What kepler’s laws of planetary motion says?

All the planet move around the sun in elliptical orbits, with the sun being at rest at one focus of the orbit.

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

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

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

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 T^2 proportional r^3.

Clearly distant planets 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.

• What is the orbital speed of a satellite?

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

Orbital speed of a satellite depends upon the radius 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 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

period of revolution of a satellite depends upon the height of satellite from the surface of the earth.

Greater the height, more will be the period of revolution.

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).

• Geo-stationary satellite

If a satellite revolves in equatorial plane in the direction of earth’s rotation i.e. from west to east with a period of revolution equal to time period of rotation of earth on its own axis i.e. 24 hours, then the satellite will appear stationary relative to earth. Such a satellite is called geo-stationary satellite. Such a satellite revolves around the earth at a height of 36000 km. the orbit of geo-stationary satellite is called parking orbit. Arthur c. clarck was first to predict that a communication satellite can be stationed in the geosynchronous orbit.

• Escape velocity

Escape velocity is that minimum velocity with which a body should be projected from the surface of earth so as it goes out of gravitational field of earth and never return to earth.

Escape velocity is independent of the mass, shape and size of the body and its direction of projection.

Escape velocity is also called second cosmic velocity.

For earth escape velocity = 11.2 km/s.

For moon escape velocity =2.4 km/s.

Orbital velocity of a satellite V0 =√g R and escape velocity Ve = √2gR

Where R = radius of earth i.e. Ve = √2V0 i.e. escape velocity is √2 times the orbital velocity.

Therefore if the orbital velocity of a satellite is increased to √2 times (increased by 41%), the satellite will leave the orbit and escape.