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0 votes
1 answer
443 views

How to calculate acceleration due to gravity in a 3D $N$-Body system?

How do you calculate acceleration due to gravity for objects in 3D space? My current understanding for the force due to gravity on object $i$ from object $j$ is $$\mathbf{F}_g=(\mathbf{r}_j-\mathbf{r}...
maxbear123's user avatar
0 votes
1 answer
571 views

How can I use Runge-Kutta4 to solve this orbit in polar coordinates?

I want to simulate a simple orbit of a planet moving around a star which is fixed in position. I have formulated the ODEs for this problem using Lagrangian Mechanics and have found the equations of ...
Oliver Smith's user avatar
4 votes
0 answers
350 views

$N$-body gravity simulator: why does energy conservation break down when introducing an adaptive timestep?

I am playing with an N-body gravity simulator using the velocity-verlet algorithm. In the actual simulation I normalize everything so that it is nicely behaved numerically, but I'll express things in ...
KBriggs's user avatar
  • 439
2 votes
1 answer
276 views

Could you use the Barnes-Hut algorithm iteratively-- with multiple center quadrants?

I was wondering if you could use Barnes-Hut simulation beyond what it was originally intended to be. For many Barnes-Hut algorithms, the forces are only considered for a single quadrant, the centroid, ...
Magic Octopus Urn's user avatar
0 votes
1 answer
188 views

How to simulate gravitational interaction of bodies in space?

I want to try simulating some bodies in space using the basic formulas I learned in my college mechanics class. So I know Newton's Law and some basic mechanics equations: $\vec{F} = G\frac{m_1m_2}{r^...
rcplusplus's user avatar