# Kepler's Laws & Planetary Motion: Simulation Study
> Learn Johannes Kepler's three laws of planetary motion, barycentres, and orbital velocity through physics simulation data and gravitational formulas.

Tags: astrophysics, kepler-laws, planetary-motion, orbital-mechanics, gravity, astronomy, physics-simulation
## Planetary Motion & Kepler's Laws
- Introduction to orbital motion and the role of gravity in the Solar System using simulation-based study.

## Kepler's Three Laws
- **Law I (Ellipses):** Planets move in elliptical orbits with the Sun at one focus.
- **Law II (Equal Areas):** A line from planet to Sun sweeps equal areas in equal time; speed increases near the Sun.
- **Law III (Periods):** The square of the orbital period is proportional to the cube of the orbital distance ($T^2 \propto r^3$).

## Planet–Moon System & The Barycentre
- Definition of the barycentre as the shared centre of mass.
- Explanation of why the Sun appears stationary vs. why planets wobble due to moons.

## Simulation Results — Orbital Data
- Scale: 1 AU ≈ 73.6 million km.
- Graph showing the non-linear relationship between orbital distance and orbital period.
- Empirical support for $T^2 \propto r^3$.

## Orbital Speed in the Solar System
- **Mercury:** Fast orbital velocity (≈ 47.9 km/s) due to proximity to the Sun.
- **Neptune:** Slow orbital velocity (≈ 5.4 km/s) due to distance.
- Formula: $v \propto \sqrt{GM/r}$ (Newton's law of universal gravitation).

## Conclusions & Key Learnings
- Orbits are elliptical and speeds vary based on distance (Kepler's 2nd Law).
- Gravity is the fundamental force determining both velocity and period.
- Physics simulations accurately predict planetary behavior using these harmonic laws.
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