Minimum energy required to escape the grav field

[lizzyb]

Homework Statement

When it orbited the Moon, the Apollo 11 spacecraft 's mass was 13400 kg, and its mean distance from the Moon's center was 2.56393 X 10^6 m. Assume its orbit was circular and the Moon to be a unform sphere of mass 7.36 X 10^22 kg.

a) Given the gravitational constant G is 6.67259 X 10^-11 N m^2/kg^2, calculate the orbital speed of the spacecraft . DONE

b) What is the minimimum energy required for the craft to leave the orbit and escape the Moon's gravitational field? Anser in units of J.

Homework Equations

$$KE = \frac{1}{2}m v^2$$

$$v_{esc} = sqrt{ \frac{2 G M}{R}}$$

The Attempt at a Solution

I did this: $$KE = \frac{1}{2} m_c v^2 = \frac{1}{2} m_c \frac{2 G M_m}{R} = \frac{G M_m m_c }{R}$$

Where M_m is the mass of the moon and m_c is the mass of the spacecraft .

I plugged in the numbers but the anser was wrong. What else would they mean by energy required? Thanks.

 

[EthanB]

Perhaps they wanted you to find the work required to move the craft from its orbit to the point at which the gravitational force from the moon and Earth are equal and opposite.

 

[lizzyb]

how do i go about doing that?

 

[EthanB]

Solve for where the forces are equal. Then, find the work required to move from your current radius to the calculated height.