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Our teacher told us today:

Suppose a satellite is moving around the earth in a circular orbit of radius $r$. Suddenly an external agent stops its motion so that its kinetic energy becomes zero but its gravitational potential energy remains the same. Assume there is no air friction or drag. The satellite starts to fall towards the earth's surface and it will follow an elliptical orbit in its motion towards the earth.

Please tell me if this is correct because according to my intuition it should follow a straight-line trajectory towards the earth.

Please help me with this. I am not very good at English so pardon me for any grammatical mistakes in my question.

Deschele Schilder
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gurdeep singh
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3 Answers3

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Short answer: you are both right.

Suppose that the satellite did not stop completely, but still have some very-very-very small speed. The orbit of this satellite will be a very stretched ellipse. It will not be much different from the straight line, but still an ellipse.

So, it is possible (and convenient!) to consider the straight line towards Earth's center as a degenerate ellipse.

lesnik
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If the satelite is slightly accelerated or decelerated, its trajectory will change to an elipse.

But if it is stopped, that is: no angular velocity with the center of the earth, it will fall radially.

If it starts to fall over one of the poles, its trajectory will be vertical to an observer on earth. Otherwise, it will follow (for a observer on earth) a curved shape (I see no reason to be an elipse) depending on the latitude and the initial height.

Claudio Saspinski
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The satellite will stop but the rotation of the Earth no. The satellite will fall vertically but the trajectory of the satellite will be an ellipse relative to the vertical point where the satellite was stopped because of the rotation of the Earth.

user36636
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