## Info

If we know the material that is likely to make up the mantle and the core, we can estimate pM and Pc- The average density is easily determined, so we can find (RC RP). For planets on which we can place seismometers, we can learn about interior activity. We can also learn about how seismic disturbances move through the interior. For example, one Apollo experiment involved allowing a spent Lunar Module to crash into the Moon, going on to measure the seismic disturbances with seismometers that had...

## Xce

In terms of observed Doppler shifts, the virial mass is given by equation (13.52) Example 18.2 Virial mass of cluster For the Coma cluster we have vrms 860 km s and a cluster radius of 6.1 Mpc. Find the virial mass of the cluster. (5)(8.6 X 107 cm s)2 (6.1 Mpc)(3.1 X 1024 cm Mpc)

## Solution

Since the mass of the Sun is so much greater than that of the Earth, we can approximate the sum of the masses as being the mass of the Sun, M0. Equation (5.20) then becomes (6.67 X 108 dyn cm2 g2)(3.16 X 107 s)2 2 X 1033g We call this quantity a solar mass. It becomes a convenient quantity for expressing the masses of other stars. From the Earth and Sun we know that for a pair of objects orbiting with a period of 1 yr, at a distance of 1 AU (defined in Section 2.6), the sum of the masses must...

## Pluto

Pluto was discovered in 1930, following an extensive search, by Clyde Tombaugh. The search was initiated by Percival Lowell after it was thought that a planet beyond Neptune might be perturbing Neptune's orbit. Calculations narrowed the range of possible locations on the sky, and a search was carried out. As Fig. 26.1 shows, Pluto doesn't stand out very well against the background of stars. It is detectable as a planet only by its very slow motion with respect to the stars. For Pluto to have a...

## Meteoroids

Meteoroids are small chunks of matter left in space. They are up to tens of meters in diameter. When the Earth encounters a meteoroid (Fig. 26.9), the meteoroid may fall through the Earth's atmosphere. It is then heated by the friction between the air and the meteoroid. It glows brightly as it streaks across the sky, as shown in Fig. 26.10. At this point, we refer to it as a meteor. Most meteors burn up as they pass through the atmosphere. However, some do reach the ground. The ones that reach...

## Binary stars and circular orbits

In this section we will see how Newton's laws of motion and gravitation can be applied to binary stars in circular orbits. Circular orbits are not the most general case of orbital motion, but the analysis is most straightforward, and most of the basic points are clearly illustrated. In the next section we will go to the general case of elliptical orbits. We consider two stars, of masses m1 and m2, orbiting their common center of mass at distances r1 and r2, respectively (Fig. 5.8). From the...

## E

Geometry for parallax measurements.The figure is not to scale. In reality the distance to the star, d, is much greater than 1 AU, so the parallax angle, p, would normally be very small. where p() is the parallax angle measured in arc seconds. Substituting this into equation (2.15) gives The natural unit for measuring angles is the radian. If we have a circle of radius R, and two lines from the center making an angle 9 with each other then the length of the arc bounded by the two lines is where...

## Radio tracers of spiral structure

We can view the situation on a larger scale by using radio observations to look at the distribution of interstellar gas. This allows us to see across the whole galaxy. We can utilize kinematic distances, Spiral structure of the galaxy as determined from giant molecular cloud complexes inside the solar circle. The sizes of the circles indicate the masses of the complexes, as indicated in the upper right.The 4 kpc and Scutum arms are drawn from the 21 cm maps.The Sagittarius arm is drawn as it...

## Determination of the rotation curve

We then assign that Doppler shift to material at the subcentral point (the point of closest approach to the galactic center) for that particular longitude. We can see from Fig. 16.6 that the distance of the subcentral point to the galactic center, Rmin, is From equation (16.11), we see that if vmax is the maximum radial velocity along a given line of sight, then the angular speed (Rmin) for that line of sight is given by The rotation curve for material within the Sun's...

## Tests of general relativity

Over the years since Einstein's publication of general relativity, a number of exacting tests have been carried out to test observational predictions of the theory. Some of the tests are really only tests of the principle of equivalence, while others are true tests of the full theory. A direct test of the principle of equivalence involves the measurement of the attraction of two different objects by some third body. A class of such experiments are called Eotvos experiments, after the person who...

## Chapter summary

In this chapter we saw how the general theory of relativity has changed our thinking about the nature of space and time. We then saw how the ideas of space-time carry over to a theory of gravitation - general relativity. The interpretation of gravitational fields is that they alter the geometry of space-time, causing it to behave like that on a curved surface. The starting point for general relativity is the principle of equivalence, which tells us that inertial and gravitational masses are the...

## Origin of life on Earth

Whether as a result of conditions like those simulated by the Miller-Urey experiments, or as a result of deposition from comets, it is possible that the early atmosphere was enhanced in these prebiotic organic molecules. So the question is how we go from these simple organic molecules to the life that is around us now. Evidence suggests that there was a gap of almost 1 Gyr between the formation of the Earth and the appearance of the first multicell organisms. At the molecular and cellular...

