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A satellite which is moving around a planet of mass $M$ in a circular orbit of radius $R$ is given a sudden thrust into the center of the planet, so that it deviates an angle $a$.

Find the latus-rectum $l$ and the eccentricity $e$ of the new orbit.

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    $\begingroup$ What do you mean by "into the center of the earth"? Do you mean towards the center of the earth? $\endgroup$ – LDC3 Jan 3 '15 at 4:19
  • $\begingroup$ i mean directing to the centre of the planet. $\endgroup$ – NIkhil Reddy Ramolla Jan 3 '15 at 10:28
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    $\begingroup$ This question appears to be off-topic because it is about homework. $\endgroup$ – David Hammen Jan 3 '15 at 12:17
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    $\begingroup$ @DavidHammen AFAIK homework isn't itself off topic in Astronomy. That said, the question could probably use some rewording. $\endgroup$ – Mitch Goshorn Jan 3 '15 at 14:13
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    $\begingroup$ Don't expect to get your homework done by others. Put some effort into it, show what you tried. Say where you stumble. $\endgroup$ – guntbert Jan 3 '15 at 16:13
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As a hint: a force directed inward does not change the angular momentum, and therefore does not change the semi-major axis nor the period. It's not clear which angle you're talking about, but knowing that the semi-major axis did not change should let you set the problem up as a simple geometry problem.

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  • $\begingroup$ But the force did change the angular momentum, otherwise it would stay in the circular orbit. In fact, it increased the momentum by increasing the velocity. There are now two force towards the earth, the applied force and gravity. $\endgroup$ – LDC3 Jan 4 '15 at 0:13
  • $\begingroup$ Nope. It changed the momentum, but not the angular momentum. That was the gist of Kepler's second law, that an orbit sweeps out equal areas in equal time. He didn't know about angular momentum (or about momentum), and didn't know that for it to be constant meant that the force was a central force, directed toward the Sun. (He didn't know about forces, either.) Your thrust is defined as a "sudden" thrust, meaning it's momentary, and the only force still acting on the satellite is gravity. $\endgroup$ – ganbustein Jan 4 '15 at 0:27
  • $\begingroup$ Unfortunately, I can't include an image. If the satellite has a velocity vector of (12m/s,0) before and (12m/s,5m/s) after, how is that not a change in angular momentum. After all, the satellite is in the same position and the magnitude of the velocity changed from 12m/s to 13m/s and it's in a different direction. $\endgroup$ – LDC3 Jan 4 '15 at 0:44
  • $\begingroup$ I don't want to see your image. You need to learn the difference between angular momentum and (linear) momentum. $\endgroup$ – ganbustein Jan 4 '15 at 0:48
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    $\begingroup$ Think it through. $\endgroup$ – ganbustein Jan 4 '15 at 1:39

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