## Wednesday, August 27, 2008

### Kepler’s Laws of Planetary Motion - July Dec Revision

Kepler’s Laws of Planetary Motion
1. All planets move in elliptical orbits with the sun at a focus.

2. The radius vector from the sun to the planet sweeps equal area in equal time.

3. The square of the time period of a plant is proportional to the cube of the semimajor axis of the ellipse.

(Chapter: Gravitation)

1. All planets move in elliptical orbits with the sun at a focus.

Circular path is a special case of an ellipse when the major and minor axes are equal. For a circular apth, the planet should have velocity perpendicular to the line joining it with the sun and the magnitude has to be

v = √(GM/a)

If these conditions arenot satisfied, the planet moves in an ellipse.

2. The radius vector from the sun to the planet sweeps equal area in equal time.

For a circular orbit, as the speed of the particle remains constant, it will sweep equal area in equal time.

3. The square of the time period of a plant is proportional to the cube of the semimajor axis of the ellipse.

For circular orbits this law is proved.

Past JEE Questions

According to Kepler’s second law, the radius vector to a plant form the sun sweeps out equal areas in equal intervals of time. This law is a consequence of the conservation of -----------------.

(JEE 1985)