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 P² ~ a³.

Movie of orbits:
orbit2.avi [MS MPEG-4v2]
orbit2.mp4 [H.264]

Show equal areas in equal times, by shading the area swept out by a planet in equal time intervals.

second law animation:
second_law.avi [MS MPEG-4v2]
second_law.mp4 [H.264]

A simple figure plotting the period of planets (+ pluto optionally) in our solar system vs. semi-major axis on a log-log plot, showing the P² ~ a³ relation. Optionally plot the Galilean moons of Jupiter on the same axes, showing that they obey a P² ~ a³ relation as well, but with a different constant.

Harmonic law figure (just planets): harmonic_law.png
Harmonic law figure (planets + pluto + Galilean moons): harmonic_pluto_moons.png

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.

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Movie of retrograde motion:
retrograde.avi [MS MPEG-4v2]
retrograde.mp4 [H.264]

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.

Parallax animation:
parallax.avi [MS MPEG-4v2]
parallax.mp4 [H.264]

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.

Mercury rotation animation:
mercury.avi [MS MPEG-4v2]
mercury.mp4 [H.264]

Illustrate the synchronous rotation of the Moon. The black dot represents a person standing on the surface. The orbit is taken to be circular, for simplicity.

Moon rotation animation:
moon_rotation.avi [MS MPEG-4v2]
moon_rotation.mp4 [H.264]

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.

Orbital energy animation:
orbitalenergy.avi [MS MPEG-4v2]
orbitalenergy.mp4 [H.264]

A simple animation showing how the time between successive full Moons (the synodic lunar period) is greater than the true (sidereal) orbital period of the Moon.

Orbital energy animation:
lunar_period.avi [MS MPEG-4v2]
lunar_period.mp4 [H.264]

A simple animation showing how the true rotation period of Earth (the sidereal day) is shorter than the time between noons (the solar day).

Orbital energy animation:
earth.avi [MS MPEG-4v2]
earth.mp4 [H.264]

A simple animation showing the phases of the Moon and the corresponding point in the Moons orbit around the Earth, with respect to the Sun.

Phases animation:
lunar-phases.avi [MS MPEG-4v2]
lunar-phases.mp4 [H.264]

A simple animation showing the Earth at either solstice or and equinox (with the time set as noon UTC).

Summer Solstice:
summer_solstice.avi [MS MPEG-4v2]
summer_solstice.mp4 [H.264]

Winter Solstice:
winter_solstice.avi [MS MPEG-4v2]
winter_solstice.mp4 [H.264]

Equinox:
equinox.avi [MS MPEG-4v2]
equinox.mp4 [H.264]

Another rendering, this time from noon to noon, centered on Stony Brook, NY

Summer Solstice:
sb_summer_solstice_ortho.avi [MS MPEG-4v2]
sb_summer_solstice_ortho.mp4 [H.264]

An animated diagram pointing out how latitude, zenith, and horizon are defined, as well as showing the orientation of Earth on the Summer Solstice and showing the tropics and (ant)arctic circles.

earth_summer_solstice.avi [MS MPEG-4v2]
earth_summer_solstice.mp4 [H.264]

A simple animation showing how the Earth's axial tilt does not change direction over the course of an orbit, giving rise to the seasons.

Seasons animation:
seasons.avi [MS MPEG-4v2]
seasons.mp4 [H.264]

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.

Seasons animation:
asteroids.avi [MS MPEG-4v2]
asteroids.mp4 [H.264]

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.

Tidal locking animation:
tidal_locking.avi [MS MPEG-4v2]
tidal_locking.mp4 [H.264]

A simple figure used to illustrate the geometry of an ellipse. Here, a is the semi-major axis, e is the eccentricity, and b is the semi-minor axis. r and r' are lines connecting a point on the ellipse (the black dot) to the foci.

Ellipse geometry figure: ellipse_geom.png

A demonstration of how varying the eccentricity of an ellipse changes the shape.

