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Unformatted text preview: 3 4. [5 pts] Derive the conditions under which h ˙ S i = 0, where S = ~ p · ~ r . (We used this in connection with the Virial Theorem.) 4 5. [5 pts] The equation for an elliptical orbit can be written in the form 1 r = C 1 + C 2 cos θ . Express this equation in terms of Cartesian ( x and y ) coordinates and use your result to derive the condition on C 1 and C 2 for the orbit to be elliptical. 5 6. [5 pts] A satellite of small mass m is in a circular orbit of radius R about a planet of large mass M . At a certain instant of time, a powerful rocket motor on the satellite is Fred brie±y, so as to increase the velocity without changing its direction. As a result, the satellite goes into an elliptical orbit as shown. ²ind the total energy (kinetic + potential) in the elliptical orbit in terms of G , m , M , and R . 6...
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This note was uploaded on 07/25/2008 for the course PHY 321 taught by Professor B.pope during the Spring '08 term at Michigan State University.
 Spring '08
 B.Pope
 mechanics, Mass

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