**Answer the following question.**

State the conditions for various possible orbits of satellite depending upon the horizontal speed of projection.

#### Solution

The path of the satellite depends upon the value of the horizontal speed of projection v_{h} relative to critical velocity v_{c} and escape velocity v_{e}.

**Case (I)** v_{h} < v_{c}:

The orbit of the satellite is an ellipse with a point of projection as 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)** v_{h} = v_{c}:

The satellite moves in a stable circular orbit around the Earth.

**Case (III)** v_{c} < v_{h }< v_{e}:

The satellite moves in an elliptical orbit around the Earth with the point of projection as perigee.

**Case (IV)** v_{h} = v_{e}:

The satellite travels along the parabolic path and never returns to the point of projection. Its speed will be zero at infinity.

**Case (V)** v_{h} > v_{e}:

The satellite escapes from the gravitational influence of Earth traversing a hyperbolic path.