ASTR 1010 – Homework Assignment 2 – Spring 2009

Chapter 2

Question 1 - #5. In order to measure linear distances between objects, or between two points, you need to know the distance to each object. When you don’t know the distance to the objects whose separation you are trying to measure, then the only thing you can do is measure the angular distance between them. In the celestial sphere, there is no sense of “depth”, so you don’t know how far away things are and, so, you cannot know the linear distance between objects; you can only determine the angular distance or separation between two points or two objects. One degree is broken up into sixty arcminutes, and one arcminute is broken up into sixty arcseconds.

Question 2 - #10. The solstices and equinoxes are both times of year and positions on the celestial sphere. When the Sun is at the summer solstice, it reaches its highest point at noon in the Northern Hemisphere. At the winter solstice, it reaches its lowest point at noon in the Northern Hemisphere. As far as the positions on the celestial sphere, the summer solstice is when the ecliptic is farthest in angular separation from the celestial equator. The equinoxes are where the ecliptic and the celestial equator meet. As far as the Sun’s behavior, it’s when the Sun rises due east, sets due west and spends 12 hours in the sky (so there’s twelve hours of day and twelve of night).

Question 3. - #11. Precession is the slow movement of the earth’s axis in a circle with radius of about 23.5 degrees. Over 26,000 or so years, the North Celestial Pole (and the South Celestial Pole) move in a circle on the celestial sphere with radius 23.5 degrees. This slowly but inexorably shifts the entire coordinate system of the sky in a 26,000 year cycle.

Question 4. - #12. The Moon’s cycle of phases is best explained by looking at Figure 2.22 in your book. As you can see from the picture, it is impossible to see a full moon from Earth at 12 noon.

Question 5. - #15. The apparent retrograde motion of planets refers to the outer planets (the ones beyond the Earth) and is their brief westward motion with respect to the background stars on the celestial sphere (most of the time they move eastwards from day to day). In a geocentric system, this motion is difficult to explain because the Earth in that model is a stationary platform, so a motion that goes in the opposite direction from the “normal” motion can only be explained by having the planet physically move backward. In the heliocentric model, the retrograde motion is produced as the Earth catches up and passes the outer planet (see Figure 2.33).

Question 6. - #41. a) New Moon (it has to be the opposite of the Earth’s phase, see Figure 2.22) b) “New” Earth c) Waning Crescent d) Total Solar Eclipse (the Earth would completely blot out the Sun – see Figure 2.26)

Question 7. - #43. If the Moon was twice as far as it is now, its angular size would be half of what it is today (recall from class S = qd / 206265), thus, the Moon’s angular size could not completely cover the Sun’s angular size (which would stay together) and you could no longer have total solar eclipses.

Question 8. - #44. If the Earth were smaller, we still would have solar eclipses (because the Earth’s size doesn’t play a role in whether you have them or not). For total lunar eclipses, it would depend on just how small the Earth got…Earth’s angular size would have to be at least half a degree as seen from the Moon and then you could have total lunar eclipses.

Question 9. - #49. a) 24° 18’ 00”

b) 1° 35’ 24”

c) 0° 6’ 00”

d) 0° 0’ 36”

e) 0° 0’ 3.6”

Question 10. - #50. a) 7.645°

b) 0.215°

c) 1.99972°

d) 0.016667°

e) 0.000274°

Question 11. - #54. S = qd / 206265

q must be measure in arcseconds, and 0.5 degrees is 1800 arcseconds, so

S = 1800 * 1.5 x 10⁸ km / 206265 = 1.31 x 10⁶ km

Question 12. - #56. a) Moon’s angular diameter at minimum distance: 2012”

At maximum distance: 1763”

b) Sun’s angular diameter at minimum distance: 1940”

At maximum distance: 1880”

c) If both the Sun and the Moon are at their max distance from the Earth, the Moon’s angular size will be too small to completely cover the Sun and so you can’t have a total solar eclipse.