Question

Calculate the acceleration due to gravity at a height of 300 km from the surface of the Earth. (M = 5.98 × 10²⁴ kg, R = 6400 km).

Answer 1

To find: Acceleration due to gravity at height (g_h)

Formula: g_h = GM/(R + h)² 

Calculation: From formula,

6.67 X 10” x 5.98 X iO

= antilog {log(6.67) + log(5.98) – 2log(6.7)} × 10 

= antilog{0.8241 + 0.7767 – 2(0.8261)} × 10 

= antilog {1.6008 – 1.6522} × 10

= antilog \(\{\bar{1}.9486\}\times 10\)

= 0.8884 × 10 = 8.884 m/s² 

Acceleration due to gravity at 300 km will be 8.884 m/s².