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When the speed of a Satellite travelling in a perfectly circular orbit is increased does the path of the satellite remain circular and the radius is increased OR does the path of the satellite follow an elliptical path after the speed has been changed OR are there some other possibilities that I am missing? Also, would the answer be different if the speed is instantaneously increased and not over a period of time? The satellite may be assumed to be a point object and the planet to be perfectly spherical. Thanks!

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  • $\begingroup$ The info in my answer to this related question may be helpful: physics.stackexchange.com/q/677465/123208 $\endgroup$
    – PM 2Ring
    Mar 27 at 18:32
  • $\begingroup$ @PM2Ring I am grateful for the explanation the problem had, but I am just a high schooler and the equations seem to be out of my realm of knowledge $\endgroup$ Mar 27 at 18:48
  • $\begingroup$ Ok. The important thing to remember is that the orbital energy (sum of kinetic & potential energy) is constant, unless the body is acted on by some other force (like firing a rocket engine). If you give a body in a circular orbit a single "kick" to change its velocity, the orbit becomes an ellipse, and the new orbit will pass through the point where the kick was applied. $\endgroup$
    – PM 2Ring
    Mar 27 at 19:01
  • $\begingroup$ @PM2Ring Wow I needed a diluted answer and you delivered, very well explained. $\endgroup$ Mar 27 at 19:33
  • $\begingroup$ A game that shows orbital mechanics really well is Kerbal Space Program $\endgroup$ Mar 27 at 19:41

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Firstly, a perfectly circular orbit is an idealization which simplifies physical scenarios to help build understanding of concepts using easier mathematics. All orbits are elliptical. See: Kepler's First Law

Secondly, a satellite velocity in order to maintain orbit will only depend on the mass of the object being orbited, and the distance of the satellite from that object. That is, $$v_{sat} = \sqrt{\frac{GM_{central}}{R}}$$

If that velocity decreased suddenly, what happens? The satellite does not have enough speed to maintain orbit and it falls inwards until collision.

Conversely, if that velocity increased suddenly, this brings the risk of escaping the orbit and skipping off into empty space as the velocity is too large to maintain stable orbit.

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  • $\begingroup$ So, just to clarify, the change in velocity does change the shape of the orbit that the satellite follows. $\endgroup$ Mar 27 at 18:45
  • $\begingroup$ Yes, it does change the shape of the orbit $\endgroup$
    – trula
    Mar 27 at 19:33

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