Spacecraft Propagators

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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.

 

If an Analytic Propagator is used, the equations modeling the Spacecraft's motion over time can be evaluated to compute the Spacecraft's position at any epoch.

If an Integrator is used, the forces acting on the Spacecraft are defined by its ForceModel object. There are many high-fidelity Integrators available in FreeFlyer to propagate the Spacecraft, applying the accelerations from the user-selected forces.

If an Ephemeris File is used, the ForceModel object is not used. The Spacecraft's initial state (epoch, position, velocity, etc.) will be overwritten with the first state in the ephemeris file.

 

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

 

Spacecraft Propagator Editor

Spacecraft Propagator Editor

 

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.

 

See Working with Integrators and the Propagator Summary Table for more information.

 

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).

 

See Working with Ephemerides and Ephemerides and Attitude History Files for more information.

 

 

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

 

Note: The specific Runge-Kutta integration method used in FreeFlyer is the Runge-Kutta-Verner method.

 

See Also


Integrator Properties and Methods

Setting up an Integrator

Solar System settings that affect Spacecraft Propagation