KEPLER’S LAW OF PLANETARY MOTION

Previous year papers questions related to Kepler’s Law

1.Write a note on Kepler’s law of Planetary motion.                     (2009-10, 5 marks)

2. Write the Kepler’s law of planetary motion.                               (2016-17, 2marks)

3. Show the analytical proofs and corrections made to Kepler’s law with its

    mathematical calculations.                                                        (2016-17, 10marks)

4. State Kepler’s law of planetary motion and show how they can be deduced from 

    Newton’s law of gravity.                                                          (2017-18, 10 marks)

KEPLER’S LAW OF PLANETARY MOTION

Kepler's three laws of planetary motion can be described as follows:

·         The path of the planets about the sun is elliptical in shape, with the center of the sun being located at one focus. (The Law of Ellipses)

·         An imaginary line drawn from the center of the sun to the center of the planet will sweep out equal areas in equal intervals of time. (The Law of Equal Areas)

·         The ratio of the squares of the periods of any two planets is equal to the ratio of the cubes of their average distances from the sun. (The Law of Harmonies)

Kepler’s Laws of Planetary Motion

1. Kepler’s first law (Law of Orbits): All planets move in elliptical orbits, with the sun at one focus.

·         This means that the orbit or path of a planet around the sun is an ellipse i.e. an oval-shaped and not an exact circle. An elliptical path has two foci and the sun is at one of the two foci of the elliptical path. This law is important for us as it helps us discover if other stars have planets! We cannot see those planets but if the star wiggles back and forth in a complicated way, it may be because a planet makes it move so.

·         2. Kepler’s second law (Law of Areas): A line that connects a planet to the sun sweeps out equal areas in equal times.

·         We know that a planet moves around the sun in an elliptical orbit with sun at one of its focus. Now, since the line joining the planet and the sun sweeps over equal areas in equal intervals of time, it means that a planet moves faster when it is closer to the sun and moves slowly when it is farther from the sun.

With the help of second law of Kepler’s we come to know that the Earth is closest to the Sun on 4th January, when day and night are equal etc.

3. Kepler’s third law (Law of Periods): 

·         The square of the period of any planet (P) is proportional to the cube of the semimajor axis of its orbit (R).

·         This means that the cube of the mean distance of a planet from the sun is directly proportional to the square of time it takes to move around the sun.

                                                   P²is propotional to R³

The ratio of the squares of the revolutionary periods for two planets is equal to the ratio of the cubes of their semimajor axes:

·         With the help of Kepler’s third law of planetary motion we can show how long does it takes to reach Mars, how long would it take for a spacecraft from earth to reach the Sun, how far from the center of Earth do synchronous satellites orbit, how far does Halley’s comet go etc.
Though Kepler gave the laws of planetary motion but he could not give an explanation about the motion of planets. It was Newton who showed that the cause of motion of planets is the gravitational force which the sun exerts on them. In fact, Newton used the Kepler’s third law of planetary motion to develop the law of universal gravitation.