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

Marks: 5 M

Year: May 2014, May 2012

Kepler’s law applies to any two bodies in space which interact through gravitation. The more massive of the two is referred to as primary body and the other as secondary body.

I. Kepler’s first law:

• The path followed by a satellite around the primary body will be an ellipse.

• The semimajor axis of ellipse is given by ‘a’ and semiminor axis by ‘b’. The eccentricity is given by : $e= \frac{\sqrt{a^2- b^2 }}{a}$

• The center of mass of two body system is termed as barycenter and is located at one of the two foci $(F_1 or F_2)$.

II. Kepler’s second law:

• For equal time interval satellite will sweep out equal areas in its orbital plane focused at the barycenter.

• The areas $A_1$ and $A_2$ swept out in unit time interval are equal so the velocity at $S_2$ is less than that of $S_1$.

III. Kepler’s third law:

• The square of the periodic time of the orbit is proportional to the cube of the mean distance between the two bodies

$T^2∝ a^3$

• It is also given as:

$a^3= \frac{μ}{n^2}$

where,

$µ=3.986×10^{14} \frac {m^3}{s^2}$

μ is earth's geocentric constant and n is mean motion