Problem:
$F = \frac{(G m_1 m_2)}{r^2}$
An object of unknown mass is placed directly between the Earth and the Moon such that the forces of gravity acting on the object are equal from both the Earth and the Moon. The distance from the Moon to the object is exactly one-tenth of the distance from the Moon to Earth. Using the above formula, determine the distance from the Moon to the Earth.
Given is:
The factor $G≈6.67∙10−11\mathbf{N(\frac{m^2}{kg^2})}$ is a universal constant.
Mass of Earth $≈5.972∙10^{24}\mathbf{kg}$
Mass of the Moon as $≈7.348∙10^{22}\mathbf{kg}$
Mass of unknown object = $m$
My solution:
$F = \frac{(6.67 *10^-11) m (7.348*10^{24})}{R^2}$
$F = \frac{(6.67 *10^-11) (5.92* 10^22) m}{10R^2}$
As gravitational force acting on the object is equal
$\frac{(5.92\cdot 10^22)}{100r^2} = \frac{(7.348*10^{24})}{r^2}$
$R = 1.24 \cdot 10^4 KM$
Is this a viable solution to the problem? Please provide feedback. Thank you!
Best Answer
While I haven't checked that you got the right numbers, I would make the following comments:
The approach looks correct. However, you need to put some more context around your equations. Don't just write "F = blah, F = blah, therefore blah = blah". Set out that $r$ is the distance from x to y, then say that the gravitational force due to the moon is $F_1$, and due to the Earth is $F_2$, and that they're equal so therefore blah.
The more context and information you provide, the easier it is to see how much you actually understood of the problem, and the easier it is to spot where you might have made a mistake, which lets the marker be more generous about applying partial marks (and it makes it easier for you to spot the mistakes and correct them before you hand the homework in).