# Integrating gravitational acceleration of particles for simulation

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1. Apr 9, 2013

### caspernorth

I've tried out the two body problem and tried to work out the trajectories with respect to their center of mass frame(located at the origin) as follows (it worked!):

particles = m1 and m2
Fm1 = force of m2 on m1
Fm2 = force of m1 on m2

a = Gm2$\hat{r}$ / r2
$\hat{r}$ is the unit vector
$\hat{r}$ = r/|r|
a m1 = Gm2 r / |r|^3
r = √(x^2 + y^2)

and did this for both a1 and a2 but my doubt is this:
why is there a substitution for r vector only when the denominator term stays constant (magnitude).
Wouldn't this imply that particles slows down when r vector decrease?!

also why can't type in complex equation forms (am1 = $\frac{Gm2$\hat{r}$ }{r2}$). it shows the syntax instead of formatted text.

Last edited: Apr 9, 2013
2. Apr 9, 2013

### Staff: Mentor

What do you mean with that?
The denominator stays constant for circular orbits only.
In general, it does.

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