Kepler's Laws & Planetary Motion: Simulation Study

Orbital Distance & Period:<br/>A Simulation Study

Demonstrating Kepler's Third Law Through Simulation

Scale: 1 AU ≈ 73.6 million km

Simulation Scale & Setup

The simulation used a custom scale to model orbital mechanics

<strong style="color: #B3E5FC;">1 Astronomical Unit (AU)</strong> = approximately 73.6 million kilometres

Four different orbital distances were tested

Orbital period was recorded for each distance

Results compared against Kepler's Third Law predictions

Scale: 1 AU ≈ 73.6 million km

Simulation Results — Orbital Data

As distance increases, orbital period increases significantly.

0.98

67

1.59

189

2.04

248

2.25

513

Distance vs. Orbital Period

The relationship is non-linear — period grows much faster than distance, consistent with <strong style="color: #4FC3F7;">Kepler's Third Law (T² ∝ r³)</strong>.

Kepler's Third Law

The square of the orbital period is proportional to the cube of the orbital radius

As the orbital distance from the central body increases, the time it takes to complete one full orbit increases at an even greater rate

This law applies to all planets in the Solar System

First described by Johannes Kepler in 1619

Law of Harmonies

Conclusion

The simulation clearly demonstrated that orbital period increases with orbital distance

Results are consistent with Kepler's Third Law (T² ∝ r³)

Scale used: 1 AU ≈ 73.6 million kilometers

Four test distances (0.98, 1.59, 2.04, 2.25 AU) all confirmed the trend

While values may not perfectly match real Solar System data, the proportional relationship is clearly evident

The simulation successfully models the fundamental mechanics of planetary orbits

Distance shapes time — the further the orbit, the longer the journey.