The masses and radii of the moon and the earth are $$\mathrm{M_1, R_1}$$ and $$\mathrm{M_2, R_2}$$ respectively. Their centres are at a distance $$\mathrm{d}$$ apart. What should be the minimum speed with which a body of mass '$$m$$' should be projected from a point midway between their centres, so as to escape to infinity?

Two satellites of same mass are launched in circular orbits at heights '$$R$$' and '$$2 R$$' above the surface of the earth. The ratio of their kinetic energies is ($$R=$$ radius of the earth)

At a height 'R' above the earth's surface the gravitational acceleration is (R = radius of earth, g = acceleration due to gravity on earth's surface)

For a body of mass '$$m$$', the acceleration due to gravity at a distance '$$R$$' from the surface of the earth is $$\left(\frac{g}{4}\right)$$. Its value at a distance $$\left(\frac{R}{2}\right)$$ from the surface of the earth is ( $$R=$$ radius of the earth, $$g=$$ acceleration due to gravity)