
KeplerSystem
General Description
This simulations illustrates Kepler's final theory of planetary motion. In this theory the planets orbit in ellipses with Sun at one focus (Kepler's First Law). These elliptical orbits are not necessarily all in the same plane. A line from Sun to the planet sweeps out equal areas in equal times (Kepler's Second Law). The square a planet's period is directly proportional to the cube of the semimajor axis of its elliptical orbit (Kepler's Third Law).
The simulation shows Earth's orbit around Sun, as well as the orbit of one other planet. The user can choose to show one of the five visible planets (Mercury, Venus, Mars, Jupiter, or Saturn), or a fictitious planet. The top window shows the orbits of the planets around Sun. The view can be changed by clicking and dragging in the window, and a zoom slider is provided to zoom in or out. The bottom window shows the view of Sun and planet against the background stars as seen from Earth.
Orbit Frame
- Display Options Menu
- Show Ecliptic Plane: show a wire mesh or transparent surface (see below) representing the plane of Earth's orbit.
- Show Planet's Orbital Plane: show a wire mesh or transparent surface representing the plane of the planet's orbit.
- Show Trace of Earth's Orbit: show a trace of Earth's orbit.
- Show Trace of Planet's Orbit: show a trace of the planet's orbit.
- Show Earth-Sun Line: show a line connecting Earth and Sun.
- Show Earth-Planet Line: show a line connecting Earth and the planet.
- Show Ecliptic Grid: show a grid of lines with constant ecliptic longitude/latitude, in ten degree increments.
- Show Direction to Vernal Equinox: show an arrow pointing in the direction of the vernal equinox on the celestial sphere.
- Show Line of Sight Vector: show a vector that points from the center of the celestial sphere to the apparent location of the planet as seen from Earth. This line is parallel to the Earth-planet line, but it does not start at Earth because Earth's orbit as shown is far too large in comparison to the celestial sphere. If it were to scale it would be contained inside the ball representing Sun.
- Show Stars: show stars on the celestial sphere.
- Use Transparent Planes: use partially transparent surfaces instead of wire mesh to represent the ecliptic and orbital planes. Note that on many systems this may slow down the performance of the simulation considerably.
- Select Planet Menu: allows the user to select one of the five visible planets (Mercury, Venus, Mars, Jupiter, or Saturn) or a user-defined planet. Selecting the user-defined planet will bring up a panel in which the user can specify the orbital parameters of the planet (see below).
- Visual Elements
- Blue sphere: Earth.
- Blue trace: Earth's elliptical orbit.
- Red/yellow sphere: the other planet (yellow=inferior, red=superior).
- Red/yellow trace: the planet's elliptical orbit.
- Red/yellow arrow: the line of sight from Earth to planet. This arrows properly indicates where the planet would appear on the celestial sphere, as seen from Earth.
- Red/yellow line: connects Earth and planet. Note that this line does not point to the planet's apparent position on the celestial sphere because the celestial sphere should be much larger than it is shown to be.
- Orange disk: Sun.
- Orange line: connects Earth and Sun. Points to the correct apparent location for Sun on the celestial sphere.
- Pink plane/mesh: the eclitpic plane.
- Green plane/mesh: the planet's orbital plane.
- Light gray grid lines: the ecliptic coordinate grid (lines of constant ecliptic longitude and latitude).
- Orange arrow with "VE" label: the arrow points toward the vernal equinox on the celestial sphere.
- White dots: stars on the celestial sphere.
- Controls
- Play/Pause: start and stop the simulation.
- Step: advance the simulation by one time step.
- Reset Simulation: reset simulation to its initial state.
- Clear Traces: clears traces in both frames.
- Time Step: size of time step used on computations. Increase this value to speed up the simulation. Decrease it to slow the simulation down.
- Zoom: slider lets the user zoom in for a close-up view or out for a comprehensive view.
Ecliptic View Frame
- Display Options Menu
- Show Trace of Planet's Path: trace the path of the planet against the background stars.
- Show Stars: show background stars near the ecliptic.
- Visual Elements
- Red/yellow disk: the planet.
- Orange disk: Sun.
- White dots: background stars.
- Green line: trace of the planet's motion against the background stars.
Orbital Parameters
This panel appears if the user selects a user-defined planet.
- a: planet's semimajor axis, or half the length of the long axis of the planet's elliptical orbit, measured in Astronomical Units (so the Earth's semimajor axis is 1 AU).
- e: eccentricity of the planet's orbit. Eccentricities near zero produce almost circular orbits, while eccentricities near 1 produce highly elongated ellipses.
- i: inclination, or tilt, of the plane of the planet's orbit relative to the plane of Earth's orbit, in degrees.
- Omega: ecliptic longitude of the ascending node of the planet's orbit (where the planet passes from the south ecliptic hemisphere to the north ecliptic hemisphere), in degrees.
- omega: argument of perihelion for the planet's orbit, in degrees. This is the angle between the ascending node and the perihelion (point of closest approach to Sun), measured in the direction of the planet's motion.
Orbital Data for Visible Planets
All data is taken from the National Space Science Data Center's fact sheets found at http://nssdc.gsfc.nasa.gov/planetary/.
Planet |
Semimajor Axis |
Eccentricity |
Inclination |
Longitude of Ascending Node |
Argument of Perihelion* |
Mercury |
0.3871 AU |
0.2056 |
7.0049 deg |
48.3317 deg |
29.1248 deg |
Venus |
0.7233 AU |
0.0068 |
3.3947 deg |
76.6807 deg |
54.8523 deg |
Earth |
1 AU |
0.0167 |
0 |
NA |
102.9472 deg* |
Mars |
1.5237 AU |
0.0934 |
1.8506 deg |
49.5785 deg |
286.4623 deg |
Jupiter |
5.2034 AU |
0.0484 |
1.3053 deg |
100.5562 deg |
274.1977 deg |
Saturn |
9.5371 AU |
0.0542 |
2.4845 deg |
113.7150 deg |
338.7169 deg |
*The Argument of Perihelion value for Earth is actually the ecliptic longitude of Earth's perihelion.
Todd K. Timberlake (ttimberlake@berry.edu)