SGP4
Encyclopedia
Simplified perturbations models are a set of five mathematical models (SGP, SGP4, SDP4, SGP8 and SDP8) used to calculate orbital state vectors
Orbital state vectors
In astrodynamics or celestial dynamics orbital state vectors are vectors of position and velocity that together with their time uniquely determine the state of an orbiting body....

 of satellites and space debris
Space debris
Space debris, also known as orbital debris, space junk, and space waste, is the collection of objects in orbit around Earth that were created by humans but no longer serve any useful purpose. These objects consist of everything from spent rocket stages and defunct satellites to erosion, explosion...

 relative to the Earth-centered inertial coordinate system. This set of models is often referred to collectively as SGP4 due to the frequency of use of that model particularly with two-line element sets produced by NORAD and NASA
NASA
The National Aeronautics and Space Administration is the agency of the United States government that is responsible for the nation's civilian space program and for aeronautics and aerospace research...

.

These models predict the effect of perturbations
Perturbation (astronomy)
Perturbation is a term used in astronomy in connection with descriptions of the complex motion of a massive body which is subject to appreciable gravitational effects from more than one other massive body....

 caused by the Earth’s shape (spherical
harmonics), drag, radiation, and gravitation effects from other bodies such as the sun and moon. Simplified General Perturbations (SGP) models apply to near earth objects with an orbital period
Orbital period
The orbital period is the time taken for a given object to make one complete orbit about another object.When mentioned without further qualification in astronomy this refers to the sidereal period of an astronomical object, which is calculated with respect to the stars.There are several kinds of...

 of less than 225 minutes. Simplified Deep Space Perturbations (SDP) models apply to objects further from Earth or those with an orbital period
Orbital period
The orbital period is the time taken for a given object to make one complete orbit about another object.When mentioned without further qualification in astronomy this refers to the sidereal period of an astronomical object, which is calculated with respect to the stars.There are several kinds of...

 greater than 225 minutes.

The SGP4 and SDP4 models were published along with sample code in FORTRAN IV in 1988 with refinements over the original model to handle the larger number of objects in orbit since. SGP8/SDP8 introduced additional improvements for handling orbital decay
Orbital decay
Orbital decay is the process of prolonged reduction in the altitude of a satellite's orbit.This can be due to drag produced by an atmosphere due to frequent collisions between the satellite and surrounding air molecules. The drag experienced by the object is larger in the case of increased solar...

.

The SGP4 model has an error ~1 km at epoch
Epoch (astronomy)
In astronomy, an epoch is a moment in time used as a reference point for some time-varying astronomical quantity, such as celestial coordinates, or elliptical orbital elements of a celestial body, where these are subject to perturbations and vary with time...

 and grows at ~1–3 km per day. This data is updated frequently in NASA and NORAD sources due to this error. The original SGP model was developed by Kozai in 1959, refined by Hilton & Kuhlman in 1966 and was originally used by the National Space Surveillance Control Center (and later the United States Space Surveillance Network
United States Space Surveillance Network
The United States Space Surveillance Network is a critical part of United States Strategic Command's mission and involves detecting, tracking, cataloging and identifying artificial objects orbiting Earth, i.e. active/inactive satellites, spent rocket bodies, or fragmentation debris...

) for tracking of objects in orbit. The SDP4 model has an error of 10 km at epoch.

Deep space models SDP4 and SDP8 use only 'simplified drag' equations. Accuracy is not a great concern here as high drag satellite cases do not remain in "deep space" for very long as the orbit quickly becomes lower and near circular. SDP4 also adds Lunar–Solar gravity perturbations to all orbits, and Earth resonance terms specifically for 24-hour geostationary and 12 hour Molniya orbit
Molniya orbit
Molniya orbit is a type of highly elliptical orbit with an inclination of 63.4 degrees, an argument of perigee of -90 degree and an orbital period of one half of a sidereal day...

s.

Additional revisions of the model were developed and published by the Goddard Space Flight Center
Goddard Space Flight Center
The Goddard Space Flight Center is a major NASA space research laboratory established on May 1, 1959 as NASA's first space flight center. GSFC employs approximately 10,000 civil servants and contractors, and is located approximately northeast of Washington, D.C. in Greenbelt, Maryland, USA. GSFC,...

 in support of tracking of the SeaWiFS
SeaWiFS
SeaWiFS stands for Sea-viewing Wide Field-of-view Sensor. It was the only scientific instrument on GeoEye's OrbView-2 satellite, and was a follow-on experiment to the Coastal Zone Color Scanner on Nimbus 7...

 mission and the Navigation and Ancillary Information Facility at the Jet Propulsion Laboratory
Jet Propulsion Laboratory
Jet Propulsion Laboratory is a federally funded research and development center and NASA field center located in the San Gabriel Valley area of Los Angeles County, California, United States. The facility is headquartered in the city of Pasadena on the border of La Cañada Flintridge and Pasadena...

in support of Planetary Data System for navigational purposes of numerous, mostly deep space, missions. Current code libraries have merged SGP4 and SDP4 algorithms into a single codebase handling the range of orbital periods which are usually referred to generically as SGP4.

External links

Source code for algorithm implementations, and TLE interpretation in some cases:
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