Kepler’s laws

Kepler’s laws:

1. Kepler’s law Introduction:

Satellites (spacecraft) orbiting the earth follow the same laws that govern the motion of the planets around the sun.

Kepler’s laws apply quite generally to any two bodies in space which interact through gravitation. The more massive of the two bodies is referred to as the primary, the other, the secondary or satellite.

2. Kepler’s First Law:

Kepler’s first law states that the path followed by a satellite around the primary will be an ellipse. An ellipse hast Two focal points shown as F1  and F2  in Fig. 2.1. The center of mass of the two-body system, termed the bary center, is always center of the foci.

The semi major axis of the ellipse is denoted by a, and the semi minor axis, by b. The eccentricity e is given by

3. Kepler’s Second Law :

Kepler’s second law states that, for equal time intervals, a satellite will sweep out equal areas in its orbital plane, focused at the barycenter. Referring to Fig. 2.2, assuming the satellite travels distances S₁ and S₂ meters in 1 s, then the areas A₁ and A₂ will be equal. The average velocity in each case is S₁ and S₂ m/s, and because of the equal area law, it follows that the velocity at S₂ is less than that at S₁.

4. Kepler’s Third Law:

Kepler’s third law states that the square of the periodic time of orbit is proportional to the cube of the mean distance between the two bodies. The mean distance is equal to the semi major axis a. 

For the artificial satellites orbiting the earth, Kepler’s third law can be written in the form

Where n is the mean motion of the satellite in radians per second and is the earth’s geocentric gravitational constant µ=3.986005 X 10¹⁴m³/s²