Below are some simple animations that I put together for for
AST 105: Introduction to the Solar System, AST 203:
Astronomy, and AST 205: Introduction to Planetary Sciences.
All of these are coded in python, using the matplotlib library for
plotting. The source code is provided in each case. These codes are
not meant to be interactive -- they simply dump out frames of the
animation that can be assembled into a movie using a program like
mencoder.
You are free to use these codes or animations for teaching purposes
(please credit Michael Zingale).
If you find a mistake or make an improvement, please send it along
to mzingale @ mail.astro.sunysb.edu.
Many of these animations are now up on YouTube:
Solar System Motion / Kepler's Laws
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 P2 ~ a3.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
If you change the seed used for the random number generator,
you will get a different result.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
The frames are usually about 600 pixels in dimension, and the movies
can be quite large, ~ 15-20 MB each.
Most movies are in MS MPEG-4v2 format, created with:
