Perihelium Shift Simulator

This JAVA application simulates the motion of a planet under a potential that reads:

The factor Is added to the typical central gravity motion that reads

In order to simulate the motion of a planet around the Sun, according to Einsteins theory of gravitation. It is really difficult to solve the EDP that this new potential implies so the program uses a numerical method called the 'Runge Kutta Method 4th order', that is explained below.

The EDP that we have to solve numerically is the following:

But we can transform it into a system of 4 simple EDPs:

Now, it is easy to use the Runge Kutta method using the following iteration:

Of course, we have 4 EDPs so we will have to do that iteration 4 times each period of time. The program uses this method and shows us how the planet moves acelerating time because if not, we would have to wait more than a year to detect the perihelium shift predicted by Einstein. The program looks like the following image:

As you can see, in the left we can study the motion predictedbyNewton, and in the righ, the one predicted by Einstein.

We can change some variables such as the initial velocity, the initial distance from the planet to the Sun, the mass of the planet and the Sun, and the initial angle. Moreover, there are two graphics of the energy of the system, where we will be able to see the variation of kinetic and potential energy experimented by the planet.

To download the .JAR, please click HERE.