Gravitation Important formulas

The rate of variation of g w.r.t height (very near the surface of the earth) is twice the rate of variation of g w.r.t depth below the surface of the earth

The value of g decreases as we go above the surface of earth by an amount 

The maximum decrease in value of g due to rotation of earth is at equator and is given by

Gravitational potential at a distance r from the centre of the earth

Gravitational potential energy of a mass m at a height r above the centre of earth is

 

  

If r1 > r2, the change in PE is negative i.e. the body is being brought closer to the surface of earth

If r1 < r2, then the change in potential energy of the body will be positive and the body is being moved away from the surface of earth.

If the body is moved from a point r1 = Re to a point r2 = (Re + h), then the change in potential energy will be

If the gravitational force varies inversely as the nth power of distance (R) then the orbital velocity of a satellite is given by

 

Total energy of the satellite is given by

 

Potential energy of a satellite at a height equal to the radius of earth is given by 

When a body falls from a height h above the surface of the earth, its velocity on reaching the surface of the earth is given by 

Intensity of gravitational field at a point lying at a distance x from centre on the axis of a ring is given by

 

Intensity at a point on the axis distant x from the centre of a disc is

The potential at a distance x from the centre of disc on the axis is