like Minnesota and be thankful that no such fluctuations in temperature occurred on Uranus. The season would evolve, the Sun would move further toward the celestial pole, and the hours of daylight would grow long. For a while, the Sun would follow a path similar to that in midsummer in Minneapolis, but it would still be early spring on Uranus. The daylight hours would grow longer yet and the darkness hours shorter. One night darkness would never fall. After that, you would have a full 18 hours of daylight every day, and as the Earth years continued to progress, the Sun would describe a smaller and smaller circle in...


But it was reserved for Galileo himself to make that application of the instrument to the celestial bodies by which its peculiar powers were to inaugurate the new era in astronomy. The first discovery that was made in this direction appears to have been connected with the number of the stars. Galileo saw to his amazement that through his little tube he could count ten times as many stars in the sky as his unaided eye could detect. Here was, indeed, a surprise. We are now so familiar with the elementary facts of astronomy that it is not always easy to realise how the heavens were interpreted by the observers in those ages prior to the invention of the telescope. We can hardly, indeed, suppose that Galileo, like the majority of those who ever thought of such matters, entertained the erroneous belief that the stars were on the surface of a sphere at equal distances from the observer. No one would be likely to have retained his belief in such a doctrine when he saw how the number of...

Pluto and Charon

The Pluto-Charon system makes exactly two solar orbits for every three orbits of Neptune as a result, the two systems can never get any closer than 17 AU to each other. Unless some other celestial object intervenes and gravitationally upsets the orbit of Neptune or the orbit of Pluto-Charon, a cosmic collision will never take place.

What Makes a Planet

We might say that in order to be a planet, a celestial object must be spherical, must orbit the Sun (and not some other planet), and must be larger than a certain diameter (say, 500 kilometers) or have more than a certain amount of gravitation (say, 5 percent that of the Earth). However, no official standard yet exists. Depending on the set of criteria adopted, assuming scientists ever agree on one, Pluto-Charon may be demoted to the status of a double comet or else hundreds, maybe thousands, of objects now considered primordial matter will be reclassified as planets.


It must be remembered that it was the almost universal belief in those days, that all the celestial spheres revolved in some mysterious fashion around the earth, which appeared by far the most important body in the universe. It was imagined that the sun, the moon, and the stars indicated, in the vicissitudes of their movements, the careers of nations and of individuals. Such being the generally accepted notion, it seemed to follow that a professor who was charged with the duty of expounding the movements of the heavenly bodies must necessarily be looked to for the purpose of deciphering the celestial decrees regarding the fate of man which the heavenly luminaries were designed to announce. Kepler must also be remembered as one of the first great astronomers who ever had the privilege of viewing celestial bodies through a telescope. It was in 1610 that he first held in his hands one of those little instruments which had been so recently applied to the heavens by Galileo. It should,...

Isaac Newton

It then occurred to Newton, that though the moon is at a distance of two hundred and forty thousand miles from the earth, yet the attractive power of the earth must extend to the moon. He was particularly led to think of the moon in this connection, not only because the moon is so much closer to the earth than are any other celestial bodies, but also because the moon is an appendage to the earth, always revolving around it. The moon is certainly attracted to the earth, and yet the moon does not fall down how is this to be accounted for The explanation was to be found in the character of the moon's present motion. If the moon were left for a moment at rest, there can be no doubt that the attraction of the earth would begin to draw the lunar globe in towards our globe. In the course of a few days our satellite would come down on the earth with a most fearful crash. This catastrophe is averted by the circumstance that the moon has a movement of revolution around the earth. Newton was...


Other branches of astronomy began also to claim his attention. We learn that in 1669 and 1670 he compared the planets Jupiter and Mars with certain fixed stars near which they passed. His instrumental means, though very imperfect, were still sufficient to enable him to measure the intervals on the celestial sphere between the planets and the stars. As the places of the stars were known, Flamsteed was thus able to obtain the places of the planets. This is substantially the way in which astronomers of the present day still proceed when they desire to determine the places of the planets, inasmuch as, directly or indirectly those places are always obtained relatively to the fixed stars. By his observations at this early period, Flamsteed was, it is true, not able to obtain any great degree of accuracy he succeeded, however, in proving that the tables by which the places of the planets were ordinarily given were not to be relied upon.


On the one hand, while the impetus given to exact observation by Tycho Brahe had not yet spent itself, the invention of the telescope and its gradual improvement opened out an almost indefinite field for possible discovery of new celestial objects of interest On the other hand, the remaikable character of the three laws in which Kepler had summed up the leading characteristics of the planetary motions could haidly fail to suggest to any intelligent astionomer the question why these particulai laws should hold, or, m other words, to stimulate the inquiry into the possibility of shewing them to be necessary consequences of some simpler and more fundamental law or laws, while Galilei's researches into the laws of motion suggested the possibility of establishing some connection between the causes underlying these celestial motions and those of ordinary terrestrial objects.


The first exhibition of Bradley's practical skill seems to be contained in two observations which he made in 1717 and 1718. They have been published by Halley, whose acuteness had led him to perceive the extraordinary scientific talents of the young astronomer. Another illustration of the sagacity which Bradley manifested, even at the very commencement of his astronomical career, is contained in a remark of Halley's, who says Dr. Pound and his nephew, Mr. Bradley, did, myself being present, in the last opposition of the sun and Mars this way demonstrate the extreme minuteness of the sun's parallax, and that it was not more than twelve seconds nor less than nine seconds. To make the significance of this plain, it should be observed that the determination of the sun's parallax is equivalent to the determination of the distance from the earth to the sun. At the time of which we are now writing, this very important unit of celestial measurement was only very imperfectly known, and the...

Neutron Stars

At the radio-telescope observatory of the Cambridge University in England, an antenna was specially assembled in the mid-1960s for the purpose of conducting an investigation of the rapid variation, or scintillation, of celestial radio-wave sources. The array was made up of more than 2,000 smaller antennas that covered several acres of ground. Scintillations were observed and analyzed by a graduate student, Jocelyn Bell, and her professor, Anthony Hewish. Special electronic circuits were designed to scrutinize the scintillations, making graphs of the radio-wave strength as a function of time. This led to an unexpected discovery.

Angel Ascendancy

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