Binary Systems / Exoplanets#
Binary Star Orbits#
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.
Energy in Binary Orbits#
A version of the above binary star orbits with a mass ratio of 4 and eccentricity of 0.4 that shows the energies in the system: kinetic energy of both stars, potential energy, and total energy. This shows that the total energy is conserved in the system.
download MP4: binary_mratio=4_e=0.4_energy.mp4
Binary System Reference Frame#
A comparison of different reference frames for a binary system: the center of mass frame and the frame centered on the more massive star. This demonstrates that the eccentricity of the ellipses and their orientation are the same in the two frames.
download MP4: binary_reference_mratio=4_e=0.4.mp4
Planetary Orbit + Stellar Motion#
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.
download MP4: planetary_orbits.mp4
Radial Velocity Exoplanet Detection#
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. A circular and elliptical version is provided.
- download MP4:
Eclipsing Binary System#
Show an eclipsing binary system and the resulting lightcurve. Here we assume that the smaller star is hotter (e.g., a white dwarf).
download MP4: eclipsing_binary.mp4
Transiting Planet System#
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.
download MP4: planetary_transit.mp4
Equipotentials#
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.
download MP4: equipotentials.mp4