Question

A space vehicle, of mass 555 kg, experiences a gravitational pull from Earth of255 N. The mass of Earth is 5.98 x 10^24 kg. How far is the vehicle above the surface of Earth?

Answer 1

2.95 * 10^7 meters

Explanation:

Given:

mass of space vehicle (m) = 555 kg

mass of earth (M) = 5.98 * 10^24 kg

Gravitational force (F) = 255 N

G = 6.67 * 10^-11 N m^2/kg​^2

We calculate the distance using the gravitational force formula:

`F=(G\cdot m\cdot M)/(r^2)`

We substitute and solve for r, just like this:

`\begin{gathered} 255=(6.67\cdot 10^(-11)\cdot 555\cdot 5.98\cdot 10^(24))/(r^2) \\ \\ r^2=(6.67\cdot10^(-11)\cdot555\cdot5.98\cdot10^(24))/(255) \\ \\ r=\sqrt{8.68\cdot10^(14)} \\ \\ r=2.95\cdot10^7\text{ m} \end{gathered}`

They are at a distance of 2.95 * 10^7 meters