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In the figure here, a space shuttle is initially in a circular orbit of radius r about Earth. At point P, the pilot briefly fires a forward-pointing thruster to decrease the shuttle’s kinetic energy K and mechanical energy E. (a) Which of the dashed elliptical orbits shown in the figure will the shuttle then take? (b) Is the orbital period T of the shuttle (the time to return to P) then greater than, less than, or the same as in the circular orbit?

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Hello. I have a major trouble understanding this question. How do we know that the space shuttle passes throught the point P after losing speed ? Also, the lower orbits must have greater speeds. Doesn't that mean the pilot must increase the shuttle's kinetic energy to go to lower orbits ? Appreciate any help! Thanks!

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  • $\begingroup$ Hi and welcome to the Physics SE! Please note that this is not a homework help site. Please see this Meta post on asking homework questions and this Meta post for "check my work" problems. $\endgroup$ – John Rennie Nov 13 '15 at 18:25
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    $\begingroup$ @pooja: "Doesn't that mean the pilot must increase the shuttle's kinetic energy to go to lower orbits?" You need to take into account kinetic and potential energy of the shuttle. T=K+U. $\endgroup$ – Gert Nov 13 '15 at 18:34
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    $\begingroup$ Most of the really interesting questions are labeled as homework and closed, all the time by the same people. $\endgroup$ – Energizer777 Nov 13 '15 at 18:34
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    $\begingroup$ I want to see different people labeling various questions as homework not all the time the same individuals because they can be subjective. It is not so evident why all orbits should have a common point P. $\endgroup$ – Energizer777 Nov 13 '15 at 18:38
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    $\begingroup$ I have gone through the meta post on homework questions. This queston doesn't fall under that category. I am asking specifically about the part that's troubling me. I am not asking for any help in answering the question. $\endgroup$ – AgentS Nov 13 '15 at 19:00
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It is assumed that the spacecraft fires changes its velocity in an instant, not over a period of time. Its velocity is decreased exactly at the point in time it passes through P.

It is true that spaceships in lower circular orbits have greater orbital velocities, but in elliptical orbits the velocity changes with the distance between the two masses (since the potential energy increases with distance, the kinetic energy must decrease).

It is therefore the case that a spacecraft in the orbit 1 has a lower velocity at point P than a spacecraft in the initial Orbit at point P.(Think about it, they are both the same distance away, so the potential energy is the same)

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You're on the right track.

"How do we know that the space shuttle passes throught the point P after losing speed ?"

The assumption (in these types of problems) is that the thruster is applied for a very short time compared to the duration of the orbit. In that way, we can assume that applying the thruster is effectively instantaneous. So if the shuttle applies the thruster at point P, we can assume that once they're done, they will still be (roughly) at point P. Then, because of the nature of the two-body problem --- they are assured to come back to the same point P.

So what happens to the kinetic energy before and after the thruster fires (while still at point P)?
What happens to the potential energy?
The total energy?

What does that tell you about the resulting orbit?

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