Question

State Kepler's laws of planetary motion.

Answer 1

Johannes Kepler, working with data painstakingly collected by Tycho Brahe without the aid of a telescope, developed three laws which described the motion of the planets across the sky.

1. The Law of Orbits: All planets move in elliptical orbits, with the sun at one focus.

2. The Law of Areas: A line that connects a planet to the sun sweeps out equal areas in equal times.

3. The Law of Periods: The square of the period of any planet is proportional to the cube of the semimajor axis of its orbit.

Kepler's laws were derived for orbits around the sun, but they apply to satellite orbits as well.

Answer 2

Kepler's laws of planetary motion are three scientific laws describing motion of planets around the sun as stated in the following :

(a) $\textbf{Law of orbits}$ : all the planets move around the sun in an elliptical orbit with sun at one of the focus of ellipse.

(b) $\textbf{law of areas}$ : The radius vector drawn from the sun to the planet sweeps out equal areas in equal intervals of time, i.e., the areal velocity of a planet is constant.
$\qquad\frac{dA}{dt}=\frac{L}{2m}$
where, angular momentum (L) and mass of a body (m) are constant, $\frac{dA}{dt}$ is constant.

(c) $\textbf{law of period or harmonic law}$ : The square of the time period of revolution (T) of a planet around the sun is directly proportional to the cube of the semi - major axis r of the ellipse.
$i.e.,\qquad T^2\propto r^3$