Gravitational force, `F=Gm_(1)m_(2)//r.`

A mass M is split into two parts m and (M-m) which are then separated by certain distance. Find ratio (m/M) to maximise the gravitational force F=(Gm(M-m))/(r^(2)) between the parts. Here G = gravitational constant and r is the distance between m and (M-m).

Two stars of mass m_(1) and m_(2) are parts of a binary star system. The radii of their orbits are r_(1) and r_(2) respectivey, measured from the centre of mass of the system. The magnitude of gravitational force m_(1) exerts on m_(2) is

Supposing Newton's law of gravitation for gravitation force F_(1) and F_(2) between two masses m_(1) and m_(2) at positions r_(1) and r_(2) read F_(2)=-F_(2)=(r_(12))/(r_(12)^(3))GM_(0)^(2)((m_(1)m_(2))/(M_(0)^(2)))^(n) where M_(0) is a constant dimension of mass, r_(12)=r_(1)-r_(2) and n is number. In such a case.

Supposing Newton's law of gravitation for gravitation forces F_(1) and F_(2) between two masses m_(1) and m_(2) at positions r_(1) and r_(2) read where M_(0) is a constant of dimension of mass, r_(12) = r_(1) - r_(2) and n is a number. In such a case,

Derive the dimension of gravitation constant G. Given F_("gravitation")=G(m_(1)m_(2))/(r^(2)) .

Two concentric shells of masses M_(1) and M_(2) are concentric as shown. Calculate the gravitational force on m due to M_(1) at points P,Q and R .