Propagation modes

Depending on the needs of the calling application, all propagators can be used in different modes:

• slave mode: This mode is used when the user wants to completely drive evolution of time with his own loop. The (slave) propagator is passive: it computes this result and returns it to the calling (master) application, without any intermediate feedback. Users often use this mode in loops, each target propagation time representing the next small time step. In that case the events detection is made but the step handler does nothing, actions are managed directly by the calling application.
• master mode: This mode is used when the user needs to have some custom function called at the end of each finalized step during integration. The (master) propagator is active: the integration loop calls the (slave) application callback methods at each finalized step, through the step handler. Users often use this mode with only a single call to propagation with the target propagation time representing the end final date.
• ephemeris generation mode: This mode is used when the user needs random access to the orbit state at any time between the initial and target times, and in no sequential order. A typical example is the implementation of search and iterative algorithms that may navigate forward and backward inside the propagation range before finding their result. CAVEATS: Be aware that this mode cannot support events that modify spacecraft initial state. Be aware that since this mode stores all intermediate results, it may be memory-intensive for long integration ranges and high precision/short time steps.

The recommended mode is master mode. It is very simple to use and allow user to get rid of concerns about synchronizing force models, file output, discrete events. All these parts are handled separately in different user code parts, and Orekit takes care of all management. The following class diagram shows the main interfaces used for master mode.

This mode also lets the propagator choose its own step size, but still let user choose a different step size for its output, which greatly increases performances. The following sequence diagram shows how a user-provided step handler is called when propagation is done in master mode.

The following sequence diagram shows how user can handle themselves time when propagation is done in slave mode, with a loop managed at user level.

The following sequence diagram shows how user can use ephemeris generation mode to do a two phases propagation, one first phase to generate the epehemeris, and a second phase using the generated ephemeris.

Events management

All propagators, including analytical ones, support discrete events handling during propagation. This feature is activated by registering events detectors as defined by the EventDetector interface to the propagator, each EventDetector being associated with an EventHandler that will be triggered automatically at event occurrence. The following class diagram shows the main interfaces used for event handling.

At each propagation step, the propagator checks the registered events detectors for the occurrence of some event, as shown in the following sequence diagram. If an event occurs, then the corresponding action is triggered, which can notify the propagator to resume propagation (possibly with an updated state) or to stop propagation.

Resuming propagation with changed state is used for example in the ImpulseManeuver class. When the maneuver is triggered, the orbit is changed according to the velocity increment associated with the maneuver and the mass is reduced according to the consumption. This allows the handling simple maneuvers transparently even inside basic propagators like Kepler or Eckstein-Heschler.

Stopping propagation is useful when some specific state is desired but its real occurrence time is not known in advance. A typical example would be to find the next ascending node or the next apogee. In this case, we can register a NodeDetector or an ApsideDetector object and launch a propagation with a target time far away in the future. When the event is triggered, it notifies the propagator to stop and the returned value is the state exactly at the event time.

Users can define their own events, typically by extending the AbstractDetector abstract class. There are also several predefined events detectors already available, amongst which :

• a simple DateDetector, which is simply triggered at a predefined date, and can be reset to add new dates on the run (which is useful to set up delays starting when a previous event is been detected),
• an ElevationDetector, which is triggered at raising or setting time of a satellite with respect to a ground point, taking atmospheric refraction into account and either constant elevation or ground mask when threshold elevation is azimuth-dependent,
• an AltitudeDetector which is triggered when satellite crosses a predefined altitude limit and can be used to compute easily operational forecasts,
• a CircularFieldOfViewDetector and a DihedralFieldOfViewDetector, which are triggered when some target enters or exits a satellite sensor field of view,
• an EclipseDetector, which is triggered when some body enters or exits the umbra or the penumbra of another occulting body,
• an ApsideDetector, which is triggered at apogee and perigee,
• a NodeDetector, which is triggered at ascending and descending nodes,
• an AlignmentDetector, which is triggered when satellite and some body are aligned in the orbital plane...

An EventShifter is also provided in order to slightly shift the events occurrences times. A typical use case is for handling operational delays before or after some physical event really occurs.

An EventFilter is provided when user is only interested in one kind of events that occurs in pairs like raising in the raising/setting pair for elevation detector, or eclipse entry in the entry/exit pair for eclipse detector. The filter does not simply ignore events after they have been detected, it filters them before they are located and hence save some computation time by not doing an accurate search for events that will ultimately be ignored.

Event occurring can be automatically logged using the EventsLogger class.

