Planetary Orbit Simulation - Interactive Visualization

Simulation Time: 0.00 yrs

Total Energy: 0.00 J

Momentum: 0.00 kg·m/s

Planets: 3

Orbital Energy

Distance from Star

Orbital Velocity

Parameters

Star Mass (M): 1.0 M☉

Planet 1 Mass: 1.0 M⊕

Planet 1 Distance: 1.0 AU

Planet 1 Velocity Multiplier: 1.0x

Planet 2 Mass: 1.0 M⊕

Planet 2 Distance: 1.5 AU

Planet 2 Velocity Multiplier: 1.0x

Planet 3 Mass: 1.0 M⊕

Planet 3 Distance: 2.0 AU

Planet 3 Velocity Multiplier: 1.0x

Simulation Speed: 1.0x

Multi-body Mode

Show Trails

Show Velocity Vectors

G Constant: 1.0x

Zoom: 1.0x

Orbital Mechanics Equations

Gravitational Force: F = GMm/r²

Acceleration: a = -GM/r² · (r/r)

Orbit Equation: r = p/(1+e·cos(θ))

Vis-viva Equation: v² = GM(2/r - 1/a)

What is Planetary Orbit Simulation?

This simulation demonstrates how planets orbit around a star under the influence of gravitational force. The central star remains fixed while planets follow elliptical orbits determined by their initial position, velocity, and mass.

Kepler's Laws of Planetary Motion

1) The orbit of a planet is an ellipse with the star at one focus. 2) A line connecting the planet to the star sweeps out equal areas in equal times. 3) The square of the orbital period is proportional to the cube of the semi-major axis.

Multi-body Dynamics

In multi-body mode, planets also exert gravitational forces on each other, leading to complex orbital interactions. This demonstrates how gravitational perturbations can cause orbital precession and chaotic behavior in multi-planet systems.

Energy Conservation

In a two-body system (without multi-body interactions), the total mechanical energy remains constant. The planet continuously exchanges kinetic and potential energy as it moves closer to and farther from the star, with maximum velocity at periapsis (closest approach) and minimum velocity at apoapsis (farthest point).