## J

This is done by adding a I through V following the Hubble classification, with I being the brightest (just as for stars). Efforts are still underway to find other properties of spirals that correlate with luminosity class. In this way, the luminosity of a galaxy can be determined without needing to know its distance. (Similarly, the luminosity class of a star can be determined from the shapes of certain spectral lines, allowing us to know the absolute magnitude of a star without...

## A

When spectra were taken of stars other than the Sun, they also showed absorption spectra. Presumably, the continuous radiation produced in a star passes through an atmosphere in which the absorption lines are produced. Not all stars have absorption lines at the same wavelength. Astronomers began to classify and catalog the spectra, even though they still did not understand the mechanism for producing the lines. This points out an important general technique in astronomy -studying large numbers...

## Abbreviations used in the figure credits

Figure credits are given in the captions. Abbreviations used are as follows. 2MASS Two Micron All Sky Survey AUI Associated Universities Inc. AURA Association of Universities for Research in Astronomy Caltech California Institute of Technology ESO European Southern Observatory GSFC ADF Goddard Space Flight Center Astrophysics Data Facility IRAM Institut de Radioastronomie Millim trique JCMT James Clerk Maxwell Telescope MIT Massachusetts Institute of Technology MPIFR Max Planck Institut f r...

## Elliptical galaxies

Elliptical galaxies have, as their name suggests, simple elliptical appearances. Some examples of ellipticals are shown in Fig. 17.2. The ellipticals are classified according to their degree of eccentricity. The ones that look spherical (zero eccentricity) are called E0, and the most eccentric are called E7. The most common type of elliptical galaxies are called dwarf ellipticals, since they are also the smallest. Their sizes are typically a few kilopar-secs and their masses are a few million...

## Appendix F Astronomical coordinates and timekeeping

When we want to locate a star, or any other astronomical object, we only need to specify its direction. We don't need its distance. We therefore need only two coordinates, two angles, to locate an astronomical object. Sometimes, it is convenient to think (as the ancients did) of the stars as being painted on the inside of a sphere, the celestial sphere. Just as we can locate any place on the surface of Earth with two coordinates, latitude and longitude, we need two coordinates to locate an...

## Btl

The Seyfert galaxy NGC l566.This is at a distance 15 Mpc.The active region in the center is found to vary on a time scale of less than a month. (a) HST Wide Field Planetary Camera 2 (WFPC2) image of the oxygen emission (5007 A) from the gas at the heart of NGC 4151. Though the twin cone structure can be seen, the image does not provide any information about the motion of the oxygen gas. (b) In this STIS (imaging spectrometer) spectral image of the oxygen gas, the velocities of the knots are...

## Problems

For all problems, unless otherwise stated, use H0 70 km s Mpc. 18.1. For the cluster in Example 18.2, what is the total kinetic energy 18.2. For some cluster of galaxies, the radius is 500 kpc, and the rms radial velocity is 300 km s. What is the mass of the cluster 18.3. Rewrite equation (18.1) so that if velocities are entered in km s and distances in Mpc, the mass results in solar masses. 18.4. Suppose that one-half of the mass of the cluster in Example 18.2 is in the form of hot...

## R

J L (6.67 X 10 8dyn cm2 g2)(1.67 X 10 24g)2(105cm) _ 6.1 X 1017 cm 0.2 pc We find the mass by multiplying the density by the volume MJ (4 3)(1.67 X 10-24 g)(105 cm 3)(6.1 X 1017 cm)3 1.5 X 1035 g 76 M0 We could have obtained the same mass directly from equation (15.5). As we will see below, not all the mass will end up in the star. Once a cloud becomes gravitationally bound, it will begin to collapse. We would like to be able to estimate the time for the collapse to take place. We begin by...

## T

Radiative transport in the troposphere.We are considering material a height z above the ground, and the top of the troposphere is at a height zt. producing gases that will enhance the greenhouse effect. If there is an increase in these gases, then it is possible that the Earth's temperature will go into steady increase. This phenomenon is called global warming. The problem with measuring the effects of global warming is that the increase in any one year is small, and fluctuations due to...

## Opb

M Meteorite crater on Earth.This is the Barringer Crater, just east of Flagstaff,Arizona.The bowl has a 1 km diameter. Notice the elevated rim. It is the first terrestrial crater recognized as coming from a meteor impact. USGS M Meteorite crater on Earth.This is the Barringer Crater, just east of Flagstaff,Arizona.The bowl has a 1 km diameter. Notice the elevated rim. It is the first terrestrial crater recognized as coming from a meteor impact. USGS types. In this picture, the C type asteroids...

## E0 E4 E7 So

Ellipticals range from E0 (round) to E7 (the most oblate).The regular spirals are divided according to the relative size of the nucleus and the disk, and the tightness of the spiral arms.The Sa have the largest nuclei and the most open arms.The barred spirals, SB, follow the same classification as the normal spirals. S0 galaxies have nuclei and small disks but no spiral arms. metal abundances are not low. Giant ellipticals have metal abundances that are quite...

