Donovan Magney

Overview

I've always been fascinated by games like Universe Sandbox that utilize real life physics in a space enviroment. I've been wanting to learn how games like these actually implement real world physics equations into their games. One of my favorite physics equations is Newtons Law of Universal Gravitation. I decided to make a small orbital simulation project to explore implementing this equation in the game engine. I take it a step further and also implement Keplarian orbits (ellipses) for a more rigid soloar system, which appear in games like Kerbal Space Program.

Final Product

Newtonian Gravity

To start, all I need are a couple of bodies with a mass value, the distance between their centers, and a gravity constant. It starts with a master script which at the start, will find all of the bodies on screen and store them in an object array. Each frame, it will then pass on this object array to each body and tell the body to calculate the total force acting upon it, calculate its new acceleration, velocity, then finally move itself to the proper position from that velocity. The objects now will move, but its difficult to place them in an orbit without some debug lines that will show their future paths. I downloaded a script from Sebastian Lague (on YouTube) to display the path of the bodies in the editor. That was pretty much it for this portion. The code for this part of the project can be found here. The code is heavily borrowed from Sebastion, although edits have been made for my use case. After implementing this, I notice that when placing small bodies around a much larger one that is not moving, they end up spiraling in the direction normal to the orbit. This of course in analogous to what happens in real life, nothing is completely still, our sun moves as well and the orbits follow.

Keplarian Orbits

The problem with making a game strictly with Newtons Gravity is that over time, they will slowly drift away and are unpredictable in a game sense. Something could happen in the game or the player plays so long that the drift may start being a problem. In Kerbal Space Program, they place all of their bodys on "rails", or predefined paths to avoid the previously mentioned issues. Keplarian parameters can be used to define orbits. This also makes it really easy to change orbits to whatever I like at anytime. This is less realistic since it only creates eliiptical orbits and does not take other bodies into account, or have the spiraling I mentioned earlier. The script also draws orbit lines like previously, but its much easier since the body will always follow the same path relative to its reference body. Because of this, I was able to make optimizations by only calculating values that have changed since the previous frame. This code was a bit more complicated, but mostly due to the math involved.

Conclusion

From this project I learned that the it is not actually too difficult to use these real life equations (as long as you understand them mathmatically). The difficult part is knowing the inputs and outputs of the system. That is, theres no place to just "plug in" the equation to make it work. You must figure out how to gather all of the information you need for the equation from the objects in the scene, and then how to apply those outputs back to the objects to get your desired behavior. The equation itself is a small part of the process. If this project were to continue, it would be interesting to add collision physics, like elastic and inelastic collisions, as well as object deformation. Then these objects would have another level of interaction between them. These could get quite complicated to implement so these will have to wait for a future expansion of this project.