ER3BP Setup Tool

The elliptical restricted three-body problem (ER3BP) is an extension of the circular restricted three-body problem (CR3BP). It incorporates a nonzero eccentricity in the orbital motion of the primary-secondary system. This additional modeling fidelity introduces new implications for the existence and nature of periodic solutions for the problem, but the general mathematical form persists from the circular problem.

To access the ER3BP Setup Tool:

  • Open the properties of your Astrogator satellite.
  • Click the Component Browser icon ().
  • Click Design Tools in the left column, select the ER3BP Setup Tool template, and click the Duplicate Component icon ().
  • Enter a unique component name for your ER3BP Setup Tool instantiation.
  • Double-click your new component to open the dialog box for your ER3BP Setup Tool.

The behavior of the ER3BP Setup Tool is generally consistent with the behavior of the CR3BP Setup Tool, and the UI is almost the same, so refer to that CR3BP help topic page for most of the ER3BP Setup Tool usage. In addition to the controls, information, and objects in the CR3BP Setup Tool, the ER3BP Setup Tool includes the following unique aspects:

  • You can select an initial True Anomaly value from the source secondary orbit. Use the True Anomaly slider or enter a value in the text field. Changing the value updates the controls as well as finds the associated epoch when the secondary's orbit reflects this value of the osculating true anomaly.

    Because Astrogator must find the desired true anomaly from an osculating anomaly value, the Keplerian prediction for the associated epoch must be refined through an iterative process. Consequently, using the True Anomaly slider near the edges, particularly near 0 degrees, may cause the numerical refinement to shift into the next revolution of the secondary's orbit.

  • There is an additional Informational Output for Eccentricity for the given epoch/true anomaly.

Using the ER3BP Setup Tool to configure STK objects consistent with the elliptic restricted three-body problem will result in an idealized secondary with an eccentric orbit. In the problem formulation, the primary and secondary mutually orbit their common barycenter on eccentric orbits. STK simply reflects this by the eccentricity in the secondary's orbit with respect to the associated primary, which is typically the central body of your scenario.

All the restrictions and uses of associated objects described in the CR3BP Setup Tool help page apply to ER3BP also.