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Moon, Satellite, Probe, Orbital Calculations

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1. Compute the period of a satellite placed into orbit around the Earth at a distance of tenth that to the Moon.
2. The local solar time at 75°W is 12:00 noon. What is the longitude of an observer who sees the full moon on her meridian at this time?
3. At what longitude is an observer who sees the last-quarter moon on his meridian when I is 12:00 noon local solar time at 75°W?
4. It is 12:00 noon local solar time at 75°W. The date is March 21.At what longitude would an observer be able to see the last-quarter moon rising?
5. A high tide is occurring at Charleston, S.C. (80°W, 33°N). At approximately what other longitude is a high tide occurring?
6. A high tide is occurring at Charleston, S.C. (80°W, 33°N). What two longitudes are experiencing low tide?
7. The Ulysses space probe of the Sun encountered the planet Jupiter in 1998 and returned to make a second sweep over the Sun's poles in 2000-2001. Determine the time (in seconds and minutes) it takes a radio signal to reach the Earth when the space probe was at Jupiter. (Use 778 × 106 km for the distance from the space probe to Earth. The distance varies because the Earth and Jupiter are orbiting the Sun.)

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Dear student,
Let me give you the answers to your questions starting from question no 2. This is because question no 1 and 7 are different from other questions. I will answer them last.

Before turning to the answer let us examine the diagram above. Earth spins on its own axis from west to east. In the diagram above Earth is shown as viewed from above the North Pole. The mid point is the North Pole and the perimeter is the equator. Moon revolves around Earth in the same direction of rotation of Earth, i.e. from west to east

Suppose it is noon at any particular place on earth. At a point 180o west (or east) of this point it will be midnight. And at any point 90o W of this point sun is rising and at 90o E of this point sun is setting.

Now let us consider the phases of moon. On the full moon day, earth, moon and sun will fall in a straight line. So if it is noon at any point on earth, the diametrically opposite point on earth will see moon in its meridian, or right above the head. At a point 90o west of this point will see the moon just rising. He will also see the sun just setting at the same time.

So in the diagram at point shown as 2, it is noon. At the same time, there will be midnight at the point shown as 1. on a full moon day, when it is noon at point 2, it is midnight at point 1 and the moon is right above head, or on the meridian.

The first quarter of moon occurs after moon travels one fourth of the distance along the moon's orbit. This motion is towards east. So on the day of first quarter of moon, the angular separation of sun and moon is 90o as see from the ...

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