Ellipse eccentricity animation:
eccentricity.avi [MS MPEG-4v2]
eccentricity.mp4 [H.264]

A demonstration of how to draw an ellipse. Here we show the distance from each foci to the position on the ellipse, and show that their sum is constant. changes the shape.

Drawing and ellipse animation:
ellipsedraw.avi [MS MPEG-4v2]
ellipsedraw.mp4 [H.264]

A simple animation that shows a projectile with increasing horizontal velocity, working up to the circular velocity. (This script uses the image earth.png; image credit: NASA/Apollo 17)

Achieving orbit animation:
achieveorbit.avi [MS MPEG-4v2]
achieveorbit.mp4 [H.264]

A simple animation showing how the orbit of a projectile around Earth changes as we increase the change the tangential velocity from less than the circular velocity to greater than the escape velocity. (This script uses the image earth.png; image credit: NASA/Apollo 17)

Escape velocity animation:
escape.avi [MS MPEG-4v2]
escape.mp4 [H.264]

A simple animation showing how an initially circular orbit is changed into an elliptical one by increasing the velocity at perihelion. Two boosts are modeled. (This script uses the image earth.png; image credit: NASA/Apollo 17)

Changing orbit animation:
changing_orbit.avi [MS MPEG-4v2]
changing_orbit.mp4 [H.264]

Show how the Planck function varies as temperature is changed. A 'thermometer' on the right keeps track of the temperature. Some reference Planck function curves are plotted every 2 orders-of-magnitude in temperature to illustrate the shift in the location of peak intensity with increasing temperature. Also, the visible frequencies are highlighted with a blue shading.

Blackbody spectrum animation:
blackbody.avi [MS MPEG-4v2]
blackbody.mp4 [H.264]

Similar to the animation above, but in terms of wavelenght instead of frequency. Show how the Planck function varies as temperature is changed. A 'thermometer' on the right keeps track of the temperature. Some reference Planck function curves are plotted every 2 orders-of-magnitude in temperature to illustrate the shift in the location of peak intensity with increasing temperature. Also, the visible wavelengths are highlighted with a blue shading.

Blackbody spectrum animation:
blackbody_wavelength.avi [MS MPEG-4v2]
blackbody_wavelength.mp4 [H.264]

A demonstration of a random walk process. A number of small hops are taken in random directions, until the overall displacement is equal to the radius of the circle.

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If you change the seed used for the random number generator, you will get a different result.

Random walk animation: random_walk.avi [MS MPEG-4v2]
Random walk animation: random_walk.mp4 [H.264]

A demonstration of the effect of temperature on random thermal motion. Many particles in a gas are shown at two different temperatures.

Note: for simplicity, we do not model collisions between the particles.

Thermal motion animation:

• cool:
  thermal_motion_normal.avi [MS MPEG-4v2]
  thermal_motion_normal.mp4 [H.264]
  
• hot:
  thermal_motion_hot.avi [MS MPEG-4v2]
  thermal_motion_hot.mp4 [H.264]
  

Show two waves of different wavelengths to illustrate the difference between wavelength and frequency. The propagation speed of the two waves is the same. The wavelengths are 1 and 1/4 cm, and the velocity is 2.0 cm/s. A point 'fixed' to a vertical line moves up and down as the wave passes by, to illustrate the concept of frequency.

Wave propagation animation:
waves.avi [MS MPEG-4v2]
waves.mp4 [H.264]

Show a moving source emitting waves. The wavefronts are plotted as red circles. The source has a speed of 1 m/s and the waves have a propagation speed of 2 m/s. The wave frequency is 3 Hz.

Doppler effect animation:
doppler.avi [MS MPEG-4v2]
doppler.mp4 [H.264]

Show two moving sources emitting waves. The top source has a speed of 1 m/s and the bottom source has a speed of 0.5 m/s. The waves have a propagation speed of 2 m/s and frequency of 3 Hz. This version shows how the compression of wave fronts depends on the line of sight velocity.

