The following are my doubts:

1. Show that angular momentum of a satellite of mass M s , revolving around the earth of mass Me in an orbit of radius, R is (GMs 2MeR)1/2.

2. Wind is blowing west to east along two parallel tracks. Two trains are moving with the same speed in opposite directions along the parallel tracks. If the relative velocity of one is double the other, what is the speed of each train?

Thanks.

(1)

For a satellite, moving in a circular orbit, to remain in equilibrium around the Earth it is required that the centripetal force acting outwards equals the gravitational force acting between them.

So,

mv2/r = mw2r = GMm/r2 

 

here

m is the mass of the satellite

M is the mass of the Earth

r is the radius of separation

and 

w is the angular velocity

 

so, by multiplying both sides of the equation by 'm' and by  'r3', we get

(mwr)2 = GMm2

or

 as L = mrw

 

we have

L2 = GMm2

 

or finally, the angular momentum of a satellite in a circular orbit would be

L = [GMm2r]1/2 

 

(2) This question seems incomplete, please revise it and get back to us. We will be glad to help out.

 

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Oops. I'm sorry. The topic is not only Gravitation.

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