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Question
State the conditions for various possible orbits of satellite depending upon the horizontal/tangential speed of projection.
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Solution
The path of the satellite depends upon the value of the horizontal speed of projection vh relative to critical velocity vc and escape velocity ve.
Case (I) vh < vc:
The orbit of the satellite is an ellipse with a point of projection as the apogee and Earth at one of the foci. During this elliptical path, if the satellite passes through the Earth’s atmosphere, it experiences a nonconservative force of air resistance. As a result, it loses energy and spirals down to the Earth.
Case (II) vh = vc:
The satellite moves in a stable circular orbit around the Earth.
Case (III) vc < vh < ve:
The satellite moves in an elliptical orbit around the Earth with the point of projection as perigee.
Case (IV) vh = ve:
The satellite travels along the parabolic path and never returns to the point of projection. Its speed will be zero at infinity.
Case (V) vh > ve:
The satellite escapes from the gravitational influence of Earth traversing a hyperbolic path.
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