## Satellite Orbit Coordinate Transformations

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How to interpret TLE and convert its unperturbed orbit into various coordinate systems.

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There are several coordinate systems used to describe the motion of a satellite:
1) The p-q orbital plane. Here the p-axis is through the center of the orbit to perigee. The q-axis is through the focus (center of Earth) and normal to the p axis.
2) Earth Centered Inertial coordinates. The origin is at the center of the Earth. The z-axis is aligned with the Earth's spin axis. The x-axis points to the Vernal Equinox. The y-axis completes a right-hand rule Cartesian system. The distance from the center of the Earth to the satellite is distance = sqrt(x^2 + y^2 + z^2). The Right Ascension = atan2(y/x) (wrapped 0 to 2pi) and the Declination = asin(z/distance). It is defined by an epoch that is the times valid when the x-axis is pointing at the Vernal Equinox, since the Earth's spin axis precesses slowly and other small changes exist in the location and rate of the spin axis itself.
3) Earth Centered Earth Fixed (Rotating). The origin is at the center of Earth. The z-axis is aligned with the Earth's spin axis. The x-axis points to the crossing of the latitude = 0 longitude=0 point (Greenwich line at the equator). The y-axis completes a right-hand rule Cartesian system. The conversion between ECI and ECEF depends on the time. To be very accurate the current time is expressed in UT1 (https://en.wikipedia.org/wiki/DUT1) rather than UTC values.
4) Latitude, Longitude, Altitude. The Cartesian ECEF are converted to spherical coordinates Latitude, Longitude, and Altitude. The values depend on the reference Earth ellipsoid that the user selects. Here, WGS84 is used (it is the default of matlab's eci2lla).

This projection illustrates how to:
* Interpret the TLE of a satellite.
* Find the Common (Kepler) Orbital Elements from the TLE
* Convert the orbital elements to the inertial p-q orbital plane.
* Transform the p-q orbital plane coordinates to ECI coordinates.
* Transform the ECI coordinates to ECEF and/or LLA coordinates.

Note: No satellite propagation is performed, so this code is not sufficient for predicting the accurate location of a satellite at a given time.

### 引用

Meg Noah (2023). Satellite Orbit Coordinate Transformations (https://www.mathworks.com/matlabcentral/fileexchange/73873-satellite-orbit-coordinate-transformations), MATLAB Central File Exchange. 取得済み .

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