Question

Two satellites of same mass m are revolving round
of earth (mass M) in the same orbit of radius r.
Rotational directions of the two are opposite
therefore, they can collide. Total mechanical
energy of the system (both satallites and earths)
is (m << M) :-o ar ol be
GMm
(2) 2GMm
GMm
(3) - 2
slow (4) Zero​

Answer 1

• Total mechanical energy of the system (both satellites and earth ) is -mMG/r.

Given-

Mass of satellites = m (Both satellites have same mass)

Mass of earth = M

Radius of orbit = r

Velocity must be in the orbit of radius r.

So, v = $\sqrt{\frac{GM}{r} }$

where G is the universal gravitational constant and M is the mass of earth.

So, total mechanical energy is

ME = -GM(2m)/r + 2× mv²/2

ME = -GM(2m)/r + mGM/r

ME = - mMG/r

Hope this helps you.