## Fundamental Measurements in Astronomy

Positions in the Sky

An astronomer needs to find his or her way around the night sky. The first step is learning about two coordinate systems.

The altazimuth system uses altitude for vertical measure and azimuth for horizontal measure. Altitude is measured in degrees from 0° (the horizon) to 90° (the zenith—the overhead point in the sky). Azimuth is measured in degrees from 0° (due north) around to 90° (due east) and so on around the sky to 360°—really the 0° of north again.

The equatorial system is based on the concept of a celestial sphere that is imagined to be positioned around Earth with a north celestial pole over the north geographic pole, a celestial equator over the geographic equator, and a south celestial pole over the south geographic pole. Declination on the celestial sphere is the counterpart of latitude on Earth but is measured in positive degrees (0° to +90°) north of the celestial equator and negative degrees (0° to -90°) south of the celestial equator. Each degree of declination can be further divided into 60 minutes (written as 60') of declination and each minute into 60 seconds (written as 60") of declination. Right ascension (RA) on the celestial sphere is the counterpart of longitude on Earth, but instead of using a 0° line that forms the prime meridian running through Greenwich, England, it uses a 0 h (zero hour) line that runs through the vernal equinox point in the sky (the point the Sun is at in the sky at the start of spring in Earth's northern hemisphere). Also, instead of RA being measured in degrees, 180° West from the prime meridian and 180° East from the prime meridian as longitude is, RA is measured in 24 hours of right ascension east around the celestial sphere. Each hour of right ascension is further divided into 60 minutes (written as 60 m) of right ascension and each minute into 60 seconds (written as 60 s) of right ascension.

### Angular Distances

Observers also have a need to determine how many degrees it is from, say, a star to a galaxy in the sky or how many degrees long a comet's tail appears. Here, we can divide each degree into 60 arc-minutes (written as 60') and each arc-minute into 60 arc-seconds (written as 60"). And we can do a rough estimate of angular measure in the sky by holding out our fist or finger at arm's length. The width of a person's fist at arm's length is about 10°, the width of a little finger at arm's length about 1V2°. In comparison, the Big Dipper is more than 25° long, the Moon is about V2° (30") wide, and Venus, when it appears largest, is about 1' (60") wide.

### Distance in Space

The most famous unit of measure for interstellar and intergalactic distances is the light-year. It is the distance that light (or any form of electromagnetic radiation), the fastest thing in the universe (at about 186,000 miles per second or 300,000 kilometers per second), can travel in one year. A light-year is about 6 trillion (that is, 6 million million) miles.

### Brightness

In astronomy, brightness is measured by magnitude. Originally, all naked-eye stars were categorized in six classes of brightness, from 1st magnitude (brightest) to 6th magnitude (faintest). In modern times, the scale has been extended to zero and to negative magnitudes for very bright objects (remember, the lower the magnitude, the brighter the object). It has also been extended to numbers higher than 6 for objects so faint they require optical aid to see. Decimals are used between two magnitudes: a star midway in brightness between 1.0 and 2.0 is 1.5. A difference of one magnitude means one object is about 2.512 times brighter than the other. This is because it was considered useful to set a difference of five magnitudes as equal to 100 times—2.512 (actually 2.512 . . .) multiplied by itself 5 times is 100.

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