Additional states

All propagators can be used to propagate user additional states on top of regular orbit attitude and mass state. These additional states will be available throughout propagation, i.e. they can be used in the step handlers, in the event detectors and events handlers and they will also be available in the final propagated state. There are three main cases:

• if a deterministic way to compute the additional state from the spacecraft state is known, then the user can put this computation in an implementation of the AdditionalStateProvider interface and register it to the propagator, which will call it each time it builds a SpacecraftState.
• if a differential equation drives the additional state evolution, then the user can put this equation in an implementation of the AdditionalEquations interface and register it to an integrator-based propagator, which will integrated it and provide the integrated state.
• if no evolution laws are provided to the propagator, but the additional state is available in the initial state, then the propagator will simply copy the initial value throughout propagation, without evolving it.

  The first two cases correspond to additional states managed by the propagator, the last case not being considered as managed. The list of states managed by the propagator is available using the getManagedAdditionalStates and isAdditionalStateManaged.

Analytical propagation

Numerical propagation

Numerical propagation is one of the most important parts of the Orekit project. Based on Apache Commons Math ordinary differential equations integrators, the NumericalPropagator class realizes the interface between space mechanics and mathematical resolutions. Despite its utilization seems daunting on first sight, it is in fact quite straigthforward to use.

Simple propagation of equations of motion

The mathematical problem to integrate is a dimension-seven time-derivative equations system. The six first elements of the state vector are the orbital parameters, which may be any orbit type (KeplerianOrbit, CircularOrbit, EquinoctialOrbit or CartesianOrbit) in meters and radians, and the last element is the mass in kilograms. It is possible to have more elements in the state vector if AdditionalEquations have been added (typically PartialDerivativesEquations which is an implementation of AdditionalEquations devoted to integration of Jacobian matrices). The time derivatives are computed automatically by the Orekit using the Gauss equations for the first parameters corresponding to the selected orbit type and the flow rate for mass evolution during maneuvers. The user only needs to register the various force models needed for the simulation. Various force models are already available in the library and specialized ones can be added by users easily for specific needs.

The integrators (first order integrators) provided by Apache Commons Math need the state vector at t0, the state vector first time derivative at t0, and then calculates the next step state vector, and asks for the next first time derivative, etc. until it reaches the final asked date. These underlying numerical integrators can also be configured. Typical tuning parameters for adaptive stepsize integrators are the min, max and perhaps start step size as well as the absolute and/or relative errors thresholds. The following code snippet shows a typical setting for Low Earth Orbit propagation:

// steps limits
final double minStep  = 0.001;
final double maxStep  = 1000;
final double initStep = 60;

// error control parameters (absolute and relative)
final double positionError = 10.0;
final double[][] tolerances = NumericalPropagator.tolerances(positionError, orbit, orbit.getType());

// set up mathematical integrator
AdaptiveStepsizeIntegrator integrator =
    new DormandPrince853Integrator(minStep, maxStep, tolerances[0], tolerances[1]);
integrator.setInitialStepSize(initStep);

// set up space dynamics propagator
propagator = new NumericalPropagator(integrator);

The following sequence diagram show the internal calls triggered during a numerical propagation. The important thing to note is that the force model are decoupled from the integration process, they only need to compute an acceleration.

Propagating both equations of motions and additional equations

Sometimes, simple equations of motion are not enough. Some additional parameters can be useful alongside with the trajectory, like dual parameters in optimal control or Jacobians (also called state-transition matrices). This second case especially useful for computing sensitivity of a trajectory with respect to initial state changes or with respect to force models parameters changes.

Orekit provides a common way to handle both cases: additional equations. Users can register sets of additional equations alongside with additional initial states. These equations will be propagated by the numerical integrator. They will not be used for step control, though, so integrating with or without these equations should not change the trajectory and no tolerance setting is needed for them.

One specific implementation of additional equations is the partial derivatives equations which propagate Jacobian matrices, both with respect to initial state and with respect to force model parameters.

The above class diagram shows the design of the partial derivatives equations. As can be seen, the PartialDerivativesEquations class implements the AdditionalEquations interface and as such can be registered by user in a numerical propagator. the propagator will propagate both the main set of equations corresponding to the equations of motion and the additional set corresponding to the Jacobians of the main set. This additional set is therefore tightly linked to the main set and in particular depends on the selected force models. The various force models add their direct contribution directly to the main set, just as in simple propagation. They also add a contribution to the Jacobians thanks to the AccelerationJacobiansProvider interface, each force model being associated with an acceleration Jacobians provider. Some force models like solar radiation pressure implement this interface by themselves. Some more complex force model do not implement the interface and will be automatically wrapped inside a Jacobianizer class which will use finite differences to compute the local Jacobians.

Semianalytical propagation

Semianalytical propagation is an intermediate between analytical and numerical propagation. It retains the best of both worlds, speed from analytical models and accuracy from numerical models. Semianalytical propagation is implemented using Draper Semianalytical Satellite Theory (DSST).

As of writing (end 2013), only the mean elements equations of motion models have been implemented; the short periodic terms are still missing. They will be added later on.