## Refracting telescopes

In a refracting telescope, the light first passes through a large lens, called the objective lens. The objective is the part that intercepts the incoming light, so it determines the light-gathering power of the telescope. The larger the objective is, the greater the light-gathering power. The light passing through the objective is concentrated on a second lens, called the eyepiece. The eyepiece is used to inspect the image formed by the objective. The image formed by the eyepiece is viewed...

## Dua

More blue light is removed from the incoming beam than red. can see the effect of reddening in the various wavelength images of the globule in Fig. 14.1. More stars shine through at longer wavelengths. Suppose we measure the magnitude of a star in two different wavelength ranges, say those corresponding to the B and V filters. Then, from equation (14.4) we have mV MV + 5 log (r 10 pc)+ Av mB Mb + 5 log (r 10 pc) + AB If we take the difference mB mV, the distance r drops...

## Z

Each positive ion has a mass of Amp, if we ignore the difference between the proton and neutron masses. The total density of the gas is then In going to the second line we have ignored the mass of the electrons relative to the mass of the nucleons. Using equations (10.8) and (10.9), the electron density is related to the total density by Substituting this into equation (10.7) and adding the factor of two to account for the difference between our estimate and the detailed calculation, we have P...

## General relativity

General relativity is Einstein's theory of gravitation that builds on the geometric concepts of spacetime introduced by special relativity. Einstein was looking for a more fundamental explanation of gravity than the empirical laws of Newton. Besides coming up with a different way of thinking about gravity (in terms of geometry), general relativity makes a series of specific predictions of observable deviations from Newtonian gravitation, especially under strong gravitational fields. These...

## Superclusters and voids

Now that we have seen that galaxies are gathered into clusters, we might ask if the clusters are gathered into larger groupings, called superclusters. The answer is that they are. The first supercluster identified (in the 1950s) is the one in which we live, called the local supercluster. The Virgo cluster of galaxies is near the center of the local supercluster. The local group, our cluster of galaxies, is near the edge. The local supercluster contains 106 galaxies in a volume of about 1023...

## Questions

If we see a spiral galaxy edge-on, how do we 17.6.How do the relative abundances of atomic know that it is a spiral and molecular hydrogen vary within a spiral 17.2. (a) Why is it not likely that single spirals galaxy formed from single ellipticals (b) Why is it 17.7.What parts of the interstellar medium would not likely that ellipticals formed from spirals you expect to best trace out spiral arms (Hint Think of the effects of rotation.) Explain your answer. 17.3.Compare the properties of...

## Doppler shift

Doppler shift for waves in an elastic medium, such as sound waves. (a) Moving observer. On the left the observer is moving toward the source, encountering wave crests more frequently than for a stationary observer.The frequency appears to increase (and the wavelength to decrease). On the right, the observer is moving away from the source, encountering waves at a lower frequency, corresponding to a lower frequency, corresponding to a longer wavelength. (b) Moving source.The motion of the source...

## Clusters of stars

When we look at the spatial distribution of stars in our galaxy, we find that most of the light is concentrated in a thin disk. We are inside this disk, so we see it as a band of light on the sky, called the Milky Way. We will discuss this farther in Part III, but we will see in this chapter that location of stars in the galaxy can tell us something about those stars. In particular, some stars are confined to the thin disk of the Milky Way, while others form a more spherical distribution. In...

## Length contraction

Once the concept of time becomes suspect, the concept of length must also be reinvestigated. Think of how we measure the length of an object. We measure the positions of the two ends and take the difference between the two positions. For this procedure to have any meaning, the measurements must be carried out simultaneously. (If I measure the position of the front of an airplane, when it is in NY, and the position of the tail 6 hours later when it is in LA, I should not conclude that the...

## Superfluid Helium Iank

TELESCOPE WITH SCIENTIFIC INSTRUMENTS I STA SENSOR S (Continued) (b) Space Infrared Telescope Facility (SIRTF) in the laboratory for testing. (a) ESA ISO (b) NASA S (Continued) (b) Space Infrared Telescope Facility (SIRTF) in the laboratory for testing. (a) ESA ISO (b) NASA a particular object can check the data at the Infrared Processing and Analysis Center (IPAC), at Caltech, which is not too far from the Jet Propulsion Laboratory (JPL). IPAC has also become the curator of other infrared...

## Examine The Stability Of A Rotating Object Against Centrifugal Disruption

11.10. (a) Examine the stability of a rotating object against centrifugal disruption. Show that, for a rotating object, the requirement that the gravitational force must at least balance the centrifugal force, produces an expression for the minimum radius like equation (11.9). (b) Using this result, what is the minimum rotation period for a white dwarf *11.11. Suppose we approximate the rate of change of a magnetic field for a stationary observer near a neutron star as the field strength...

## L

This still leaves us a factor of five short of closing the universe. We have said that the best way to measure the mass of any object is to measure its gravitational effect on something. If we want to determine the mass of the Earth, we measure the acceleration of gravity near the surface. Therefore, instead of trying to find all of the matter needed to close the universe, we can look for its gravitational effects. We can try to measure the actual slowing down of the expansion of the...