GR8677 #2 (Classical Mechanics Problem)

Hi, here we go:

2. A satellite orbits the Earth in a circular orbit. An astronaut on board perturbs the orbit slightly by briefly firing a control jet aimed toward the Earth’s center. Afterward, which of the following is true of the satellite’s path?
(A) It is a 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.


Why is it (A) ? in particular, if we imagined the "brief firing" as infinitismal
and causing the actual path to be deviated by ds (where ds is perpindicular
to the tangent of the circle), then we could see that the path will remain
circular with either a larger radius or a smaller one, depending on the
direction of the jet.

firing a jet does not translate to "moving by ds", it means getting some extra momentum in that direction. This extra momentum isn't canceled by anything, so clearly the orbit won't be circular any longer.

Sure, as dP -> 0, the orbit approaches a circle. But it's an ellipse until dP = 0, which the problem clearly states is not true. Chalk this one up to overthinking it.

-Riley

So we cannot just consider the act of the jet to be just "causing ds displacement"...

Also, as Riley said, the problem itself talks about perturbation in the orbit, so it
cannot be "circular".

Thanks everyone.

Acceleration (with a jetpack) always causes change in momentum (not position--relativistic or non). It's F=ma