The animation simulates the gravitational force between celestial bodies. Planets with different masses and initial velocities attract each other, form orbits, and can merge upon collision – an interactive model for exploring Newtonian gravitation.
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Description of the animation
The animation shows a space with freely placeable planets that attract each other according to Newton’s law of gravitation:
[ F = frac{G cdot m_1 cdot m_2}{r^2} ]
The gravitational force between two bodies is proportional to the product of their masses and inversely proportional to the square of their distance. This fundamental interaction determines the motion of all celestial bodies in the universe.
- Orbit trails: Colored lines trace the trajectories of the planets and make elliptical, parabolic, or hyperbolic orbits visible.
- Momentum arrows: Yellow arrows show the current velocity and direction of motion of each planet.
- Planet merging: In collisions, planets merge while conserving momentum and area – the larger planet absorbs the smaller one.
Interactive controls
The animation offers extensive control options for creating your own planetary systems:
- Create planets: A click in the simulation area generates a new planet with the properties set in the control panel (mass, radius, color).
- Set initial momentum: Clicking and dragging on a planet sets its initial velocity. The length and direction of the red arrow determine the momentum.
- Start/pause simulation: Starts or pauses the calculation of gravitational forces and movements.
- Gravitation G: The slider adjusts the gravitational constant. Higher values increase the attraction between the bodies.
- Reset all: Removes all planets and resets the simulation.
Physical background
Newton’s law of gravitation describes the attractive force between two masses. In this simulation, the force is calculated for each pair of planets and the resulting acceleration is applied to both bodies. Numerical integration produces the characteristic Keplerian orbits: circles, ellipses or – with sufficient velocity – open parabolas and hyperbolas.
The merging during collisions demonstrates conservation of momentum: The total momentum of the system remains constant while kinetic energy is partly converted into “deformation energy.” The new radius is calculated from area conservation, which corresponds to a simplified 2D model of mass conservation.