# Thread: Help calculating acceleration due to gravity.

1. ## Help calculating acceleration due to gravity.

Hi there.

I'm looking for an equation to calculate the rate at which 2 bodies of known mass m1 and m2 will accelerate towards each other for any given distance. Just want to check that I've got this right.

Using the gravitational equation

F=G*m1*m2/r2

then substitute

F=ma where m = m1+m2

therefore

(m1+m2)a = G * m1 * m2/r2

therefore

a = G * m1 * m2 / (m1+m2)r2

2. ## Re: Help calculating acceleration due to gravity.

Originally Posted by Ollie999
Hi there.

I'm looking for an equation to calculate the rate at which 2 bodies of known mass m1 and m2 will accelerate towards each other for any given distance. Just want to check that I've got this right.

Using the gravitational equation

F=G*m1*m2/r2

then substitute

F=ma where m = m1+m2

therefore

(m1+m2)a = G * m1 * m2/r2

therefore

a = G * m1 * m2 / (m1+m2)r2

each mass has its own acceleration dependent upon the magnitude of the other mass.

your substitution of $\displaystyle (m_1+m_2)$ into Newton's 2nd law equation is incorrect.

case 1 ... if $\displaystyle m_1 = m_2 = m$ , then $\displaystyle a_1 = a_2 = a = \frac{Gm}{r^2}$

case 2 ... if $\displaystyle m_1 \ne m_2$, then $\displaystyle a_1 \ne a_2$ ...

$\displaystyle a_1 = \frac{Gm_2}{r^2}$

$\displaystyle a_2 = \frac{Gm_1}{r^2}$