1. The Moon orbits Earth in an elliptical orbit. Look up the values of the relevant parameters on https://nssdc.gsfc.nasa.gov/planetary/factsheet/moonfact.html, and calculate the maximum and minimum angular sizes of the Moon as seen from Earth. Express your answers in degrees to three significant figures, and be sure to show your work.
2. In class we calculated the average angular size of the Sun to be 0.533o. Compare this value with your answers to question 1. Does a total solar eclipse occur every time the Sun, Moon and Earth are aligned? Explain.
3. In worksheet 1 we analyzed qualitatively how, during a solar eclipse, the Moon’s umbra moves across Earth’s surface due to Earth’s rotation and the Moon’s orbital motion. Now let us get quantitative. For a solar eclipse on the equator, how fast (in km/s) and in what direction (east-to-west or west-to-east) does the umbra move due to Earth’s rotation? Draw a diagram to show your reasoning.
4. Similarly, for a solar eclipse on the equator, how fast (in km/s) and in what direction (east-to-west or west-to-east) does the umbra move due to the Moon’s orbital motion? Again, draw a diagram to show your reasoning. What is the umbra’s resulting net motion (speed and direction)?
5. Consider a latitude-longitude grid on the Moon analogous to that on Earth. Look up the radius of the Moon and calculate the distance in km corresponding to a degree of latitude on the Moon.
6. Imagine that Earth’s rotation was reversed, so that it now rotated clockwise with the same period as before. Assume its revolution around the Sun remained counterclockwise. a. Sketch this imaginary situation, indicating the directions of rotational and orbital motions.
b. What would be the new lengths of sidereal and solar days in hours and minutes? Show your work.