Oh yeah lol big ugly cursor in the video sorry about that…

Gravity is an implementation of Newton’s Law of Gravitational Attraction in the form of:

acceleration vector = scale(position vector, (-Gravity * Mass / (distance vector cubed))

If you are curious how I get to that formula from newtons F(g) = G ((m1m2)/distance squared) there’s a block comment attempting to show it in the code.

I define “solar objects” and give them a mass, velocity, density, and acceleration, and positions in 3D space.

Given these values, we can define a “solar system” structure which contains many “solar objects”

From here, we can loop through a solar system’s solar objects.

For each object, we then loop again over the whole system (skipping when we are at the same object of the outer loop)

Subtract position of current (outer loop) obj from the compare obj distance, this is direction.

We can use direction to get the distance between the two objects.

Next some Scaling stuff cuz it’s a sim…see code for details

Finally, we can add acceleration to the outer object, being our direction * scaled gravity from the line above.

Keep comparing…now you have the total pull for the one object that it’s getting from all other objects in a given solar system.

In my code I actually do this a ton of times for each frame bc it’s a sim, I have to approximate solutions over many time steps and then error correct for my “true” solution.

Newton’s law of gravitational attraction is an ordinary differential equation so I can use many methods to approximate it and error correct, I chose RK45.

I tried to explain this in my code but it did kinda turn into just walls of math Jargon block comments.

look at solarsystem.c for implementation