A satellite is orbiting the earth in a circular orbit once

Question

Question 1: The mass of Phobos (One of the moons of Mars) is m_p = 1.08 x 10¹⁶ kg. The "radius" of Phobos (it is only approximately spherical) is 13.5 km. Would it be possible for you to leap off of Phobos? (In other words, could you personally achieve Phobos' escape speed by jumping?)

Question 2: A satellite is orbiting the Earth in a circular orbit once every four hours. What is the altitude of the satellite?

Question 3: Find the percent difference in gravitational field between Chico (elevation 60.00 m) and the top of Mt. Shasta (elevation 4392 m). You may assume that the Earth is spherical, and that the difference in latitude between Chico and Mt. Shasta is negligible.

Question 4: Find the gravitational force between you and your evil twin, who is presently on the other side of the planet.

Question 5: Earth orbits the Sun with period T = 1 year in an elliptical orbit with semi-major axis a = 1 A.U. (by definition). Halley's Comet orbits once every 76 years. What is the semi-major axis of the orbit of Halley's Comet, in A.U.?

Question 6: Phobos orbits Mars at a mean distance of 9,380 km, and has an orbital period of 0.319 days. From this information we can determine the mass of Mars. What is that mass?

Question 7: The space shuttle typically orbits at an altitude of 300 km above the surface of the Earth. The mass of the shuttle is roughly 99,300 kg.

(a) Draw a free-body diagram for the shuttle.

(b) What is the shuttle's linear velocity during orbit?

Question 8: Mars has mass m_M = 6.42 x 10²³ kg. It has radius r = 3.37 x 10⁶ m. What would be your weight on Mars? Express your answer as a percentage of your weight on Earth.

Question 9: Which is greater, the gravitational force on the Moon due to the Earth, or the gravitational force on the Moon due to the Sun? Does the Moon orbit the Earth or the Sun? Explain.

Question 10: Oceanic tides are caused by the gradient of the gravitational field: since the field only depends on r (not other spherical coordinates) we can say that

∇(field) = d/dr [field]

Calculate the gravitational field gradient at the center of the Earth due to the Moon and due to the Sun. Which has a greater effect on the tides: the Sun or the Moon? Explain.

Question 11: The space shuttle typically orbits 300 km above the surface of the earth. The mass of the shuttle is 99,300 kg.

a) Draw a freebody diagram for the shuttle.  

b) Find the shuttle's velocity.