1. Kepler’s law Introduction
2. Kepler’s First Law
3. Kepler’s Second Law
4. Kepler’s Third Law

**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 S_{1} and S_{2} meters in 1 s, then the areas A_{1}
and A_{2} will be equal. The average velocity in each case is S_{1}
and S_{2} m/s, and because of the equal area law, it follows that the
velocity at S_{2} is less than that at S_{1}.

**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 10^{14}m^{3}/s^{2}

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