Kepler’s Laws of planetary motion

(i)                  All planets move around the sun in elliptical orbits, with the sun being at rest at one focus of the orbit.

(ii)                The position vector of the planet with sun at the origin sweeps out equal area in equal time i.e. the areal velocity of planet around the sun always remains constant.

A consequence of this law is that the speed of planet increases when the planet is closer to the sun and decreases when the planed is far away from sun.

Speed of a plant is maximum when it is at perigee and minimum when it is at apogee.

(iii)               The square of the period of revolution of a planet around the sun is directly proportional to the cube of mean distance of planet from the sun.

If   T is period of revolution and r is the mean distance of planet from sun then T² ∞ r³.

Clearly distant plants have larger period of revolution. The time period of nearest planet Mercury is 88 days where as time period of farthest planet Pluto is 247.7 years.

Satellite: Satellites are natural or artificial bodies revolving around a planet under its gravitational attraction. Moon is a natural satellite while INSAT- IB is an artificial satellite of earth.

Orbital speed of a satellite

(i)                  Orbital speed of a satellite is independent of its mass. Hence satellites of different masses revolving in the orbit same radius have same orbital speed.

(ii)                Orbital speed of a satellite depends upon the radious of orbit (height of satellite from the surface of earth). Greater the radius of orbit, lesser will be the orbital speed.

The orbital speed of a satellite revolving near the surface of earth is 7.9 km/ sec.

Period of Revolution of a satellite: Time taken by a satellite to complete one revolution in its orbit is called its period of revolution.

i.e period of revolution = circumference of orbit   /     orbital speed

(i) Period of revolution of a satellite depends upon the height of satellite from the surface of earth. Greater the height more will be the period of revolution.

(ii) Period of revolution of a satellite is independent of its mass.

The period of revolution of satellite revolving near the surface of earth is 1 hour 24 minute (84 minute)