Determine the orbit of an object that you have observed. You will determine the object state vector at a time of the first observation and create a simulations of the orbital trajectory.
The steps followed to solve the problems are as follows:
Determine the UTC (Coordinated Universal Time) for the three observations to calculate the Local Sidereal Time for each observation. Nairobi is located at UTC + 3 so the time in UTC is the time given – 3.
Calculate the Local Sidereal Time for each observation
Azimuth Angle (deg.)
Elevation Angle (deg.)
Local Sidereal Time
Calculate the three geocentric position vectors corresponding to the three sets of azimuth, elevation and slant range data at each time given the earth observation location:
Using the altitude H, latitude φ and local sidereal time θ of the site, calculate its geocentric position vector R from the following equation:
Calculate the topocentric declination δ using the following equation:
Calculate the topocentric right ascension α using the following equations:
Calculate the direction cosine unit vector using the following equation:
Calculate the geocentric position vector r using the following equation:
The results obtained by MATLAB were as the following:
Applying Gibbs’ Method to the three obtained position vectors to get the velocity vector corresponding to the second position vector: - The result was as following: We take the initial r and v to be r2 and v2:
Knowing r and v the 6 COE could be obtained easily using the below flow graph  and the results were:
Since the eccentricity is between 0 and 1, the orbit is elliptical.