I want to implement a gravity system in shadertoy without using any storage/buffer. So I can't save any variable and my animations must be a function of time. Is it possible to make a function of time to calculate the current position of the planet?!

I'm confused at all, because the next position depends on the current velocity and the current velocity depends on the former acceleration and that depends on former position. Is it theoretically implementable as a function of time?

The more general general question is that are can such semicircular relations be subject to be a regular function?

![Initial values](https://wikimedia.org/api/rest_v1/media/math/render/svg/05b6d26ad3cf608398e3015f06af158ebefeeb6d)

![Formulas](https://wikimedia.org/api/rest_v1/media/math/render/svg/0df686bb7caa953daf6e0495aa9e1703e1be0ec4)
`f(x)=? as simple form`

This function has the above problem, because f(x) depends on the former values of the function.

Note that planets aren't located in circular and stable orbits. But they have initial position and velocity.