I'm creating a space exploration game in Unity 3D, written in C# and I'm currently working on a system where I plot the new position of a celestial object as a function of time. This way, I don't have to constantly calculate the position of an object, but I can use the time that has passed since the player has started playing.
I have an adequate understanding of Kepler's three laws of planetary motion and the six orbital elements. I can also calculate or randomly generate these elements.
The problem is true anomaly, as it does not change with a constant value like in a circular orbit. I need to calculate the true anomaly for my time problem.
I understand the main equations behind this element and why it is neccesary to use the mean anomaly and the eccentric anomaly. But here is where my limited knowledge of math leaves me stranded. I can not figure out how to calculate the mean anomaly and use the eccentric anomaly to reach the true anomaly. I've used many sources: Basics of orbital mechanics, Youtube etc.
The part where I get stuck is where I need to calculate the eccentric anomaly from the mean anomaly. I can not find any sources online that explain how to do this.
Can anyone explain how this works?