Spacecraft Propagators

Spacecraft motion modeling through time is accomplished in FreeFlyer via a Propagator object.

Propagators are used to evolve, or "step", a Spacecraft state forward or backward in time. Each Spacecraft has its own Propagator object, which can be an Analytic Propagator, an Integrator, or an Ephemeris.

For more information on the relationship of Propagators, Integrators, and Ephemeris Objects in FreeFlyer, see Type Casting and the Object Hierarchy list.

Analytic Propagators

Analytic Propagators use pre-defined equations of motion to compute Spacecraft motion, rather than directly modeling forces as an Integrator does. These propagators tend to be very computationally efficient, but can be lower fidelity than integrators. Examples within FreeFlyer are the TwoBody, J2Mean, and SGP4 propagators.

Integrators

A numerical Integrator can be used to calculate the state of a spacecraft at a point in time using an initial state and a definition of the forces acting upon the spacecraft as input. It is used to step the spacecraft in time with a user-defined step size.

Choosing a variable step size (instead of fixed step size) for long duration propagation may improve performance. Using a variable step size allows FreeFlyer to increase or decrease the propagation step size based on a user-defined tolerance; however, output data will not be reported at a constant interval.

Force Model

The Force Model object defines the forces that will be modeled in the accelerations that are applied when a Spacecraft or Formation are propagated using the Step or Maneuver commands.

Ephemerides and Attitude History Files

As an alternative to using a ForceModel, FreeFlyer can base calculations on an imported Ephemeris as specified by a location and file name. Similarly, as an alternative to modeling the Spacecraft attitude in FreeFlyer Script, the attitude can be specified using an Attitude History File (AHF).

Propagator Summary Table

Choosing a propagator appropriate to the task can significantly improve FreeFlyer's performance. FreeFlyer can utilize several propagators with varying degrees of accuracy and speed, from a simple Two Body, to the robust Runge-Kutta 8(9). The following table summarizes details about the propagators that are provided for the Spacecraft. For detailed information on a specific propagator, follow the links shown below. In every propagator's case, it is especially helpful for Spacecraft in specific orbits and orbital regimes such that its advantages come into play. Because of that, some insight is provided below into what each propagator is recommended for and what it isn't recommended for. Speed and accuracy were determined by varying the propagator type and step size in sample LEO, GPS, and GEO orbit regimes, illustrating common propagation scenarios. Individual results will vary. All speed values are percentages relative to the run time of the RK89 integrator. All accuracy values are expressed as orders of magnitude relative to the accuracy of the Two Body propagator.

Propagator	Characteristics	Accuracy	Speed	Recommended For:	Not Recommended For:
Runge Kutta 8(9)	•Single step •Uses fixed or variable step size •Takes fewest propagation steps of RK integrators to reach a desired accuracy	107 times more accurate	--	•General orbit propagation •Impulsive maneuvers •Finite maneuvers •Interplanetary Design	•When speed is more important than accuracy.
Runge Kutta 4(5)	•Single step •Uses fixed or variable step size •low CPU usage compared to other RK integrators	106 times more accurate	55% faster	•General orbit propagation •Impulsive maneuvers •Finite maneuvers	•Interplanetary Design •When accuracy is more important than speed.
Runge Kutta 7(8)	•Single step •Uses fixed or variable step size •Equations of motion expressed in Cartesian	2•106 times more accurate	20% faster	•General orbit propagation •Impulsive maneuvers •Finite maneuvers	•Interplanetary Design
Runge Kutta 7(8) VOP	•Single step •Uses fixed or variable step size •Equations of motion expressed in Equinoctial	5•106 times more accurate	5% faster	•Smooth slow-varying force models •Lifetime studies where constant intervals in the output data are required.	•Interplanetary Design
Bulirsch Stoer	•Self-starting •Single large step •Uses fixed or variable step size •Equations of motion expressed in Cartesian	100 times more accurate	75% faster	•Smooth force models •Orbital decay analysis •Lifetime studies	•Short duration perturbations •Finite maneuvers
Bulirsch Stoer VOP	•Self-starting •Single large step •Uses fixed or variable step size •Equations of motion expressed in Equinoctial	100 times more accurate	70% faster	•Smooth slow-varying force models •Orbital decay analysis •Lifetime studies	•Short duration perturbations •Finite maneuvers
Cowell	•Multi-step predictor/corrector •Uses a variable step size	103 times more accurate	80% faster	•Multiple spacecraft with stable orbital elements	•Impulsive maneuvers •Finite maneuvers
SGP4	•Used to propagate SGP4 two-line elements (TLE’s)	105 times more accurate	90% faster	•Stable orbital elements with short propagation time period
J2Mean	•First-order propagator •Accounts only for Earth oblateness in model •Only takes RAAN and Argument of Perigee rates into account.	10 times more accurate	90% faster	•Only when modest accuracy requirements are needed such as for early mission concept development or visualization	•When detailed analysis with high accuracy is required •When 3+ body forces are required in model.
Two Body	•Simple orbit propagator •Assumes unperturbed central force motion •Produces Keplerian motion around the central body •Fixed step size	--	95% faster	•Only when modest accuracy requirements are needed such as for early mission concept development or visualization	•When detailed analysis with high accuracy is required
Ephemeris	•Requires pre-computed state data •Step directly to data points or interpolate with a fixed step size •Does not use a Force Model	Varies depending on interpolation method used and propagation model used when creating the ephemeris	Varies depending on interpolation algorithm	•Fast vector lookup •Generating many orbit products with pre-computed data (for example, stationkeeping maneuvers)	•Simulating new data •Analyzing force model perturbations