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hw3_solutions

# hw3_solutions - Homework#3 Solutions Astro 10 spring 2010...

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Homework #3: Solutions Astro 10, spring 2010 General Notes to Graders: If numerical answers are roughly correct, do not take marks off. Award part marks if the student has made some progress with the question. 1. [10 points] One solar day is one full revolution with respect to the Sun . One sidereal day is one full revolu- tion with respect to the background stars . If both Earth’s spin and orbit are counterclockwise, then we will reach one sidereal day first (see Figure 1 - ”Real Case”). This is the real case - the sidereal day is shorter by about 4 minutes every revolution. If the Earth spun clockwise , while it still orbited counterclockwise, then we would reach a solar day first (see Figure 1 - ”Imaginary Case”). Thus the solar day would be shorter . We can use what we know about the real case and deduce that the solar day would be about 4 minutes shorter than the sidereal day. Note, however that the length of the sidereal day in both cases is the same. It’s the length of the solar day that changes depending on which direction Earth rotates. Notes to graders: Students should have a discussion equivalent to this in content to receive full credit, but they need not note how much longer or shorter the solar day would be. Also, they should have a diagram or illustration to prove their point. If no diagram, 3 points off. Figure 1: Here you see Earth on two separate days in its orbit. The arrows show the direction to the Sun and to the Background stars from Earth’s perspective. The spin of the Earth and its orbital direction are also shown. One solar day is one full revolution with respect to the Sun; the sidereal day is a full revolution with respect to the background stars. In the real case, with the spin CCW, you can see that Earth will reach back to the face the background stars before the Sun. Hence the sidereal day is shorter than the solar day. In the imaginary case, the opposite is true and thus the sidereal day is longer than the solar day. 1

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2. [10 points] The key thing to remember from our class discussions is what is meant by a sidereal day. The sidereal day is a full rotation with respect to the stars . Therefore, the rising and setting of stars is governed by the sidereal day! Since the sidereal day is 4 minutes shorter for every solar day , we can say the following things. If the star rises at 9 pm tonight, then it will rise at:
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