# Orbit Propagators for Satellites

Propagation concerns the determination of the motion of a body over time. According to Newton’s laws, the motion of a body depends on its initial state (i.e., its position and orientation at some known time) and the forces that act upon it over time. High fidelity propagators attempt to include all significant force models acting on the body; low fidelity propagators approximate the effects of some forces while completely disregarding others. High fidelity propagators solve Newton’s laws using numerical methods; low fidelity propagators tend to be analytic (i.e., formula-based) ; medium fidelity models are a hybrid (i.e., semi-analytical) which combines a simple numerical technique with formulas.)

Low fidelity propagators are the fastest to use and thus are appropriate for design and what-if scenario planning; high fidelity propagators are the slowest to use but most appropriate when accuracy is a premium, like in operations. Users should use a propagation model appropriate for the type of analysis needed.

There are three types of orbit propagators available in STK:

• Analytic. These propagators use a closed-form solution of the time-dependent motion of a satellite to produce ephemeris or to provide directly the position and velocity of a satellite at a particular time.
• Semi-analytic. These propagators incorporate some numerical techniques instead of using only approximations.
• Numerical. Numerical propagators numerically integrate the equations of motion for the satellite.

In addition, STK offers external propagators: StkExternal, SPICE, GPS (SP3), SP3, and Real-Time.

Following is a list of propagators for satellites available with STK and a short description of each. The parameters that you must define and the data that you must provide depend on the propagator chosen.

Note: Available propagators depend on the STK modules for which you are licensed.

## Analytic Propagators (Low Fidelity)

Analytic propagators approximate the motion of the object. They are best when needing to model a maintained orbit without having to model the maintenance maneuvers themselves.

Propagator Description
TwoBody The Two-Body, or Keplerian motion, propagator considers only the force of gravity from the Earth, which is modeled as a point mass.
J2 Perturbation The J2 Perturbation (first-order) propagator accounts for secular variations in the orbit elements due to Earth oblateness. This propagator does not model atmospheric drag or solar or lunar gravitational forces.

J2 is a zonal harmonic coefficient in an infinite series representation of the Earth's gravity field. It represents the dominant effects of Earth oblateness. The even zonal harmonic coefficients of the gravity field are the only coefficients that result in secular changes in satellite orbital elements. The J2 propagator includes the first-order secular effects of the J2 coefficient.
J4 Perturbation The J4 Perturbation (second-order) propagator accounts for secular variations in the orbit elements due to Earth oblateness. This propagator does not model atmospheric drag or solar or lunar gravitational forces. The J4 propagator includes the first- and second-order effects of J2 and the first-order effects of J4. The J3 coefficient, which produces long period periodic effects, is not included in either propagator. J4 is approximately 1000 times smaller than J2 and is a result of Earth oblateness. Since the second-order J2 and the first-order J4 secular effects are very small, there is little difference between the orbits generated by the two propagators.
SGP4 for LEO satellites The Simplified General Perturbations (SGP4) propagator, a standard AFSPACECOM propagator, is used with two-line mean element (TLE) sets. It considers secular and periodic variations due to Earth oblateness, solar and lunar gravitational effects, gravitational resonance effects and orbital decay using a simple drag model.
11Parameter The 11-Parameter propagator models geostationary satellites using 11-Parameter files. The propagator uses an algorithm documented in Intelsat Earth Station Standards (IESS) IESS-412 (Rev. 2), available at www.celestrak.com. 11-Parameter files can be found at and downloaded from the websites of IntelSat, SES NewSkies, and TelenorSBC.
GPS using SEM or YUMA files The GPS Propagator uses the algorithm from the standard ICD-GPS-200 to model the motion of a GPS spacecraft using either SEM- or YUMA-formatted almanac files.

## Semi-Analytic Propagators (Medium Fidelity)

These propagators provide for more accuracy by incorporating some numerical techniques rather than having to make so many approximations.  The results are quicker than full Numerical Integrations.

Propagator Description
LOP The Long-term orbit predictor (LOP) allows accurate prediction of the motion of a satellite's orbit over many months or years. The LOP propagator uses the same orbital elements as those required by the Two-Body, J2 and J4 propagators.
SGP4 for non-LEO satellites The Simplified General Perturbations (SGP4) propagator, a standard AFSPACECOM propagator, is used with two-line mean element (TLE) sets. It considers secular and periodic variations due to Earth oblateness, solar and lunar gravitational effects, gravitational resonance effects and orbital decay using a simple drag model.

## Numerical Integration Propagators (High Fidelity)

The numerical approach to propagation is much more accurate then either Analytic or Semi-Analytic with the selection of the correct step-size in time. Here, speed is sacrificed during computation for the sake of accuracy. The orbit modeling is derived using full algorithms, correct ephemerides and is typically the best solution to model realistic problems.

Propagator Description
Astrogator The Astrogator propagator provides for trajectory and maneuver planning and includes targeting capabilities.
HPOP The high-precision orbit propagator (HPOP) can handle circular, elliptical, parabolic and hyperbolic orbits at distances ranging from the surface of the Earth to the orbit of the Moon and beyond. This propagator uses the same orbital elements to set the state at epoch as those used by the Two-Body, J2 and J4 propagators.

## External Propagators

These propagators are used to add external, user-created files that can be either analytic, semi-analytic, or numerical.

Propagator Description
StkExternal The StkExternal propagator allows you to read the ephemeris for a satellite from a file. The file must end in an .e extension.
SPICE The SPICE propagator reads ephemeris from binary files that are in a standard format produced by the Jet Propulsion Laboratory (JPL). They are intended for ephemeris for celestial bodies but can be used for spacecraft.