Forces

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). Our implementation is based on S. A. Holmes and W. E. Featherstone (Department of Spatial Sciences, Curtin University of Technology, Perth, Australia) 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 ; several occulting bodies can be defined as oblate spheroids

• Earth Albedo and IR emission force model. Our implementation is based on paper: EARTH RADIATION PRESSURE EFFECTS ON SATELLITES", 1988, by P. C. Knocke, J. C. Ries, and B. D. Tapley.

• solid tides, with or without solid pole tide,

• ocean tides, with or without ocean pole tide,

• post-Newtonian correction due to general relativity with De Sitter and Lense-Thirring terms,

• 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.

• parametric accelerations, to model lesser-known forces, estimating a few defining parameters from a parametric function using orbit determination. Typical parametric functions are polynomial (often limited to a constant term) and harmonic (often with either orbital period or half orbital period). An important operational example is the infamous GPS Y-bias.

Spacecraft shapes

Surface forces like atmospheric drag or radiation pressure can use either a simple spherical shape using the various Isotropic classes 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 panels 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. The box can have any number of panels, and they can have any orientation as long as the body remains convex. The coefficients (drag, lift, absorption, reflection) are panel-dependent. As of 12.0, the box and solar array does not compute yet shadowing effects.

All these shapes define various ParameterDrivers that can be used to control dynamic parameters like drag coefficient or absorption coefficient. Several conventions are available. For estimation purposes, it is possible to use a global multiplication factor that is applied to the acceleration rather than attempting to estimate several coefficients at once like absorption and specular reflection for solar radiation pressure. For BoxAndSolarArraySpacraft shape, as each panel has its own set of coefficients and this would not be observable, the coefficients are fixed and only the global multiplication factor is available and can be estimated. For Isotropic shapes, it is possible to estimate either the coefficients or the global multiplication factor. Of course in order to avoid ill-conditioned systems, users should not attempt to estimate both a coefficient and a global multiplication factor at the same time in Isotropic cases; they should select one parameter to estimate and let the other one fixed.