Kepler Laws of Planetary Motion

On the basis of astronomical observations, Johannes Kepler discovered the laws of planetary motion. These laws describe the motion of planets around the Sun and are known as Kepler's laws of planetary motion.

First Law: Law of Orbits

Every planet moves in an elliptical orbit with the Sun situated at one of the foci of the ellipse.

Thus, the orbit of a planet is generally an ellipse rather than a perfect circle. The distance of the planet from the Sun therefore changes continuously during its revolution.

Second Law: Law of Areas

The line joining a planet and the Sun sweeps out equal areas in equal intervals of time.

If \(dA\) is the area swept by the radius vector in a time interval \(dt\), then the rate at which area is swept is constant:

\[ \frac{dA}{dt} = \text{constant} \]

This means that the areal velocity of the planet is constant. Consequently, a planet moves faster when it is closer to the Sun and slower when it is farther from the Sun.

Third Law: Law of Periods

The square of the time period of revolution of a planet is directly proportional to the cube of the semi-major axis of its elliptical orbit.

\[ T^2 \propto a^3 \]

Therefore,

\[ \frac{T^2}{a^3} = K \]

where \(K\) is a constant for all planets revolving around the same central body.

Here:
\(T\) = time period of revolution of the planet
\(a\) = semi-major axis of the planetary orbit
\(K\) = constant of proportionality