You can figure this out either of two ways:

time from moon = [ distance to moon/speed of light] = [(3.84x10⁵ km)/(3.00x10⁵ km)] = 1.28 seconds

Or, using the given information:

[ time from moon/time from sun] = [ distance to moon/distance to sun]

time from moon = [ time from sun*distance to moon/distance to sun]

time to moon = [((480 sec)(3.84x10⁵ km))/(1.5x10⁸ km)] = 1.28 seconds

The easiest way to answer this question may be by imagining you are at a place on the Earth where you already know the position of the sun, and then imagine yourself walking around the Earth and what happens to the sun as you do so. A globe may help you picture it. For the first part of the question, imagine you are at the equator or the north pole. For example, if you are at the north pole, where is the north star (north celestial pole)? It is directly overhead, 90 degrees from the horizon. Now imagine yourself walking south around the Earth. As you walk, the north star will start to move toward your horizon. For each degree of latitude that you walk south, the north star will appear to move toward your horizon by one degree. How many degrees do you have to walk to get to Santa Cruz? Since Santa Cruz is at a latitude of about 37 degrees, you need to walk 90-37 = 53 degrees. As you make that walk, how many degrees has the north star moved toward your (northern) horizon? 53 degrees. Since it started out at 90 degrees from the horizon when you were at the north pole, it has gone down to 90-53 = 37 degrees. (Try to see how this works if you start at the equator instead!)

For the second part, note that during the summer solstice, the northern hemisphere is tilted toward the sun at 23.5 degrees. Where is the sun directly overhead? When you are at 23.5 degrees north latitude. (Does this make sense? Think it through before proceeding.) So the sun is 90 degrees away from the southern horizon at the summer solstice if your latitude is 23.5 degrees. Now imagine yourself walking north around the Earth. As you walk, since you are walking away from the sun, the sun will move toward your horizon. For every degree you walk north, the sun will appear to be one degree closer to your southern horizon. How many degrees do you have to walk to get from 23.5 degrees north latitude to our latitude? 37 - 23.5 = 13.5 degrees. So the sun will appear to have moved 13.5 degrees toward the horizon as we walk from 23.5 degrees to 37 degrees north latitude. It started out at 90 degrees from the horizon, so now it is 90-13.5=76.5 degrees from the (southern) horizon.

If that wasn't clear, there are other ways to see this; there's a nice figure on page 18 of the text (2nd edition) that shows you how to figure it out.

In the first figure below, the two lines labeled ``To North Star'' are parallel since the north star is so fantastically far away. You may remember from high school geometry that angle ABC equals angle BCD. Therefore:

90 degrees - angle between northern horizon and north celestial pole = 90 degrees - latitude

So:

angle between northern horizon and north celestial pole = latitude

The second part of the question was complicated. Take a look at the second figure, below. It's useful to imagine that the Earth's spin axis is not inclined and figure out the answer to the problem. Then figure out how the inclination of the Earth's axis changes things.

We know that angle BFC is the inclination of the earth's spin axis, which is 23.5 degrees. We showed that the angle between the north celestial pole and the northern horizon (AFC) is your latitude. We also know that angle BFD is 90 degrees. So angle DFC is 90-inclination. We're after angle EFD. Therefore:

Angle between noon sun and southern horizon
= angle EFD
= 180 degrees - angle DFC - angle CFA
= 180 - (90 - 23.5) - latitude
= 90 + inclination - latitude
@ 75 degrees for Santa Cruz.

The first quarter moon is when the moon is one quarter of the way through it's cycle, and the third quarter moon is when it's three quarters of the way through its cycle. The length of one complete cycle is ~ 28 days, so there are ~ 14 days between the first and third quarter.

Using Kepler's third law:

Period = (/font>{[ distance/1 AU]})³ years = 8 years

Note that the answer is not 4 years (reasoning that the planet has to travel four times as far as the Earth). Planets that are farther away from the sun take longer to go around the sun because they're ``running on a bigger track'', but they also experience a weaker gravitational force. Therefore they take even longer to go all the way around the sun.

The force of gravity due to the Earth at the Earth's surface is:

F_Earth = [(G M_Earth m )/(R_Earth²)]

The force of gravity due to the moon at the moon's surface is:

F_moon = [(G M_moon m )/(R_moon²)]

The ratio of the two is: [(F_moon)/(F_Earth)] = [(M_moon/R_moon²)/(M_Earth/R_Earth²)] = [(7.3x10²² kg/(1700 km)²)/(5.9x10²⁴ kg/(6400 km)²)] @ 1/6.

So you would, for example, be able to jump six times higher on the moon than you can on the Earth.

See Figure 2-11 (in the 2nd edition) for visual aids, or use a globe to visualize it. The north celestial pole is directly above the North Pole of the Earth, so it can only be seen from points north of the equator. Anywhere south of the equator, you would need to look through the Earth in order to see the north celestial pole. For the south celestial pole, the reverse is true; you can only see it from north of the equator. The celestial equator is a ring around the earth's equator. Since it goes all the way around the Earth, you can look up to see it from anywhere on Earth (some would argue that you can't see it if you're at exactly the north or south pole of the Earth, since it would be right on your horizon).

When the northern hemisphere is tilted toward the sun, in our summer, the southern hemisphere is tilted away from the sun, so it is winter there. When the southern hemisphere is tilted toward the sun it is summer there, but we in the northern hemisphere are tilted away from the sun so it is winter for us. Thus, in the southern hemisphere the seasons are the reverse of what we experience.

a)During the phase of full moon, the Earth is in a ``new Earth'' phase, ie you see the dark side of the Earth. Where you live on the Moon, it will be daylight. b) Since the Moon spin synchronously with its orbit around the Earth, the position of the Earth in the sky as viewed on the Moon is fixed. On the face closer to the Earth, the Earth will always be in the same position in the sky. On the other side of the Moon, you cannot see the Earth. c) When people on Earth see a solar eclipse, you (living on the face of the Moon closer to the Earth) will see a full Earth with a small dark spot moving across it. When people on Earth see lunar eclipse, you (living on the face of the Moon closer to the Earth) will see a total eclipse of the Sun by the Earth.