Forces presentation

Objects implementing the force model interface are intended to be added to a numerical propagator before the propagation is started.

The propagator will call at each step the force model contribution computation method, to be added to its time derivative equations. The force model instance will extract all the state data it needs (date, position, velocity, frame, attitude, mass) from the SpacecraftState parameter. From these state data, it will compute the perturbing acceleration. It will then add this acceleration to the second parameter which will take this contribution into account and will use the Gauss equations to evaluate its impact on the global state derivative.

Force models that create discontinuous acceleration patterns (typically for maneuvers start/stop or solar eclipses entry/exit) must provide one or more events detectors to the propagator thanks to their getEventsDetectors() method. This method is called once just before propagation starts. The events states will be checked by the propagator to ensure accurate propagation and proper events handling.

Available force models

The force models implemented are as follows:

• atmospheric drag forces, taking attitude into account if spacecraft shape is defined,
• central gravity forces, including time-dependent parts (linear trends and pulsation at several different periods). Several attraction models are available for representing the gravitational field of a celestial body (the recommended model is Holmes and Featherstone):
  • Andrzej Droziner model (Institute of Mathematical Machines, Warsaw) in his 1976 paper: An algorithm for recurrent calculation of gravitational acceleration (artificial satellites, Vol. 12, No 2, June 1977),
  • Leland E. Cunningham model (Lockheed Missiles and Space Company, Sunnyvale and Astronomy Department University of California, Berkeley) in his 1969 paper: On the computation of the spherical harmonic terms needed during the numerical integration of the orbital motion of an artificial satellite (Celestial Mechanics 2, 1970),
  • S. A. Holmes and W. E. Featherstone (Department of Spatial Sciences, Curtin University of Technology, Perth, Australia) in their 2002 paper: A unified approach to the Clenshaw summation and the recursive computation of very high degree and order normalised associated Legendre functions (Journal of Geodesy (2002) 76: 279–299).
• third body gravity force. Data for all solar system bodies is available, based on JPL DE ephemerides or IMCCE INPOP ephemerides,
• solar radiation pressure force, taking into account force reduction in penumbra and no force at all during complete eclipse, and taking attitude into account if spacecraft shape is defined,
• solid tides, with or without solid pole tide,
• ocean tides, with or without ocean pole tide,
• forces induced by maneuvers. At present, only constant thrust maneuvers are implemented, with the possibility to define an impulse maneuver, thanks to the event detector mechanism.

Spacecraft shapes

Surface forces like atmospheric drag or radiation pressure can use either a simple SphericalSpacecraft shape or a more accurate BoxAndSolarArraySpacraft shape.

The spherical shape will be independent of attitude.

The box and solar array will consider the contribution of all box facets facing the flux as computed from the current attitude, and also the contribution of a pivoting solar array, whose orientation is a combination of the spacecraft body attitude and either the true Sun direction or a regularized rotation angle. As of 6.1, the box and solar array does not compute yet shadowing effects.

Authors

• Luc Maisonobe
• Mathieu Roméro
• Edouard Delente
• Pascal Parraud