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Today we rely heavily on satellites orbiting Earth for a variety of purposes. Mapping satellites are used to collect satellite images used in maps. Communication satellites are used for both telecommunication and internet access or for navigation services like GPS and GLONASS. Other usage areas are weather study, scientific observation, and reconnaissance.
The following model, created in Wolfram SystemModeler
, is of a geocentric, inclined circular Low Earth Orbit (LEO) satellite. Geocentric means that it orbits around the Earth. An inclined circular orbit means that the orbit follows a circle, but is not aligned with the equator of the Earth. LEO is the name given to the altitude range below 2,000 kilometers (1,200 miles).
Suppose you are considering using this geocentric LEO satellite to collect image data. To achieve this, you would want to know where it is at the moment, how high it is, and how fast it's going. If you want images of cities, you want to know over which cities it currently is. A SystemModeler
model combined with data and computational resources in Mathematica
can answer all of these questions.
Creating such a model is straightforward in SystemModeler
. Using drag-and-drop, create three subsystems. Model the Earth using a mass with constant rotation, the satellite using a mass with propulsion forces, and the control logic using two proportional derivative (PD) controllers.
This blog post focuses on illustrating the orbit and flight of the satellite in the above model.