Doppler effect 2 animation:
doppler2.avi [MS MPEG-4v2]
doppler2.mp4 [H.264]

Animation of a binary pair orbiting their common center of mass (shown as the black 'x'). The case of e = 0 and e = 0.4 are shown, with a mass ratio of 1 or 2. These animations show that, in a binary system, the two stars are always opposite one another, with respect to the center of mass, and must have the same period.

binary star animations:

• mass ratio = 1; e = 0.0:
  binary_mratio=1_e=0.0.avi [MS-MPEG-4v2]
  binary_mratio=1_e=0.0.mp4 [H.264]
• mass ratio = 1; e = 0.4:
  binary_mratio=1_e=0.4.avi [MS-MPEG-4v2]
  binary_mratio=1_e=0.4.mp4 [H.264]
• mass ratio = 2; e = 0.0:
  binary_mratio=2_e=0.0.avi [MS-MPEG-4v2]
  binary_mratio=2_e=0.0.mp4 [H.264]
• mass ratio = 2; e = 0.4:
  binary_mratio=2_e=0.4.avi [MS-MPEG-4v2]
  binary_mratio=2_e=0.4.mp4 [H.264]

Animation of a small body (planet) orbiting around a larger body (star) showing the small motion of the larger body around the center of mass. This uses a mass ratio of 50 between the two objects.

planetary orbit animations:
planetary_orbits.avi [MS-MPEG-4v2]
planetary_orbits.mp4 [H.264]

Illustrate the radial velocity of a star with an unseen planet over the course of a period. Here, the planet's mass was greatly exaggerated to enhance the effect. We also restrict ourselves to being in the plane of the orbits.

radial velocity animation:
radial_velocity.avi [MS MPEG-4v2]
radial_velocity.mp4 [H.264]

Illustrate the radial velocity of a star with an unseen planet over the course of a period. Here, the planet's mass was greatly exaggerated to enhance the effect. We use an elliptical orbit but restrict ourselves to being in the plane of the orbits. The semi-major axis is not perpendicular to the observer.

radial velocity animation:
radial_velocity_ell.avi [MS MPEG-4v2]
radial_velocity_ell.mp4 [H.264]

Show an eclipsing binary system and the resulting lightcurve. Here we assume that the smaller star is hotter.

eclipsing binary animation: eclipsing_binary.avi

Show a planet transiting across its parent star, and the resulting lightcurve. This is similar to the eclipsing binary system animation above, but now we assume that the smaller object (the planet) is cool.

transiting planet animation:
planetary_transit.avi [MS MPEG-4v2]
planetary_transit.mp4 [H.264]

An animation showing the equipotentials of the gravitational and rotational potential in the co-rotating frame of a binary system. We change the mass parameter, μ = M₂/(M₁ + M₂). In the frames, the less massive star (M₂) is on the left.

equipotential animation:
equipotentials.avi [MS MPEG-4v2]
equipotentials.mp4 [H.264]

A simple H-R diagram. The main sequence properties are found from Carroll and Ostlie, Appendix G. Lines of constant radius are drawn in, as well as the location of the white dwarfs.

H-R diagram figure: HR_radius_wd.png

A sequence of figures (each represent 1 half life) illustrating the radioactive decay of a sample. Initially 2500 markers are 'parents'. Each half life, there is a 50% chance a marker decays. After a number of half lifes, no parents remain. A plot showing the exponential decay follows.

radioactive decay animation:
decay.mp4 [H.264]

radioactive decay figures:
radioactive_decay_0000.png
radioactive_decay_0001.png
radioactive_decay_0002.png
radioactive_decay_0003.png
radioactive_decay_0004.png
radioactive_decay_0005.png
radioactive_decay_0006.png
radioactive_decay_0007.png
radioactive_decay_0008.png
radioactive_decay_0009.png
radioactive_decay_0010.png
radioactive_decay_0011.png
radioactive_decay_0012.png
radioactive_decay_0013.png