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Gravitational potential, energy, field and intensity

Gravitational potential, energy, field and intensity

06/02/2021
Gravitational potential, energy, field and intensity
Edubomb Edubomb

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Gravitational potential, energy, field, and intensity

Newton’s law of gravitational

Newton's law of gravitational state that. Everybody in this universe attracts everybody with certain attractive forces, which force is directly proportional to the product of the mass of two bodies and inversely proportional to the square of the distance between them.

Let M1 and M2 be the mass of two-body and R be the distance between them then the gravitation force of attraction between them is given by  

Where G is the universal gravitational constant.  when M1 and M2 and are equal and unit Kg, as well as R, is unit distance i.e.

M1= M1= 1kg

R= 1 m

Then

F= G

Hence Universal Gravitational Constant G can be defined as the gravitational force of attraction between two bodies having unit mass and separated at a unit distance.

Gravitational potential

Gravitational potential at a point in the gravitational field can be defined as the amount of work done in bringing the unit mass body from infinity to that point in the gravitational field.

https://drive.google.com/uc?id=1RNLJto_ATl2o9wpsDCRMISZHMcoN30X5

Let us consider earth having mass Me and radius R. we have to calculate the gravitational potential of the earth. To calculate the gravitational potential of the earth let us consider the two-point B and C which are at distance dr from each other.  We have to calculate the gravitational potential of the earth by moving unit mass body from infinity to at that point A in a gravitational field (the point A distance r from the center of the earth is in a gravitational field). For this, first of all, we calculate the amount of work done in moving unit mass body from B to c and then integrate whole to calculate the total amount of work done in moving unit mass body from infinity to at that point in a gravitational field.

Let initially body is at point B in the gravitational field. Now gravitation force of attraction between the earth and that body having unit mass is given by

  [m=1kg; unit mass]

 

Amount of work done in moving body from B to C through distance dr is given by

W= Fg.dr (work done W= F×d)

Now, the total amount of work done in moving the body from ∞ point A in a gravitational field can be calculated as

 

 

 

  

 

 

  

  

 

Hence, gravitational potential energy is given by

 

Gravitational potential energy

The gravitational potential energy at a point in a gravitational field can be defined as the amount of work done in bringing a certain mass body from infinity to that point in the gravitational field.

 It is similar to gravitational potential but the difference is the concept of unit mass and certain mass. Potential is defined as unit mass and potential energy is defined as a certain mass. Hence gravitation potential energy is given by

 

Where m is the mass of body bringing from infinity to at that point in the gravitational field.

Gravitational Field  

Gravitational field can be defined as the area around the body up to where the gravitational force of attraction exists. Out of gravitational field, there is no force of attractions.

Gravitational intensity

Gravitational intensity at a point in the gravitational field of a particle of mass m at distance r is the force experience by the unit mass body placed at that point.

  





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