Find minimum energy to escape an orbit

[trivk96]

Homework Statement

When it orbited the Moon, the Apollo 11 spacecraft ’s mass was 7170 kg, its period was 121 min, and its mean distance from the Moon’s center was 1.87167 × 10⁶ m. Assume its orbit was circular and the Moon to be a uniform sphere of mass
7.36 ×10²² kg. Its orbital speed was 1619.837645 m/s

What is the minimum energy required for the craft to leave the orbit and escape the Moon’s
gravitational field?
Answer in units of J

Homework Equations

Don't know of any
maybe U_G=-Gm₁m₂/r

The Attempt at a Solution

U_G=(6.67259*10⁻¹¹*7.36*10²²*7170)/1.87167*10⁶

But I do not think this is right

 

[Delphi51]

It has to have energy zero to escape. How much energy does it have now?
Notice the minus sign in your UG=-Gm1m2/r.
Of course it has kinetic energy, too.

 

[gneill]

You're on the right track, but you need one more piece of the puzzle. The total mechanical energy of a body in orbit is given by the sum of the kinetic and potential energies. In particular,
$$E = m\left(\frac{v^2}{2} - \frac{GM}{r}\right)$$
The orbit becomes unbound (escape happens) when E ≥ 0.