Explorations: An Introduction to Astronomy (Arny), 7th Edition

Chapter 1: The Cycles of the Sky

Problems

1
If the Earth turns one full rotation in approximately 24 hours, how many degrees per hour does the sky turn?
2
From a latitude of 55°, what is the highest and lowest altitude above the horizon of the noon Sun? What will be the altitude on September 22?
3
Make a sketch to calculate what times the waxing crescent moon will rise and set. Indicate the observer's location and lines of sight to the Moon for these times.
4
Calculate how many degrees the Moon moves in its orbit in one day (use 360° and the sidereal period). Use this result and the answer to problem 1 to determine how much later the Moon rises each day.
5
The Moon crosses down through the ecliptic every 27.21222 days ("draconic period"). Its synodic period, the period of the phases, is 29.5306 days. Show that 242 draconic periods very nearly equals 223 synodic periods. How long is this in years? What does this suggest about eclipses and why? (This match of cycles is called the saros and was used by ancient astronomers to predict eclipses.)
6
Find how many hours it takes the Moon to move in its orbit a distance equal to the Earth's diameter. (You will need to determine the speed of the Moon in its orbit. You can find values for the diameter of the Earth and the radius and period of the Moon's orbit in the appendix.) How does this relate to the time it takes for a lunar eclipse to occur?
7
List some of the details left out of problem 5 that you would need to consider to exactly calculate the length of an eclipse. What effect would each have on the final answer?
8
The Moon's shadow at the Earth is much smaller than the Moon's diameter—it is only a few hundred kilometers wide. Is the Moon's speed still a good estimate of how fast the shadow moves? Repeat problem 5 to estimate the duration of a solar eclipse.
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