How do I convert ECI coordinates to longitude latitude and altitude to display on a Map?

Question

I would like to be more specific about what I want to do. I get coordinates in ECI and I need to get the latitude and longitude from this. How can I do? I was searching but I could'nt find anything about it. Thanks again.

(I'm doing a small program in java that shows the position of a satellite in a given time. So, I used the NORAD SGP algorithm, and I have the position (x,y,z) and velocity(Vx,Vy,Vz). But the coordinates system used by this algorithm is the ECI, according what I read. Now I need to draw the satellite in a map, but I can't convert this coordinates to some system that could help me. I think if I can convert it to longitude and latitude it would be easy to draw. Could you help me? how can I do it? What is the best option(UTM,etc)? Thanks.)

Answer 1

What you want to do is called ECI/ECEF (cartessian) to Geodetic (lat/lon) conversion. This conversion is the most complex of all the geodetic conversions as the closed form solution is complicated. See page 34 of Stevens and Lewis, Aircraft Control and Simulation for a discussion of the coordinate systems: http://books.google.com/books/about/Aircraft_control_and_simulation.html?id=T0Ux6av4btIC

ECI to geodetic is a two step process:

The first step is the easiest in that you need to convert ECI (earth centered inertial) to ECEF (earth centered/earth fixed).

The second step is to convert ECEF to geodetic. You can read about solving this via Newton-Ralphson here: http://en.wikipedia.org/wiki/Geodetic_system

However, if I remember correctly, Newton-Raphson becomes unstable around the poles. The closed form solutions are much more complicated. I have successfully implemented Zhu's method. The advantage of the closed form solution is no iterations and there are no singularities (technically there are singularities but not above the earth). The reference: J. Zhu. Conversion of earth-centered earth-fixed coordinates to geodetic coordinates. Technical Report IEEE Log NO. T-AES/30/3/1666, IEEE, December 1993.