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→Two Body Propagator
* Simplified General Perturbation (SGP) Model
* Simplified Deep Space Perturbation (SDP) Model
In this article, which is mainly focuses on LEO satellites, only Two body propagator, J2 Propagator and SGP models are covered. Simplified Deep Space Perturbations (SDP ) models is too not applied for LEO satellites, it is for higher altitude satellites. It is more complex and not beneficial for student missionssatellite projects.
== Two Body Propagator ==
[[File:Propagator1Object Around Earth.png|thumb| Throwing a ball horizontally from a certain height with the correct velocity. [https://commons.wikimedia.org/wiki/File:Earth_Mars_comparision_sketch.svg Source Image]]]
Assume there are only two bodies in space, one is earth and other is your satellite and only gravitational force acting between these two.
[[File:Equation9.gif|frame|center]]
As you might have heard or read that if you throw a ball horizontally from a certain height with the correct velocity then it will revolve around earth. Well this is the same thing. Once you know from where and when you throw the ball, you will get the position of the ball at any instant of time, with these equation of g by integrating it twice with respect to time. This is a very crude model and it doesn’t even generate a sun-synchronous orbit.
== J2 Propagator ==
The fact that earth rotates around its own axis makes it fat around the equator due to centrifugal force acting on it. So it becomes like orange not like a football. The earth’s equatorial radius is 21 km larger than the polar radius. This flattening at the poles is called oblateness (oblateness = [equatorial radius − polar radius]/equatorial radius). <ref>Orbital Mechanics for Engineering Students, Section 4.7, page 177-181</ref> <br \>
== Simplified General Perturbation (SGP) model ==
J2 propagator is nice, it forms sun-synchronous orbit, it is based upon numerical integration approach but it doesn’t account for many other factors which means it is not very accurate. SGP model has been developed by NORAD and NASA and uses Two line element (TLE) data and gives the position and velocity of satellite in ECI frame at given instant of time. This model is a collection of polynomial equations (no numerical integration involved) which accounts for J2 and J4 perturbations, atmospheric drag and other secular effects.<ref>The effect which is constantly increasing (or decreasing) over time. It’s magnitude might be small but over time it’s value would become large.</ref><ref>https://www.celestrak.com/NORAD/documentation/spacetrk.pdf</ref> <br \>
This model is are very popular and the code, that initially had been written in Fortran, has been translated into MATLAB, python and other languages. <br \>
Two line element is a collection of orbital parameters such as eccentricity, argument of perigee, inclination etc. and coefficient of atmospheric drag etc. TLE data is defined as the initial point of propagator after which the position and velocity is calculated. <ref>http://www.stltracker.com/resources/tle</ref> <br \> <br \> <br \>
J2 propagator and SGP propagator are very powerful and useful for orbit propagation however they drift by more than 3km a day. So over a long period of time, the drift would become problematically large. To correct this error, we use GPS from time to time. One may ask why not use GPS all the time for position determination. The answer lies in power consumption. In space we have limited power but more responsibility.<br \><vr \><br \>
== Comparison between J2 and SGP ==
{| class="wikitable"
|-
|'''J2'''
|'''SGP'''
|-
|Accounts for only earth’s oblateness.
|Accounts for earth’s oblateness, atmospheric drag and other secular effects.
|-
|Simpler model
|Little complex model but it is available. One need not to make one.
|-
|Numerical Integration involved
|Polynomial terms
|-
|No requirement of data in TLE form
|TLE data required
|}
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If you are done reading this page, you can go back to [[Attitude Determination and Control Subsystem]]
== References ==