By inserting the values in the equations above I got: rp<ro<ra , the difference is a couple of meters. This makes it consistent, so this is good news.

I also took the rp and ra values to see if it gave a close value to a : a=(rp+ra)/2 , and it gave something VERY close. So far so good.

I then calculated the velocity it has with the given a and my ro, which is about 7.7 km/s more or less. The final step was to calculate the true anomaly (with an equation that I mentioned in a previous comment): v

^{2}=((μ/r)*(2-(1-e

^{2})/(1+ecos(v))) - -> v is around 89 degrees .

I then calculated semi-parameter: p=a(1-e

^{2}) . And lastly, I used this equation: r=p/(1+ecos(v)) and got something VERY close to ro . In conclusion, it all seems to work and the analysis is correct. But my guts tells me that I need to use the given M and altitude as well. Is it necessary when I already see that it seems to be correct?