Imagine that upon passing point P the shuttle pilot fires a lateral thruster for

Question

Imagine that upon passing point P the shuttle pilot fires a lateral thruster for a very short time. (Assume that the effect of firing the lateral thruster is equivalent to adding a component of velocity perpendicular to the original velocity.) As a result, the shuttle is observed to follow a new elliptical orbit, as shown in the figure below. The semi-major axis of the new orbit is perpendicular to the imaginary line from point P to the center of the planet.

i. Did the sudden firing of the lateral thruster cause the speed of the shuttle to suddenly increase, suddenly decrease, or remain unchanged?

ii. Did the sudden firing of the lateral thruster cause the magnitude of the angular momentum of the shuttle to suddenly increase, suddenly decrease, or remain unchanged?

Explanation / Answer

i) The speed of shuttle is suddenly decreased because circular orbit has more energy than elliptical orbit. Hence, the energy of shuttle must be decreased by reducing the speed to get in an elliptical orbital.

ii) The magnitude of the angular momentum of shuttle remains unchanged since angular momentum is conserved here.

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