Lectures Table of Contents Astro 100

# The Celestial Sphere; Apparent Motions of the Sun and Stars

## Angular Sizes

Terms to Know

angular size
arcminute
arcsecond

How big is the Sun? How about the Moon? You know the Sun is physically much larger (400 times), but they appear the same size in the sky, right? This means their angular size is the same. The Sun is 400 times larger than the Moon, but it's 400 times farther away.

An object's angular size is the angle whose point is at your eyeball and whose sides encompass the object. Obviously if you move closer or further from the object, or if the object changes physical size, then its angular size will change.

Angular sizes are measured in degrees (e.g., 360o = 1 full circle, 90o = right angle, etc.), with smaller divisions of 60 "arcminutes" (') per degree, and 60 "arcseconds" ('')per arcminute ( 60 x 60 = 3600 arcseconds per degree).

Some examples:
 Betelgeuse (largest star) seen from Earth 0.004'' Smallest detail visible from Earth's surface 1'' Smallest detail visible to naked eye 1' = 60'' Sun or Moon seen from Earth 0.5o = 30' Your fingernail at arm's length 1o = 60' Your fist at arm's length 10o Thumb-to-pinky at arm's length 20o Horizon to zenith (point overhead) 90o

The View Earth: The Celestial Sphere, Daily and Annual Motions of the Sun and Stars

Terms to Know

Constellation
Asterism
Magnitude (apparent)
Intensity
Celestial Sphere:
• North and South Celestial Poles
• Celestial Equator
• Zenith
• Horizon
• Ecliptic
• Precession
Rotation
Revolution

## 1. The View from Earth: The Celestial Sphere

From a dark, clear site, you can see 3000-6000 stars with the naked eye. The sky is divided into 88 official constellations (e.g., Ursa Major, Virgo, Perseus) based on ancient Arab and Greek mythology. In addition, there are familiar asterisms (e.g., The Big Dipper, The Summer Triangle) that are common but not "official."

The contellations are only apparent lineups as seen from Earth of stars at large different distances; the stars' positions as seen in the sky of a planet orbiting a star other than the Sun would be totally different !

Stars' brightnesses are given either in units of intensity (energy received per second per unit area on the Earth's surface) or in magnitudes, which come from the Greek astronomer Hipparchus.

The Earth spins on its axis; the axis defines the North and South Poles. The Earth's equator lies exactly between the poles like a belt around a basketball.

Now imagine extending the Earth's axis like a needle north and south into the sky. If the sky were a shell surrounding the Earth (rather than an infinite void) -- the Celestial Sphere -- then the axis would intersect at two points: The North and South Celestial Poles . Likewise, if you could fling the Earth's equator out onto the shell of the sky, it would create a Celestial Equator, a Great Circle overhead exactly between the Celestial Poles.

How bright is Polaris, the North Star, in magnitudes? What's so special about Polaris?

Every person on Earth has a slightly different horizon -- the limit of what can be seen from that precise spot -- due to the Earth's curved surface. Directly overhead is the zenith.

## 2. Daily and Annual Motions of the Sun and Stars

The stars rise in the East and set in the West just as the Sun does. Why? Because the Earth rotates (spins) on its axis from West to East (how many times a day?), bringing new parts of sky into view in the East and carrying them below the horizon in the West.

How can you prove this to yourself? On a clear night, go outside, face anywhere but North (why not North?), locate a bright star, and move around until the star is just next to a tree, telephone pole, or other landmark. Now wait a few (5-10) minutes. What happens?

Are there stars in the sky during the day?

The Earth also revolves (orbits) around the Sun (how many times a year?). Therefore, the Sun appears to glide among the stars throughout the year at the rate of about 1 degree per day (why 1 degree?). The path of that glide is the ecliptic (think: eclipse). If you were standing on the surface of the Sun (whose surface is not only 5000 degrees (K) but also not solid), you would see the Earth glide through the same ecliptic path, but 6 months later (or earlier), as it orbited around you.

Day by day, degree by degree, this causes different constellations to appear in the night sky and disappear into the daylight, until finally, after a year, the same constellations reappear.

The 12 constellations along the ecliptic make up the zodiac . When does the Sun appear to lie in the zodiac sign of your birthday?
 Lectures Table of Contents Astro 100

 Houjun Mo Astronomy 100