Orbiting and Body Physics

[AlgidPlasma]

Just made a small demo that shows the interaction of gravity between two objects in a friction less environment. Turned out much better than expected. The planet and star are the mass of the earth and sun respectively. Feel free to change the mass and distance multiplication to see how it affects the orbit .

[josefnpat]

This is rather nifty. You ought to consider making it into a library where you can add multiple elements that all attract each other.

[iemfi]

What else did you expect? That Newton would turn out to have been wrong all along?

[rdlaitila]

If you hold and drag the love window for a few seconds, you throw the earth out of the suns orbit into the heavens

[FreeTom]

Reviving a long-dead thread here, I know, but this isn't quite right.

I've been trying to make orbitty things and I've been doing it exactly this kind of wrong and was hoping this code would correct me. Alas, no. Here's how the velocity is updated:

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	if planet.position.x < star.position.x then
		planet.velocity.x = planet.velocity.x + attraction * dt
	elseif planet.position.x >= star.position.x then
		planet.velocity.x = planet.velocity.x - attraction * dt
	end	
	
	if planet.position.y < star.position.y then
		planet.velocity.y = planet.velocity.y + attraction * dt
	elseif planet.position.y >= star.position.y then
		planet.velocity.y = planet.velocity.y - attraction * dt
	end

So basically the force of gravity is only ever applied in one of the four diagonal directions instead of at angle directly towards the star's centre of gravity as it should be. Playing around with this in more complex interactions (as I have been) it is sometimes very noticeable.

Anybody know how to set the X and Y velocities proportionally to the angle between the two bodies?

[ivan]

Hello FreeTom.
Just get the 'vector' between the two centers of mass:

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vx = star.position.x - planet.position.x
vy = star.position.y - planet.position.y

You now have a vector pointing from the planet to the star.
Negate vx, yv if you want to rotate the vector 180 degrees.
Once you know the vector between the two objects, you can gen the distance:

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dist = math.sqrt(vx^2 + vy^2)
-- or --
dist = math.sqrt(vx*vx + vy*vy)

The force of gravity is inversely proportional to the distance:

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force = (G*planetMass*starMass)/dist^2

We already know these variables except for G which is the gravitational constant.
If you assume that G = 6.673 x 10^-11 N m^2/kg^2
then make sure "dist" is in meters and "mass" is in kg.

So far so good, all we have to do is apply the force to both objects.
The next formula to remember is:

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force = mass*acceleration
-- so --
acceleration1 = force/planetMass
acceleration2 = force/starMass

You now know the acceleration of the two objects.

Note:Acceleration is the change in velocity per 1 second.
Once you know the acceleration caused by gravity,
you have to apply it along the axis of the vector vx, vy.
First, normalize vx, vy:

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nx, ny = 0, 0
if dist > 0 then 
  nx, ny = vx/dist, vy/dist
end

Next, multiply the normalized vector by the acceleration:

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acceleration1x = nx*acceleration1 
acceleration1y = ny*acceleration1 

This is your change in velocity per second.
So we have to multiply by "delta" for each step.

Last step:
add the change in velocity (acceleration*dt) to the current velocity of each object.

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planet.velocity.x = planet.velocity.x + acceleration1x*dt
planet.velocity.y = planet.velocity.y + acceleration1y*dt

Keep in mind that the two objects will move at different velocities
since the more massive object will be slower to accelerate.

TL;DR
Just get the vector between the two objects, normalize it
and multiply by the force of attraction.

[FreeTom]

Aha! Thanks, Ivan - probably should have been able to work that out myself.

For any (other) beginners who stumble upon this and wonder what exact difference is might make, here's the comparison of the final resting positions from my script in which lots of little circles gravitate towards a big one:

https://drive.google.com/file/d/0BzPXgv ... sp=sharing

'Four-angle' gravity on the left, vector-based gravity on the right.

Mmmm, circular.