SpaceSimulation

A simple simulation of our solar system

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🪐 Context

Passionate about astronomy, I completed this project in 2020 to simulate the solar system in 3D using Unity 2020. I created it when I was just starting to learn programming, so the calculations and the code may not be entirely accurate or optimized.

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🧾 Summary

• Installation
• Controls
• Calculations
• License

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💾 Installation

How can I get it?

You can download the installer available for Windows in the Releases section, then follow the instructions provided.

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🎮 Controls

You can modify most settings from the in-game pause menu. Here are the default controls:

Action	Key
Move Forward	Z
Move Backward	S
Move Left	Q
Move Right	F
Move Up	SPACE
Move Down	LEFT CONTROL
Speed Boost	SHIFT
Lock onto a Planet	CAPS LOCK
Next Planet	RIGHT ARROW
Previous Planet	LEFT ARROW

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📐 Calculations

Each planet has the following orbital parameters:

• $T$ : Orbital period (in ticks)
• $e$ : Orbital eccentricity (0 = circle, close to 1 = ellipse)
• $a$ : Semi-major axis (in km)
• $t$ : Time elapsed (in ticks, comparable to days)
• $i$ : Orbital inclination (in radians)
• $M$ : Mean anomaly
• $E$ : Eccentric anomaly
• $\nu$ : True anomaly
• $l$ : Semi-latus rectum
• $r$ : Distance from the Sun at a given position

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🧮 Key Equations

Mean anomaly:

$$M = \frac {2 \pi t}{T}$$

Eccentric anomaly (Kepler’s Equation, solved numerically):

$$M = E - e \sin(E)$$

True anomaly:

$$\nu = 2 \cdot \arctan\left(\sqrt{\frac{1+e}{1-e}} \cdot \tan\left(\frac{E}{2}\right)\right)$$

Semi-latus rectum:

$$l = a(1 - e^2)$$

Distance from the Sun:

$$r = \frac{l}{1 + e \cos(\nu)}$$

Coordinates (initial 2D):

$$x = r \cos(\nu)$$ $$z = r \sin(\nu)$$ By default: $$y = 0$$

Inclination transformation:

$$x = x$$ $$z = y \sin(i) + z \cos(i)$$ $$y = y \cos(i) - z \sin(i)$$

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📜 License

This project is licensed under the GPL-3.0 License.

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