L-2 Kepler’s Laws

 Ellipse :

• An ellipse is the curve obtained when a cone is cut by an inclined plane. 
• It has two focal points. 
• The sum of the distances to the two focal points from every point on the curve is constant. 
• F1 and F2 are two focal points of the ellipse.

AF1 + AF2 = BF1 + BF2 = CF1+ CF2

Kepler’s Laws :
Kepler’s first law : 

• The orbit of a planet is an ellipse with the Sun at one of the foci.
• The position of the Sun is indicated by S.

Kepler’s second law :

• The line joining the planet and the Sun sweeps equal areas in equal intervals of time.
• AB and CD are distances covered by the planet in equal time.
• The straight lines AS and CS sweep equal area in equal interval of time i.e. area ASB and CSD are equal.

Kepler’s third law :

• The square of its period of revolution around the Sun is directly proportional to the cube of the mean distance of a planet from the Sun.
• Thus, if r is the average distance of the planet from the Sun and T is its period of revolution then,

An introduction to scientists : Johannes Kepler :

• German astronomer and mathematician. 
• Started working as a helper to  Tycho Brahe in Prague in 1600. 
• Kepler used the observations of planetary positions made by Brahe to discover the laws of planetary motion. 
• His work was later used by Newton in postulating his law of gravitation.