# Change in Path of a satellite on changing its velocity

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!

• The info in my answer to this related question may be helpful: physics.stackexchange.com/q/677465/123208 Mar 27 at 18:32
• @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 Mar 27 at 18:48
• 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. Mar 27 at 19:01
• @PM2Ring Wow I needed a diluted answer and you delivered, very well explained. Mar 27 at 19:33
• A game that shows orbital mechanics really well is Kerbal Space Program Mar 27 at 19:41

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, $$v_{sat} = \sqrt{\frac{GM_{central}}{R}}$$