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conantee
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« on: December 31, 2009, 02:49:00 AM »

2. A satellite orbits the Earth in a circular orbit. An astronaut on board perturbs the orbit slightly by briefly firing control jet aimed toward the Earth's center. Afterward, which of the following is true of the satellite's path?
(A) It is an ellipse.
(B) It is a hyperbola.
(C) It is a circle with larger radius.
(D) It is a spiral with increasing radius.
(E) It exhibits many radial oscillations per revolution.
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conantee
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« Reply #1 on: December 31, 2009, 03:08:54 AM »

This question requires knowledge of mechanics, especially conservation of angular momentum.

For a first glance, (D) and (E) are too complicated answers for slight disturbance as described in the questions. You can eliminate them for keeping time.

(B) is also wrong because in order to have a hyperbola path. It requires energy to escape the earth's potential, which cannot be obtained from slight disturbance.

When the control jet is fired aimed toward the earth's center. The angular momentum of the satellite respect to earth's center does not change. However, we know that a circular motion with larger radius has higher angular motion (since higher velocity is needed to maintain the larger circular orbit, the angular momentum (product of radius vector and linear momentum) is larger.). Therefore, (C) is wrong.

Hence, the correct answer is (A), and by stats, 51 of 100 got it right.
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