The Hubble Space Telescope orbits the Earth at an altitude of approximately 612 km. Its mass is 11,100 kg and the mass of the Earth is 5.97×1024 kg. The Earth's radius is 6.38×106 m. Assume the Hubble's orbit is circular. (a) What is the gravitational potential energy of the Earth-Hubble system? (Assume that it is zero when their separation is infinite.) (b) What is the Hubble's KE? (c) What is the Hubble's total energy?

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Geosynchronous satellites orbit the Earth at an altitude of about 3.58×107 m. Given that the Earth's radius is 6.38×106 m and its mass is 5.97×1024 kg, what is the magnitude of the gravitational acceleration at the altitude of one of these satellites?

13.62. (a) Calculate how much work is required to launch a spacecraft of mass m from the surface of the earth (mass me, radius RE) and place it in a circular low earth orbit—that is, an orbit whose altitude above the earth's surface is much less than RE: (As an example, the International Space Station is in low earth orbit at an altitude of about 400 km, much less than RE = 6370 km.) Ignore the kinetic energy that the spacecraft has on the ground due to the earth's rotation. (b) Calculate the minimum amount of additional work required to move the space- craft from low earth orbit to a very great distance from the earth. Ignore the gravitational effects of the sun, the moon, and the other planets. (C) Justify the statement "In terms of energy, low earth orbit is halfway to the edge of the universe."

Earth is rotating about the Sun in our solar system. The distance between the Earth and Sun
is 1.5 × 1011m. Consider the impact of an asteroid of mass 8.9 ×1015 kg and a speed of 90,000
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×106 m, respectively. Assume that the axial and orbital axis of rotations are parallel to each
other.

(a) Calculate the axial and total angular momentum of the Earth. (4 marks)
(b) What is the change in the angular velocity of the Earth due to the collision? (6 marks)
(c) What is the maximum possible change in the length of a day due to the collision?
(3 marks)
(d) How much energy is needed to stop the Earth’s rotation about its axis after the collision?
(4 marks)
(e) What would be the moment of inertia of the Earth if the axis of rotation is parallelly
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