Critical velocity is the minimum velocity of projection for which satellite revolves in a circular orbit around the earth.

G = Universal Gravitational Constant

g_h = acceleration due to gravity at height h above earth’s surface

M= Mass of the earth

R =Radius of the earth

h = height at which satellite is orbiting

If satellite is revolving very close to the earth’s surface, then

So V_c= √ g_h(R+h) is the formula for Critical Velocity of Satellite Orbiting at height h from the Earth’s Surface

Let us consider mass of the earth as M, radius of earth as R, and the body is at an altitude h from the surface of the earth at distance r, gh is gravity at height h from the earth’s surface. The acceleration gained by an object because of gravitational force is called its acceleration due to gravity.

Acceleration due to gravity on the surface of the earth= g =  ………..(1)

Gravity at height h from the earth’s surface = gh=

Distance from surface of earth (r) = Radius of earth + height from the surface of he earth

r = R + h

Therefore,

By dividing (1) / (2),the formula for acceleration due to gravity at height h from the earth’s surface is given as,

G = Universal Gravitational Constant R = radius of the earth

M = mass of the earth

If M is the mass of the earth, m is the mass of the body which is at the surface of the earth and R is the  distance between body and centre of the earth (which is the radius of the earth) . According to the Newton’s law of gravitation the gravitational force experienced by that mass m is given as,

F  =  G M m/R ²  ………………………(1)

As per Newton’s second law of motion, Force = mass × gravity = mg

Substituting value of force in equation 1 we get,

G M m/R ² = m g

The formula for Acceleration due to gravity at the surface of the Earth is given as,

g = G M /R ²

Where g =  Acceleration due to gravity, G = Universal Gravitational Constant, M = mass of the earth and R = radius of the earth

Every particle of matter will attract other particle of matter with a force that is directly proportional to product of mass and inversely proportional to square of the distance between them.

The formula for Newton’s law of gravitation is given as,

            F ∝ m₁ m₂ / r ²

Magnitude of Gravitational Force ( F)  =  G (m₁ m₂ / r ²)

Where G = Universal Gravitational Constant, m₁= mass of particle 1, m₂ = mass of particle 2 , r = the distance between the centers of the masses

The value of Universal Gravitational Constant(G) = 6.6733 x 10 ^-11 N . (m / kg)²