Convert between state vectors and orbital elements

[napst3r]

Hi there I've been struggling to convert the following two vectors into orbital elements,
the vectors are as follows:

R = 0i - 7950j + 0k km
V = 5i + 0j + 5k km/sec

I would like someone to help with the calculations of the following COEs:
- semimajor axis (a)
- eccentricity vector
- eccentricity (e)
- inclination (i)
- RAAN (Ω)
- argument of perigee (ω)
- true anomaly (v)

I have tried to understand the following link but I am not getting the answers i should be getting
http://www.cdeagle.com/omnum/pdf/csystems.pdf

Thanks

 

[Valkarie]

in advance!The semimajor axis (a) can be calculated using the equation a = ||R||2/μ, where μ is the standard gravitational parameter of the body the orbit is around. In this case, μ = 398600.44 km3/s2. Plugging in the vector for R, we get a = 79502/398600.44 = 3.964 km. The eccentricity vector can be calculated using the equation e = V × R / μ - R/||R||, where V is the velocity vector, and R is the position vector. For this case, e = (5i + 0j + 5k) × (0i - 7950j + 0k) / 398600.44 - (0i - 7950j + 0k) / 7950 = (-39750i + 0j - 39750k)/398600.44.The eccentricity (e) can be calculated using the equation e = ||e||, where e is the eccentricity vector. For this case, e = √(397502 + 0 + 397502) / 398600.44 = 0.9974.The inclination (i) can be calculated using the equation i = arccos(e z / ||e||). For this case, i = arccos(-39750/√(397502 + 0 + 397502)) = 90°.The RAAN (Ω) can be calculated using the equation Ω = arctan(e y / e x). For this case, Ω = arctan(0 / -39750) = 180°.The argument of perigee (ω) can be calculated using the equation ω = arccos(R · e / ||R|| · ||e||). For this case, ω = arccos(0 / 7950·0.9974) = 0°.The true anomaly (v) can be calculated using the equation v = arccos(R · V / ||R|| · ||V||). For this case, v = arccos(0 / 7950·5) = 0°.