Irodov Problem 1.220

The acceleration due to gravity is at surface and at a height of h is given by,



Suppose that the acceleration falls down by a factor n, then,


With (radius of Earth) we have,

for n=0.01, h = 32 km and n=0.5, h= 2642 km.

Irodov Problem 1.219

Let the masses of Earth and Sun be m and M respectively. Let the radius of the Earth be R and the distance of the Sun from Earth be d (assuming its almost a circular orbit). Let the angular velocity of Earth be w. Then we have,
We know that,



So we have,