# Homework Help: Find minimum energy to escape an orbit

1. Oct 21, 2011

### trivk96

1. The problem statement, all variables and given/known data
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

2. Relevant equations
Don't know of any
maybe UG=-Gm1m2/r

3. The attempt at a solution
UG=(6.67259*10−11*7.36*1022*7170)/1.87167*106

But I do not think this is right

2. Oct 21, 2011

### 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.

3. Oct 21, 2011

### Staff: Mentor

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.

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