Question

What is the force of gravity acting on a 2000 kg spacecraft when it is about the Earth at a in orbit distance of 8.375 x 106 m?​

Answer 1

W = 13.44 KN

Step-by-step explanation:

First, we need to find the value of acceleration due to gravity at the specified height:

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

where,

g' = value of acceleration due to gravity at given height = ?

g = value of acceleration due to gravity at surface of earth = 9.81 m/s²

h = height of space craft = 8.375 x 10⁶ m - 6.37 x 10⁶ m = 2.005 x 10⁶ m

R = Radius of Earth = 6.37 x 10⁶ m

Therefore,

`g' = (9.81\ m/s^2)(1-2(2.005\ x\ 10^6\ m)/(6.37\ x\ 10^6\ m))\\\\g' = (9.81\ m/s^2)(1 - 0.315)\\g' = 6.72\ m/s^2`

Now, we can find the weight or force of gravity on space craft:

`W = mg'`

where,

W = Force of gravity on space craft = ?

m = mass of space craft = 2000 kg

Therefore,

`W = (2000 kg)(6.72\ m/s^2)`

W = 13.44 KN