Gravitation

Larger the distance of planet from the sun, larger will be its period of revolution around the sun.
From Kepler's third law of planetary motion, the square of the period of revolution of any planet around the sun is directly proportional to the cube of the semi-major axis of its elliptical orbit.


Given,

For day
days.

At a certain velocity of projection the body will go out of the gravitational field of the earth and will never return of the earth, this velocity is known as escape velocity

Given,

Let a satellite is revolving around earth with orbital velocity v. The gravitational potential energy of satellite is
...(i)
where, = mass of earth,
m = mass of satellite

= radius of earth
and G = gravitational constant
The kinetic energy of satellite is
...(ii)
Therefore, total energy of satellite, as energy is conserved, is
(iii)
But we know that necessary centripetal force to the satellite is provided by the gravitational force, ie,


or ......(iv)
Hence, from Eqs. (iii) and (iv), we get

Above or below the earth's surface, value of acceleration due to gravity decreases, so time period increases ie, clock will become slow.

The effective acceleration in a lift descending with acceleration is Time period of simple pendulum

Acceleration due to gravity at equator