Question

Calculate the force of Earth's gravity on a spacecraft 1.6 * 10^7 m above the surface of the Earth if the spacecraft has a mass of 2000 kg.

Answer 1

`g_h = -39.4\ m/s^2`

Step-by-step explanation:

The formula for the value of the acceleration due to gravity at a height "h" from the surface of Earth is given as follows:

`g_h = g(1-(2h)/(R) )`

where,

`g_h` = acceleration due to gravity at height h from the surface of Earth = ?

g = acceleration due to gravity on the surface of the Earth = 9.81 m/s²

h = height from the surface of the Earth = 1.6 x 10⁷ m

R = Radius of the Earth = 6.378 x 10⁶ m

Therefore,

`g_h = (9.81\ m/s^2)(1-(2(1.6\ x\ 10^7\ m))/(6.378\ x\ 10^6\ m))`

`g_h = -39.4\ m/s^2`