# Space Based Physics

How would I go about about adding space-based physics like orbital mechanics into a game engine like Unreal Engine 4 or Unity 5? The goal is to generate celestial bodies procedurally: first black holes, start around those black holes, then planetary systems around those stars, then in every instance calculate the needed velocity to make stable orbits(the system would calculate the best orbit and have cases for star systems with multiple suns) them data in the format time: position will be stored in an array for each celestial body and the body will then be rendered there when needed.

I'm actually working on a 2D project similar to what your doing, definitely less complex in scope though.

I am also a beginner at this but can give you what I've learned so far.

You're going to need to figure out your gravity mechanics first, universe generation is easier and will have to come second.

Since I'm assuming you're making a game and not a simulation, you're going to probably use two-body gravity not n-body, the more bodies effecting each other at once the more processing time youre going to be eating. You're going to have to decide how complex you want it.

If you use Unity, you're going to want to put your physics updates in

FixedUpdate()


and you will have to write your own gravity. Using Unity's rigidbody and rigidbody.addforce() will lead to problems since unity caps rigidbody velocity.

You're going to need to scale things down a lot too.

It will also probably be best to keep your black holes, Suns, planets, and moons on the rails, once you have an orbital path calculated once just move it along that path without calculating gravity anymore. (This lets you draw the orbital path without running math constantly)

I'm on mobile at the moment but when I get a chance I'll edit this to include some links to resources and some code I've done to go from the 2 state vectors to the 6 orbital elements, but hopefully someone else will be able to help you out more, I suggest you keep the space exploration stack exchange in mind as well.

Edit 1... Here are some very useful PDFs that show you how to calculate the orbital elements, then convert them back at a specific t time. I have only used the first one in my project.

State vectors to orbital elements

Orbital elements back to state vectors at given time

Edit 2... (I won't have my code until I get home) For your forces, you're going to need torque, and velocity, I'm still using Unity's addTorque() because I'm in 2D but you may want your own. As for velocity, do not use Unity's addForce(). Store velocity as a vector3 and move the position of your object by that vector each time step. You can add any velocity changes to that vector. I'll be able to get some code on gravity and the orbital elements this evening.

You're going to need to pick a scale and stick to it, as seen in my questions on space exploration losing track of the units and not converting values properly leads to problems.

Edit 3...

Here is my code for gravity:

public Vector3 Gravity(Vector3 pos1, float m1, Vector3 pos2, float m2) {
//Relative distance vector
Vector3 dvec = (pos2 - pos1);

//Relative distance
float d = dvec.magnitude;

//Direction of force
Vector3 dnorm = dvec.normalized;

//Distance Squared
float dsqrd = Mathf.Pow(d, 2);

//Mass of both bodies
float M = m1 + m2;

//Gavitational pull
float g = World.G * M / dsqrd;

//Acceleration due to gravity vector
Vector3 f = dnorm * g;

return f;
}


Edit 4...

And finally, here is my huge script that finds a bunch of sciency stuff for gravity. Some of it you will ignore, I can't confirm all of it is 100% correct, but you can use it as a resource as I suffered through it myself and wouldn't wish the same torture on my worst enemy

public OrbitData CalculateOrbitalData(Vector3 pos1, Vector3 vel1, float m1, Body body) {
if (body == null) {
return new OrbitData();
}

Vector3 pos2 = body.position;
Vector3 vel2 = body.velocity;
float m2 = body.mass;

//Relative Position Vector
Vector3 r = pos1 - pos2;

//Distance between bodies
float rmag = r.magnitude;

//Relative Velocity Vector
Vector3 v = vel1 - vel2;

//Velocity Magnitude
float v1 = vel1.magnitude;

//Relative Velocity Magnitude
float vm = v.magnitude;

//Specific Angular Momentum
Vector3 h = Vector3.Cross(r, v);

//Standard Gravitational Parameter
float µ = World.G * m2;

//Eccentricity Vector
Vector3 evec = (Vector3.Cross(v, h) / µ) - (r / Vector3.Magnitude(r));

//Eccentricity
float e = Vector3.Magnitude(evec);

//Vector to Ascending Node
Vector3 n = new Vector3(-h.x, h.z, 0);

