This project enables us to simulate gravitational forces and apply them to objects with a certain mass. It calculates the forces of n-body objects and their interactions, it can be used to see simulate the Solar System conditions. The gravity simulator could have educational porpuses.
Using a real-time force calculation we avoid the n-body problem and it does not matter how many objects we introduce in the scene. We have also implemented a static positioning that is used because if we give a certain velocity to a body, applying the first Newton ‘s Law, our system would probably experience a uniform linear movement.
It can be also used to demonstrate the Second and Third Newton’s Laws. Elliptical orbits are common, although if we set a huge initial velocity, our body will not be trapped by our center of mass.
Theory
Gravitational force (
):
![\[ \vec{F}=G\frac{Mm}{r^2} \vec{u}_r \]](https://sp-ao.shortpixel.ai/client/q_glossy,ret_img,w_106,h_37/http://dprogrammer.org/wp-content/ql-cache/quicklatex.com-88b222a8e44547a00af182244d28c752_l3.png "Rendered by QuickLaTeX.com")
Gravitational potential energy (
):
![\[U=\int{G\frac{Mm}{r^2}=-G\frac{Mm}{r} \]](https://sp-ao.shortpixel.ai/client/q_glossy,ret_img,w_199,h_40/http://dprogrammer.org/wp-content/ql-cache/quicklatex.com-08b31a64db97f383a1e166d9d1050f0b_l3.png "Rendered by QuickLaTeX.com")
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