This question appears in Mumbai University > Satellite Communication and Network subject

Marks: 5 M

Year: May 2015

Kepler’s first law states that the path followed by a satellite around the primary body (e.g. Earth) will be always an ellipse. As shown in figure 3 below, the ellipse is formed by a satellite when it orbits the Earth.

An elliptical orbit with its parameters

The semimajor axis of the ellipse is denoted by ‘a’, and the semiminor axis, by ‘b’. The eccentricitye, which means how elliptical an orbit is, is given by

$ e = \frac {\sqrt {a^2 - b^2} } a$

The eccentricity and the semi-major axis are two of the orbital parameters specified for satellites (spacecraft) orbiting the earth. For an elliptical orbit, $0\lte\lt1$

However, when $e\lt0$, the orbit becomes circular because of the following equation.

$ e = \frac {\sqrt {a^2 - b^2} } a=0$

$ \therefore 0=\sqrt {a^2 - b^2}$ (Squaring both sides)

$ \therefore 0=a^2-b^2$

$ \therefore a^2=b^2$

$ \therefore a=b$

Since the lengths of semimajor and semiminor axes are equal, reconsidering figure 3, the orbit formed will now be circular. That is why it is not possible to have an elliptical satellite orbit with zero eccentricity.