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Question
State Kepler’s laws.
Solution
In the early 1600s, Johannes Kepler proposed three laws of planetary motion.
- First Law – The Law of Ellipses
The path of the planets about the Sun is elliptical in shape, with the center of the Sun being located at one of the foci. - Second Law – The Law of Equal Areas
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. - Third Law – The Law of Harmonies
The ratio of the squares of the periods of any two planets is equal to the ratio of the cubes of their semi major axis from the Sun.
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[G = 6.67 × 10–11 SI units and M = 6 × 1024 kg]
A planet revolving in an elliptical orbit has:
- a constant velocity of revolution.
- has the least velocity when it is nearest to the sun.
- its areal velocity is directly proportional to its velocity.
- areal velocity is inversely proportional to its velocity.
- to follow a trajectory such that the areal velocity is constant.
Choose the correct answer from the options given below:
lf the angular momentum of a planet of mass m, moving around the Sun in a circular orbit is L, about the center of the Sun, and its areal velocity is ______.
Halley's Comet revolves around the sun for a time period of 76 years. The aphelion distance if perihelion is given by 8.9 × 1010 m, will be ______.
(Take, the mass of sun = 2 × 1030 kg and G = 6.67 × 10-11 Nm3/kg2)
