GR8677 #2 (Classical Mechanics Problem)

ali8
Posts: 103
Joined: Sat Aug 29, 2009 8:20 am

GR8677 #2 (Classical Mechanics Problem)

Postby ali8 » Wed Jun 22, 2011 4:51 am

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.

negru
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Joined: Wed Oct 13, 2010 3:49 pm

Re: GR8677 #2 (Classical Mechanics Problem)

Postby negru » Wed Jun 22, 2011 5:48 am

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.

bfollinprm
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Re: GR8677 #2 (Classical Mechanics Problem)

Postby bfollinprm » Wed Jun 22, 2011 7:33 am

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.

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WhoaNonstop
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Re: GR8677 #2 (Classical Mechanics Problem)

Postby WhoaNonstop » Wed Jun 22, 2011 12:59 pm

ali8 wrote:perturbs the orbit slightly


-Riley

ali8
Posts: 103
Joined: Sat Aug 29, 2009 8:20 am

Re: GR8677 #2 (Classical Mechanics Problem)

Postby ali8 » Wed Jun 22, 2011 3:12 pm

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.

bfollinprm
Posts: 1197
Joined: Sat Nov 07, 2009 11:44 am

Re: GR8677 #2 (Classical Mechanics Problem)

Postby bfollinprm » Wed Jun 22, 2011 3:40 pm

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




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