Question

State Kepler's law of orbit and law of equal areas.

Answer 1

Hint: There are three laws of kepler’s which are named as kepler’s law of orbits, kepler’s law of areas, and kepler’s law of periods. Kepler’s Law states that the planets move around the sun in elliptical orbits with the sun at one focus, so we called this law as Kepler's law of planetary motions.

Complete solution:
Kepler's law of orbit states that every planet revolves around the sun in an elliptical orbit with the sun situated at one of the foci of the elliptical orbit. The definition of Kepler's law of equal areas is the radius vector drawn from the sun to any planet sweeps out equal areas in equal intervals of time. This is the exact answer of the given question.

In Kepler's law of orbit, as we know that the orbit of any planet is an ellipse around the Sun with the Sun at one of the two foci of an ellipse. Everyone knows that planets revolve around the Sun in a circular orbit. But according to Kepler's explanation it is true that planets revolve around the Sun, but not in a circular orbit but it revolves around an ellipse. In an ellipse there we have two focuses and the Sun is located at one of the foci of the ellipse. Next talk about area The rate of change of area with time will be constant. So, Kepler's law of equal areas states that the line joining a planet to the Sun sweeps out equal areas in an equal interval of time.

Note:
Here another law is Kepler’s Law of Periods which states that the square of the time period of the planet is directly proportional to the cube of the semimajor axis of its orbit. Which is mathematically represented as ${T^2} \propto {a^3}$ . where T is time there is a small derivation to derive this expression.