# Gravitation energy 5

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

At which minimal speed must a stone be thrown from the moon in order to reach earth.

R is the earth’s radius and r the moon’s.

M is the earth’s mass and m the moon’s.

I ignore the stone’s mass, it cancels

**2. Relevant equations**

$$U=-\frac{GMm}{r}$$

G=6.7E-11

R=6.4E6 [m]

r=1.7E6 [m]

M=6E24 [kg]

m=M/81

**3. The attempt at a solution**

There is point A at a distance 54R that the forces equal. to reach there:

$$-\frac{GM}{81r}-\frac{GM}{60R-1.7E6}+\frac{V^2}{2}=-\frac{GM}{81\cdot 6R}-\frac{GM}{54R}$$

$$\frac{V^2}{2}=GM\left(-\frac{1}{81\cdot 6R}-\frac{1}{54R}+\frac{1}{81r}+\frac{1}{60R-1.7E6}\right)$$

$$V^2=2\cdot 6.7E-11 \cdot 6E24 \left( \frac{-54-81\cdot 6}{81\cdot 6\cdot 54\cdot 6.4E6}+\frac{1}{81\cdot 1.7E6}+\frac{1}{60\cdot6.4E24-1.7E6}\right)$$

$$V=1804$$

It should be V=2.26 [km/sec]

http://ift.tt/1seSmPh

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