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This video illustrates the use of state vectors to simulate a 2D space of an object in orbit, using the Godot game engine. It illustrates how the object's position and velocity can be employed to compute its orbit, rather than using Kepler elements. The video illustrates how the object's velocity changes as it moves closer or farther away from the center object, and how the position and velocity can be manipulated.

It's worth mentioning that this method of simulating orbits is more realistic when it comes to showing how a vehicle using propulsion would move through space. Check out the related video that uses Kepler orbital elements to demonstrate the same simulation.

Music: Different Universe-neilcross via Flexclip

Shout out to KSP for the original inspiration to learn this stuff!

Here is where I found most of the formulas and details on how to calculate these orbits:
https://janus.astro.umd.edu/cgi-bin/orbits/orbview.pl
https://scriptverse.academy/tutorials/c-program-newton-raphson.html
https://searchcode.com/codesearch/view/56537037/
https://elainecoe.github.io/orbital-mechanics-calculator/formulas.html
https://orbital-mechanics.space/classical-orbital-elements/orbital-elements-and-the-state-vector.html
https://downloads.rene-schwarz.com/download/M002-Cartesian_State_Vectors_to_Keplerian_Orbit_Elements.pdf
https://www.sciencedirect.com/topics/engineering/orbit-formula