(a) Derive an expression for the acceleration due to gravity at a point situated at a height h above the Earth’s surface in terms of the Earth’s radius R and the surface value g.
(a) Derive an expression for the acceleration due to gravity at a point situated at a height h above the Earth's surface in terms of the Earth's radius R and the surface value g.
(b) Using the result of part (a), obtain an approximate expression valid for h≪R by expanding the exact result in the binomial form up to the first power of h/R.
(c) Using the approximate expression, calculate the height above the Earth's surface where g decreases by 0.5%.