//True Anomaly
float ta = Mathf.Acos((Vector3.Dot(evec, r)) / (e * Vector3.Magnitude(r)));
if (Vector3.Dot(r, v) < 0)
ta = (2 * Mathf.PI) - ta;

//Longitude of Ascending Node (2D)
float Ω = 0;

//Inclination (2D)
float i = 0;

//Argument of Periapsis
float ω = Mathf.Atan2(evec.y, evec.x);
float ωdegrees = ω * (180 / Mathf.PI);
if (e == 0) {
ω = 0;
ωdegrees = 0;
}

//Eccentric Anomaly
//float E = 2 * Mathf.Atan2(Mathf.Tan(ta / 2), Mathf.Sqrt((1 + e) / (1 - e)));
float E = 2 * Mathf.Atan(Mathf.Tan(ta / 2) / Mathf.Sqrt((1 + e) / (1 - e)));

//Mean Anomaly
float M = E - (e * Mathf.Sin(E));

//Semi-Major Axis
float a = 1 / ((2 / Vector3.Magnitude(r)) - (Mathf.Pow(Vector3.Magnitude(v), 2) / µ));

//Apoapsis
float ap = a * (1 + e);

//Periapsis
float pe = a * (1 - e);

//Orbital Period
float T = (2 * Mathf.PI) * Mathf.Sqrt(Mathf.Pow(a, 3) / µ) / 60;
float fT = T * 1.205f;

//Mean motion
float m = (2 * Mathf.PI) / fT;

//Time since apoapsis
float tsa = Mathf.Sqrt(Mathf.Pow(a, 3) / µ) * ((E + Mathf.PI) - e * Mathf.Sin((E + Mathf.PI))) / 60 * 1.205f;

//Time to apoapsis
float tta = fT - tsa;

//Time since periapsis
float tsp = tsa - fT / 2;
if (tsp < 0)
tsp = fT / 2 + tsa;

//Time to periapsis
float ttp = tta - fT / 2;
if (ttp < 0)
ttp = fT / 2 + tta;

//Perifocal distance
float rp = (Vector3.Dot(h, h) / µ) / e + 1;

float pr = 0;
if (vel1 != Vector3.zero) pr = Quaternion.AngleAxis(Mathf.Atan2(vel1.y, vel1.x) * Mathf.Rad2Deg, Vector3.forward).eulerAngles.z - 90;

float rr = pr + 180;

//Counterclockwise forward rotation angle
float ccwR = 0;
Vector2 offset = transform.position - body.transform.position;
if (offset.x != 0) rad = (Mathf.Atan(offset.y / offset.x));
if (offset.x < 0) rad += Mathf.PI;
ccwR = rad * (180 / Mathf.PI);

//Clockwise forward rotation angle
float cwR = ccwR + 180;

//Up rotation angle
float uR = cwR + 90;

//Down rotation angle
float dR = cwR - 90;

//circularize dV
float circ_dV = Mathf.Sqrt(µ / ap) - Mathf.Sqrt((pe * µ) / (ap * (pe + ap) / 2));

//circularize burn tick count
float circ_btt = circ_dV / forwardThrust;

//Circularize burn time
float circ_bt = circ_btt / (1 / World.timeStep);

return new OrbitData(m1, pos1, v1, vel1, m2, vel2.magnitude, vel2, pos2, World.G,
r, v, rmag, h, µ, evec, e, n, ta, Ω, i, ω, ωdegrees, E, M, a, ap, tsa, tta,
pe, tsp, ttp, orbit.forcedApoapsisPosition, orbit.forcedPeriapsisPosition,
T, fT, rp, pr, rr, cwR, ccwR, uR, dR, circ_dV, circ_btt, circ_bt);
}

• In which class is this code located, or did you make a custom class to handle the orbital physics? – KeyboardNinja Jul 11 '16 at 8:33
• I made a custom class to hold the data, and a function to do the math. – Wafer Jul 11 '16 at 18:32
• Thank you. Literally all I needed was some basics and some here, take this code it was hard fought, but I earned it for all of us. I would like to add for the very green, World and Body are custom classes that for this example just need to hold some variables. I got this to work in Unity with just the gravity function a Body class, and two spheres controlled by a single script. Really though.. thank you. I just codedoodle when I have ideas and these simple snippets saved me a lot of time. – Dave McKelvey Jan 11 at 7:33