Gravitation


   
 
Gravitational Potential
The work done in moving a unit mass from infinity to a point in a gravitational field is called the gravitational potential at that point.
 
It is a negative, scalar quantity. The unit is JKg-1.
 
Gravitational potential difference
The work done in moving a unit mass from one point to another in a gravitational field is called gravitational potential difference. The SI unit is JKg-1.
 
Gravitational potential energy
Let a body of mass m be at a distance r from a body of mass M. The gravitational potential energy of the mass m is defined as the work done in bringing it from infinity to that point.
 
 
The work done in moving the mass m through a small distance dr in the gravitational field of M is,
 
dw = F dr
 
 
The total work done in bringing mass m from infinity to that point, is
 
 
 
 
 
 
Gravitational potential energy
 
 
Relation between gravitational field intensity and gravitational potential difference
If M is the mass of a body around which a field exists and m is the test mass placed at a distance r from M in this field then,
 
 
Potential energy per unit mass is gravitational potential (V)
 
 
 
Gravitational potential energy of a mass m at a height h above the surface of the Earth
The potential energy of a mass m at a height h is given by the  expression
 
 
 
 
 
 
Considering P.E. at the surface of the Earth to be nil.
 
 
     
   
Get unlimited tutoring in Math, English, Physics, Chemistry, Biology, Algebra, Geometry and all other subjects at $99.99 per month!