The path of a very small satellite S in an elliptical orbit around a massive sph

Question

The path of a very small satellite S in an elliptical orbit around a massive spherical planet P is shown in the figure. The distance from 3 to 4 is the same as from 4 to 5, 9 to 10, and 10 to 11. For the orbit of S shown, P could be located at X. The PE of S varies with position. S has a maximum speed at '10' The magnitude of the force on S at '8' is ... at '2' The speed at S at position '1' is ... at '7'. The total PE + KE at '10' is .... at '5'. The angular momentum of S varies with position S has a minimum speed at '4' The speed at S at position '2' is ... at '8'. The angular momentum of S is constant The total PE + KE at '3' is .... at '4'. For the orbit of S shown, P could be located at X. The KE of S varies with position.

Explanation / Answer

A) the total mechanical energy (KE+PE) is always the same B) no, as the satellite's distance from the planet varies,its speed varies (and its PE and KE change accordingly) C)ppos 1 and pos 7 look to be the same distance from the planet, if so, the speeds are the same D)the sat is farther from the planet at 5, therefore experiencing less force, thus the accel is less E) yes, the planet could be at either focus of the ellipse F) I am assuming the planet is located to the left on this image...the greatest speed is at 10 if this assumption is correct; but if not, the greatest speed is at 4 G) no, accel of the satellite does not depend on its mass: F= ma =GMm/r^2 => a=GM/r^2

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