Astronomy 110 PRINT Name   __________________________
Fall 2005   Section 006  

Homework 3 : Finding the Moon

(Due Thursday, Sep 15, 2005)

Note: Each question is worth one point, and when requested, your reasoning is worth one point.

This is supposed to be a picture of part of the sky looking roughly westwards. It shows a full moon on the horizon and two planets in the sky.

Are the Moon and planets rising or setting? _Setting_

If you were to draw the Sun, would it be in the picture? _No_

We are looking at a Full Moon, which occurs when the Sun, Earth, and Moon are lined up with Earth in the middle. So if the Moon is in the west, then the Sun must be in the east, and out of the picture.

What time of day is it? _Dawn_

The Full Moon rises as the Sun sets, and sets as the Sun is rising (since they are on a line with Earth, at this time). With the Moon setting, it must be about sunrise.

What is the angle between the Moon and the Sun? _180_Degrees_

The Moon rises about 50 minutes later each night. On the diagram, sketch in roughly where you think the Moon will be a day later, at the same time. Assume the lower of the two planets is about 10 degrees above the horizon. (Hint: How many degrees does the Moon move across the sky in a day?)

If the Moon rises 50 min later, it will set 50 min later, so exactly a day later the Moon will where it was 50 min ago on our picture. We can figure out how many degrees this is above the horizon by estimating that in 24 hours the sky appears to move 360 degrees, so that means it has a rate of 15 degrees per hour. Fifty min is equal to 5/6 of an hour, and 5/6 of 15 degrees is 12.5 degrees, so that is how high above the horizon the Moon will be after 24 hours. If the lower planet in the picture is 10 degrees above the horizon, then we can draw the Moon just above it.

Which two planets CAN'T these be? _Mercury_and_Venus_

As explained above, we are looking away from the Sun, but Mercury and Venus orbit closer to the Sun than we do. The farthest that Mercury and Venus get from the Sun is 28 degrees and 47 degrees, respectively. Our picture does not show this region of the sky, so they can't be in it.

Draw the rough position of the ecliptic on the diagram.

How did you know where to draw?
Everything in our Solar System is in a plane, so that means that they all appear to follow roughly the same path across the sky. In this picture we have three objects that are in the Solar System, the Moon and two planets, so we can guess where the ecliptic is by connecting the dots between those objects.

Is it likely that either or both of these planets is in retrograde motion at this time? _Yes_

Reason :
Retrograde motion occurs because the planets closer to the Sun orbit faster than the ones farther away. It happens when the Sun the Earth and the planet are lined up (in opposition), which is what is shown in the picture. Note: This concept makes more sense when you can see how the planets move in an animation, so follow the links on the class website on Retrograde Motion.

Suppose there is a very bright star near the upper planet when you see the Moon and planets as in the diagram and suppose you note very carefully the positions of the planet and the bright star relative to other nearby stars and also their angles above the horizon. Now suppose you look again exactly 24 hours later by your (perfect) watch. Would you expect the position of the bright star to have changed

relative to other nearby stars? _No_

When you compare the postions of stars with each other they don't change from one day to the next, because they are so far away. This is why we can see Greek constellations that were made up a thousand years ago.

relative to the horizon? _Yes_

Due to complications in the Earth's motion, stars rise about 4 minutes earlier each night (this is why you see different stars at different times of the year). So if our star is up 4 min earlier then it will be 4 min closer to the horizon a day later. Which at a rate of 15 degrees per hour is a change of 1 degree.

relative to the planet? _Yes_

The Earth and the planet are both orbiting the Sun and the star is not, so in 24 hours the planet will be in a slightly different place compared to the star.