Simplified perturbations models are a set of five mathematical models (SGP, SGP4, SDP4, SGP8 and SDP8) used to calculate orbital state vectors of

satellites A satellite or artificial satellite is an object intentionally placed into orbit in outer space. Except for passive satellites, most satellites have an electricity generation system for equipment on board, such as solar panels or radioisotop ...

and

space debris Space debris (also known as space junk, space pollution, space waste, space trash, or space garbage) are defunct human-made objects in space—principally in Earth orbit—which no longer serve a useful function. These include derelict spacecr ...

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 North American Aerospace Defense Command (NORAD ), known until March 1981 as the North American Air Defense Command, is a combined organization of the United States and Canada that provides aerospace warning, air sovereignty, and protection ...

and NASA. These models predict the effect of

perturbations Perturbation or perturb may refer to: * Perturbation theory, mathematical methods that give approximate solutions to problems that cannot be solved exactly * Perturbation (geology), changes in the nature of alluvial deposits over time * Perturbatio ...

caused by the Earth’s shape, 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 of less than 225 minutes. Simplified Deep Space Perturbations (SDP) models apply to objects with an orbital period greater than 225 minutes, which corresponds to an altitude of 5,877.5 km, assuming a circular orbit. 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 is a gradual decrease of the distance between two orbiting bodies at their closest approach (the periapsis) over many orbital periods. These orbiting bodies can be a planet and its satellite, a star and any object orbiting it, or ...

. The SGP4 model has an error ~1 km at epoch 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) 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 A geostationary orbit, also referred to as a geosynchronous equatorial orbit''Geostationary orbit'' and ''Geosynchronous (equatorial) orbit'' are used somewhat interchangeably in sources. (GEO), is a circular geosynchronous orbit in altitude ...

and 12-hour Molniya orbits. Additional revisions of the model were developed and published by 2010 by the NASA

Goddard Space Flight Center The Goddard Space Flight Center (GSFC) is a major NASA space research laboratory located approximately northeast of Washington, D.C. in Greenbelt, Maryland, United States. Established on May 1, 1959 as NASA's first space flight center, GSFC empl ...

in support of tracking of the SeaWiFS mission and the Navigation and Ancillary Information Facility at the Jet Propulsion Laboratory in support of Planetary Data System for navigational purposes of numerous, mostly deep space, missions. Current code libraries use SGP4 and SDP4 algorithms merged into a single codebase in 1990 handling the range of orbital periods which are usually referred to generically as SGP4.

References

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External links

Source code for algorithm implementations, and TLE interpretation in some cases:
python-sgp4
A Python Implementation of the sgp4 model with automatic downloading of TLE Elements from NORAD database.
PHP5
based o
Gpredict
* Java

an
predict4java

C++, FORTRAN, Pascal, and MATLAB

go-satellite
GoLang implementation of SGP4 model and helper utilities. Orbital perturbations North American Aerospace Defense Command Computational physics Japanese inventions