The SGP4 model to calculate orbital state vectors of near-Earth satellites
Updated 30 Aug 2023

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Simplified perturbations models are a set of five mathematical models (SGP, SGP4, SDP4, SGP8 and SDP8) used to calculate orbital state vectors of satellites and space debris 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. 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 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 model was developed by Ken Cranford in 1970. This model was obtained by simplification of the more extensive analytical theory of Lane and Cranford which uses the solution of Brouwer for its gravitational model and a power density function for its atmospheric model.
Hoots, Felix R., and Ronald L. Roehrich. 1980. Models for Propagation of NORAD Element Sets. Spacetrack Report #3. U.S. Air Force: Aerospace Defense Command.
Vallado D. A; Fundamentals of Astrodynamics and Applications; McGraw-Hill, New York; 4th edition (2013).

Cite As

Meysam Mahooti (2024). SGP4 (, MATLAB Central File Exchange. Retrieved .

MATLAB Release Compatibility
Created with R2021b
Compatible with any release
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Inspired: epoch2datevec(tle_epoch)

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Version Published Release Notes

test_sgp4.m was modified.


The vectorized SGP4 package was added.


satdata.xndt2o in test_sgp4.m was corrected.


Mjday.m was modified.

test_sgp4.m is modified.

Satellite's state vector is computed in four different coordinate systems, i.e. Earth-centered inertial (ECI), Earth-centered Earth-fixed (ECEF), true of date (TOD) and true equator mean equinox (TEME).