Solar System Motion#
Planetary Orbits and Kepler’s Laws#
Integrate the orbits of two planets around a star, neglecting the gravitational force between the planets themselves. This is useful for demonstrating Kepler’s third law. We work in units of AU, years, and solar masses. The semi-major axes are picked such that one planet has an orbital period of 1 year and the other of 2 years.
As the animation plays, you should see that the speed of the outer planet varies, becoming fastest at perihelion and slowest a aphelion. You will also see that the outer planet takes longer to complete its orbit around the Sun, since \(P^2 \sim a^3\).
download MP4: orbit2.mp4
Kepler’s Second Law#
A demonstration of “equal areas in equal times”, by shading the area swept out by a planet in equal time intervals.
download MP4: second_law.mp4
Retrograde Motion#
Integrate Earth and Mars in their orbits around the Sun, starting a bit before opposition, and draw a line indicating the line-of-sight to Mars from Earth against some background stars to show the change in apparent motion.
Note: the orbits are simplified here – the semi-major axis and eccentricity are correct, but it is assumed that both ellipses are oriented the same way. For demonstration purposes, this is not all that critical.
download MP4: retrograde.mp4
Parallax#
A simple animation showing how parallax works, illustrating the motion of the Earth around the Sun and the apparent shift seen in the position of a nearby star against the background, more distant stars.
download MP4: parallax.mp4
Mercury’s Rotation#
Illustrate a 3:2 resonance between the rotation period and orbital period of Mercury. The semi-major axis and eccentricity for the planet drawn match Mercury. The black dot on the surface of the planet represents a person standing initially directly under the Sun at perihelion.
download MP4: mercury_rotation.mp4
Orbital Energy#
A simple showing the orbit of a planet around the Sun, outputting the kinetic energy / unit mass, the potential energy / unit mass, and the total energy / unit mass along the way.
download MP4: orbitalenergy.mp4
Resonances in the Asteroid Belt#
A 2:1 resonance between an asteroid (shown in red) and Jupiter (black) as they orbit around the Sun. Some randomly placed asteroids are also shown.
download MP4: asteroids.mp4
Tidal Locking#
An illustration of tidal locking of a moon in orbit around a planet. The rotation of the moon is visualized by coloring alternate quadrants differently, and watching a stationary person rotate with the moon.. The tidal distortion is always along the planet-moon line.
download MP4: tidal_locking.mp4