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Three-Body Integrator
Help File

General Information

  • HELP. Displays this help screen. To exit, click one of the Exit Help buttons located at the top and bottom of this screen.

    Integration Parameters

  • ACCURACY. This number specifies the accuracy of the integration. More accurate integrations take longer and are more prone to run into numerical problems. Accordingly, you want the lowest number which gives an accurate plot. Experiment by following the same orbit at different accuracies and seeing if the output plots are similar.
  • INTEGRATION TIME. Here you specify how many years into the future the orbit should be followed. Be careful in choosing this parameter as it is directly correlated to how long you will wait before seeing a plot! A good strategy is to try a short integration time first to get an idea of how fast the program is.
  • SAVE FREQUENCY. This number determines how often a point along the orbit is saved to disk. A larger number yields a more accurately drawn orbit at the expense of plotting time and disk space. You want to choose the largest number that yields a reasonably accurate orbit. Experiment!

    2 Bodies in Bound Orbit

  • MASS OF THE SUN. Here you specify the mass of the star around which the planet will orbit. The mass is entered in units of Solar Masses. This means that if you enter "1.0" the star will have the same mass as our sun. If you enter "2.0" the star will be twice the mass of our sun, and so on...
  • MASS OF THE PLANET. In this space, you enter the mass of the planet which will orbit the star. Again, you specify the mass in units of Solar Masses. Some Examples of masses you could use:
    Venus: 0.000002 Solar Masses
    Earth: 0.000006 Solar Masses
    Jupiter: 0.000954 Solar Masses
    Saturn: 0.000286 Solar Masses
    Uranus: 0.000044 Solar Masses
    Neptune: 0.000051 Solar Masses
  • SUN TO PLANET DISTANCE. Here you specify the distance between the star and the planet at pericenter. You enter this value in units of AU which are define such that 1 AU is the average distance between the earth and the sun.
  • ECCENTRICITY. In this space, you enter the eccentricty of the planet's orbit about the star. You must enter a value greater or equal to 0 but less than 1. An eccentricity of 0.0 will produce a circular orbit. If the eccentriciy is greater than zero the orbit will be an ellipse.

    3rd Body (of Infinitesimal Mass)

  • 3RD BODY IS NEAR. You may choose to put the 3rd body near either of the two stable equillibrium points called Lagrangian Points. The Lagrangian points lie in the plane of the planet's orbit about the star. They are located at the tips of equillateral triangles whose bases are formed by the line between the star and the planet. The Leading Lagrangian Point is the equillibrium point which is located ahead of the planet as it moves around in its orbit. The Trailing Lagrangian Point is located behind the planet.
  • DISPLACEMENT FROM LAGRANGIAN POINT. Here you choose how far from the Lagrangian point the third body will initially be placed. The coordinate system in which this dispacement is specified is defined such that:
    1. The center of mass of the system is at the origin.
    2. The orbit of the planet about the star lies in the x-y plane.
    3. Initially, the star lies on the negative x-axis and the planet lies on the positive x-axis.
  • VELOCITY OF 3RD BODY IN ROTATING FRAME. Here you choose the intial velocity of the 3rd body. This velocity is specified in the Rotating Coordinate System. The Rotating Coordinate System is a coordinate system which has its origin a the center of mass. The Rotating Coordinate System rotates about the center of mass with an angular velocity equal to the average angular velocity of the planet's motion about the star.
  • SUBMIT FORM. Send the parameters that you have chosen to the orbital integration program!
  • LOAD DEFAULTS. Set all parameters back to their default values.
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