VISUAL  PHYSICS  ONLINE

5    ADVANCED MECHANICS

P50 005.m

(A)

What is Newton’s inverse square law of gravitation?

What is the meaning of the terms: centripetal force and centripetal acceleration?

(B)

Newton tested his inverse square law of gravitation by comparing it to the gravitational and centripetal acceleration of the Moon in its orbit about the Earth. What did Newton conclude about his answers?  To help answer this question, calculate the gravitational acceleration of the Moon to the Earth and calculate the centripetal acceleration of the Moon.

    Earth-Moon distance   3.846x108  m

   Period of Moon orbiting Earth   T = 27.3 days

   Mass of Earth   ME = 5.97x1024  kg

   Universal gravitational constant  G = 6.67408x10-11  N.m2.kg-2

 

 

 

View solution below only after you have completed the answering the question.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Solution

(A)

Newton's law of universal gravitation states that every particle attracts every other particle in the universe with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres

                

 

A centripetal force (from Latin centrum, "center" and petere, "to seek") is a force that makes a body follow a curved path. Its direction is always perpendicular to the motion of the body and towards the fixed point of the instantaneous centre of curvature of the path. Isaac Newton described it as "a force by which bodies are drawn or impelled, or in any way tend, towards a point as to a centre". In Newtonian mechanics, gravity provides the centripetal force responsible for astronomical orbits such as the Moon about the Earth.

         

 

The centripetal acceleration of an object is its time rate of change of its tangential velocity. For circular motion, the direction of the centripetal acceleration is towards the centre of the circle.

        

 

(B)

Gravitational acceleration   of the Moon in its orbit around the Earth

      

              

 

Centripetal acceleration of the Moon in its obit around the Earth

     

       

 

Newton concluded that the two values for the gravitational acceleration and the centripetal acceleration were nearly the same, giving him confidence in his theory of gravitation.