Converting Velocity and Position Vectors to Longitude and Latitude?

Question

I've been having a play with a satellite tracking program. You give it the TLE information and the Julian date and it returns the Position Vector and Velocity Vector in 3 parts for the given satellite. For instance the ISS's position and velocity vector at time of writing this are:

Position Vector:
1.43201229062465434E18
-2.13926476354018432E17
-9.0494444352008358E17

Velocity Vector:
3.191614378202316E-10
3.0853260273024627E-10
2.1811338307505537E-10

I wanted to look this up against a online tracker as a Longitude and Latitude and check that its correct. But I've no idea how to convert these to long and lat. Can any rocket scientists help me out? Is it even possible?

Answer 1

Orbital positions are typically expressed in Earth Centered Earth Fixed (ECEF) (Cartesian) coordinates. You appear to want to convert that representation to Latitude Longitude Altitude (LLA) representation. Mathworks has a nice description of the conversion from ECEF to LLA and from LLA to ECEF. The Naval Postgraduate School has a web application to convert between the two representations.

For orbital dynamics, the time doesn't really enter into the conversion between ECEF and LLA. That is only used to determine where the object in orbit is at that point in time (typically in ECEF). Also, the velocity vector changes over time as the object orbits the earth, but that doesn't have an impact on the conversion either.

Answer 2

first ensure that the position vectors are in ECEF or in ECI frame..... If it is in ECEF, covert it directly to Lat Long Alt. In case of ECI, convert it to ECEF frame by calculating local sidereal time using julian date and then proceed with ECEF2LLA conversion...