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
R=6.4E6 [m]
r=1.7E6 [m]
M=6E24 [kg]

3. The attempt at a solution
There is point A at a distance 54R that the forces equal. to reach there:
$$-\frac{GM}{81r}-\frac{GM}{60R-1.7E6}+\frac{V^2}{2}=-\frac{GM}{81\cdot 6R}-\frac{GM}{54R}$$
$$\frac{V^2}{2}=GM\left(-\frac{1}{81\cdot 6R}-\frac{1}{54R}+\frac{1}{81r}+\frac{1}{60R-1.7E6}\right)$$
$$V^2=2\cdot 6.7E-11 \cdot 6E24 \left( \frac{-54-81\cdot 6}{81\cdot 6\cdot 54\cdot 6.4E6}+\frac{1}{81\cdot 1.7E6}+\frac{1}{60\cdot6.4E24-1.7E6}\right)$$
It should be V=2.26 [km/sec]

Attached Images
File Type: jpg Snap1.jpg (17.9 KB)

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