# Using Newton's Law of Universal Gravitation to find distance, with the question not giving sufficient information to substitute into the equation.

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!

• First, the answer is wrong. The distance from the earth to the moon is about $384,400$ km. Next, you've used the wrong powers of ten in your equations for $F$. Third, you should be using $9R$, not $10R$. But most importantly, I don't think there's enough information to answer the question. The ratio of the two masses is (to two significant digits) $81$, so the distance could be anything. Nov 14, 2016 at 0:35
• Yeah that is actually what I thought. Me and my friend are doing this question and he asked me to check if he was right. Funny situation. Thank you for your input. Nov 14, 2016 at 1:26

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.