[Science] [Physics] [GS]
Gravitation, Newton’s Law, Gravity & Kepler’s Law

Gravitation : Every body attracts other body by a force called force of gravitation.

Newton’s law of Gravitation : The force of gravitational attraction between two bodies is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. F = (G m_{1}m_{2})/r^{2}
Here G is constant called universal gravitational constant.
The value of G is 6.67×10^{11} Nm^{2}/Kg^{2}.

Gravity : The gravitational force of earth is called gravity or gravity is the force by which earth pulls a body towards its centre.

The acceleration produced in a body due to force of gravity is called acceleration due to gravity and its value is 9.8 m/s^{2}.

Acceleration due to gravity is independent of shape, size and mass of the body.

Value of g decreases with height or depth from earth’s surface.

g is maximum at poles.

g is minimum at equator.

g decreases due to rotation of earth.

g decreases if angular speed of the earth increases.

If angular speed of the earth becomes 17 times its present value, a body on the equator becomes weightless.

On moon, the value of g is 1/6 of the value of g at the earth.

Kepler’s law :

(1) All planets move around the sun in elliptical orbits, with the sun being at rest at one focus of the orbit.

(2) The position vector of the planet with sun at the origin sweeps out equal area in equal time i.e the areal velocity of planet around the sun always remains constant.

A consequence of this law is that the speed of the planet increases when the planet is closer to the sun and viceversa.

(3)The square of the period of revolution of a planet around the sun is directly proportional to the cube of mean distance of planet from the sun.
T^{2} α r^{3}

Clearly distant planets have larger period of revolution. The time period of nearest planet Mercury is 88 days where as time period of farthest planet Neptune is 165 years.

Weight of a body in a lift :

If lift is stationary or moving with uniform speed (either upward or downward), the apparent weight of a body is equal to its true weight.

If lift is going up with acceleration, the apparent weight of a body is more than the true weight.

If lift is going down with acceleration, the apparent weight of a body is less than the true weight.

If the cord of the lift is broken, it falls freely. In this situation, the weight of a body in the lift becomes zero. This is the situation of weightlessness.

While going down, if the acceleration of lift is more than acceleration due to gravity,a body in the lift goes in the contact of the ceiling of the lift.