Solar-System-Simulation

A numeric simulation for solar system using a simple Euler integration. Initial conditions are taken from NASA JPL Horizons database.

Theoretical background

The simulation is based on Newton's law of universal gravitation. The force between two bodies is given by the formula:

$$ F = G \frac{m_1 m_2}{r^2} $$

where $G$ is the gravitational constant, $m_1$ and $m_2$ are masses of the bodies and $r$ is the distance between them.

By dividng the force by the mass of the body, we get the acceleration of the body:

$$ a = \frac{F}{m} = G \frac{m_{\text{2}}}{r^2} $$

where $m_2$ is the mass of the other body.

Using simple Euler integration, we can then calculate the new position and velocity of the body at each time step:

$$ v_{\text{k+1}} = v_{\text{k}} + a \Delta t $$

$$ x_{\text{k+1}} = x_{\text{k}} + v_{\text{k+1}} \Delta t $$

Showcase

Data

Data is taken from NASA JPL Horizons database. fetch_data.py is used to fetch data from the database and save it to a file. combine_data.py is used to combine data from planet_sizes.json and planet_data.json to a single file planets.json that is used in the simulation.

Dependencies

• SFML

Compilation

The project is compiled using Makefile. To compile the project, run make.

Execution

To run the project, run ./simulation.

Controls

• Space: Pause/Resume simulation

• Backspace: Reverse simulation speed

• x: Increase simulation speed

• y: Decrease simulation speed

• up/w: Move camera up

• down/s: Move camera down

• left/a: Move camera left

• right/d: Move camera right

• +: Zoom in

• -: Zoom out

By clicking a planet you can follow it.

Notes

I have validated the results using the simple Euler integration by crossreferencing them with the results from the NASA JPL Horizons database and the error is minimal. Due to the simplicity of the method, small computational cost and the fact that the simulation is not very sensitive to the error, I have decided to stick with the simple Euler integration. However, it should be noted that the method was not tested for long-term simulations (>100 years).