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

orbital state vectors In astrodynamics and celestial dynamics, the orbital state vectors (sometimes state vectors) of an orbit are Cartesian vectors of position (\mathbf) and velocity (\mathbf) that together with their time (epoch) (t) uniquely determine the traject ...

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 Earth-centered inertial (ECI) coordinate frames have their origins at the center of mass of Earth and are fixed with respect to the stars. "I" in "ECI" stands for inertial (i.e. "not accelerating"), in contrast to the "Earth-centered - Earth- ...

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 set A two-line element set (TLE) is a data format encoding a list of orbital elements of an Earth-orbiting object for a given point in time, the ''epoch''. Using a suitable prediction formula, the state (position and velocity) at any point in the past ...

s 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 The National Aeronautics and Space Administration (NASA ) is an independent agency of the US federal government responsible for the civil space program, aeronautics research, and space research. NASA was established in 1958, succeeding t ...

. These models predict the effect of perturbations 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 The orbital period (also revolution period) is the amount of time a given astronomical object takes to complete one orbit around another object. In astronomy, it usually applies to planets or asteroids orbiting the Sun, moons orbiting planets ...

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 In chronology and periodization, an epoch or reference epoch is an instant in time chosen as the origin of a particular calendar era. The "epoch" serves as a reference point from which time is measured. The moment of epoch is usually decided by ...

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 The United States Space Surveillance Network (SSN) detects, tracks, catalogs and identifies artificial objects orbiting Earth, e.g. active/inactive satellites, spent rocket bodies, or fragmentation debris. The system is the responsibility of Uni ...

) 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 orbit A Molniya orbit ( rus, Молния, p=ˈmolnʲɪjə, a=Ru-молния.ogg, "Lightning") is a type of satellite orbit designed to provide communications and remote sensing coverage over high latitudes. It is a highly elliptical orbit with an ...

s. 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 Navigation is a field of study that focuses on the process of monitoring and controlling the movement of a craft or vehicle from one place to another.Bowditch, 2003:799. The field of navigation includes four general categories: land navigation, ...

at the

Jet Propulsion Laboratory The Jet Propulsion Laboratory (JPL) is a federally funded research and development center and NASA field center in the City of La Cañada Flintridge, California, United States. Founded in the 1930s by Caltech researchers, JPL is owned by NASA an ...

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

{{reflist

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