State the conditions for various possible orbits of a satellite.

Explanation

To put a satellite in an orbit around the Earth, it is raised to some altidue beyond the Earth's atmosphere and then projected horizontally with a speed v. The path of the satellite depends on the value of v relative to the critical orbital speed `(v_(e))` and the escape speed `v_(e).`
(1) `v lt v_(e):` The satellite follows an elliptical path withe centre of the Earth at one focus. It may strike the Earth or just miss the Earth's surface and enter into an elliptical orbit with the point of projection as the apogee and the opposite point as the perigee. Even for low-Earth orbits, the perigee must lie above the thermosphere as otherwise the satellite will lose energy due to atmospheric drag and gradually spiral down into denser atmosphere and burn out.
(2) `v=v_(e):` The satellite enters into a circular orbit around the Earth and its motion is a UCM.
(3) `v_(e) lt v lt v_(e):` The satellite moves in an elliptical orbit with the centre of the Earth one focus.
(4) ` v ge v_(e):` The path of the satellite is no longer a closed curve and it escapes the Earth's gravitational influence. For `v=v_(e)` (total energy zero), the path is parabolic for `vgtv_(e)` (total energy positive), the path is hyperbolic.