How do I generate this orbital path without using so many parts and instantly?

Help and Feedback Scripting Support
1

I am trying to make an orbital trajectory generate instantly and be efficient
The issue is that I don’t know how to do it efficient nor calculate, kinda just waiting for it to pass by and recording
Here is a video of the orbital path

local constants = require(game.ServerScriptService.CONSTANTS)
local attractor = script.Parent.Attractor.Value
local initialDistance = (attractor.Position - script.Parent.Position).Magnitude
local velocity = constants.grav * attractor.Mass * ((2/initialDistance) - (1/275))
local gravForce = Vector3.new(-3,0,0)
while wait() do
	local part = Instance.new("Part", workspace)
	part.Position = script.Parent.Position
	part.CanCollide = false
	part.BrickColor = BrickColor.Red()
	part.Anchored = true
	part.Material = Enum.Material.Neon
	local distance = (attractor.Position - script.Parent.Position)
	local force = (constants.grav * 100 * 1) /  distance.Magnitude ^ 2
	gravForce += (force * distance.Unit)
	print(gravForce)
	script.Parent.Position += gravForce
end
2

If it’s a two-body system, the orbit is going to in the shape of an ellipsis. You can determine a number of points along that ellipsis path with just trigonometry, and then create parts that represent the straight line between these points. More line = less jagged ellipsis.

For an n-body system, the approach is the same except there’s no neat formula for points along the path. You’ll have to simulate the path of a particle by keeping track of its velocity and position, and updating it in small time-steps to get the points along the curve it follows.

3

What about if I were to use a timed integration like leapfrog, would that work?

4

I don’t know how that compares to straight up Verlet integration or Euler integration, but any method that can give you a series of points along the orbital path will work.

5

So I found a hacky way to do it with for loops but it doesnt match with my delta time reset. Any advice? https://gyazo.com/4551e5f12100a80937166b748c8fdd33

for i=0, 500 do
	if i==500 then
		generatedState = true
	end
	local distance = (attractor.Position - script.Parent.Position)
	local force = (constants.grav * 100 * 1) /  distance.Magnitude ^ 2
	gravForce += (force * distance.Unit)
	script.Parent.Position += gravForce
	local part = Instance.new("Part", workspace)
	part.Anchored = true
	part.CanCollide = false
	part.Position = script.Parent.Position
end