Question

Coordinate transformations: Consider a satellite in Earth orbit. The position vector of the satellite in ECEF coordinates (pe) is equal to: 1x 106 m pe -4.2198 -26.428 9.4295 (1) X When the satellite is at these position coordinates, its velocity vector in ECEF coor- dinates is given by: ]m/s. 2941.4 48343 2667.2 (2) Answer the following questions (you may want to write MATLAB scripts to solve some or all of the problems). (a) What are the satellites's geodetic position coordinates? (b) Over what major city is the satellite located? (c) What is the satellites's speed in km/s? (d) Consider a NED coordinate system with its origin located on the reference ellipsoid directly beneath the satellite's current position. What is the satellite's velocity vector (in m/s) expressed in this NED coordinate system? (e) What are the azimuth and elevation angle of the satellite for an observer located at Quito, Ecuador? The geodetic coordinates for Quito 29' 17" East, and 9228 feet above the reference ellipsoid are 0° 8' 28" North, 78°

Answer 1

x =   4.2198e+06;
y =   26.428e+05;
z =   9.4295e+06;
wgs84 = wgs84Ellipsoid('meters');
[lat,lon,h] = ecef2geodetic(wgs84,x,y,z)

This is code to convert your ECEF coordinates to Geodetic coordinates.

Execute it in matlab you will get

(A) Lat = 19.43628, lon= 260.92807 , h = 21999589.7m (These are the latitude, longitude and elevation of that satellite)

(B) Now put this Latitude and Longitude in google maps it will give the location of Cudad de Mexico, Internaitonal Airport.

(C) To find the speed of the satellite from velocity vector is equivalent to find the modulus of the velocity vector so square root of 2941.4 + 483.43 + 2667.3 which will give you 4000 m/s.