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Orbit of a space shuttle

Okay, so I did the following, I used the formulas for the perigee and apogee radius to get rp and ra. They are: rp=a(1-e) and ra=a(1+e) . I also calculated the absolute value of ro.
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): v2=((μ/r)*(2-(1-e2)/(1+ecos(v))) - -> v is around 89 degrees .
I then calculated semi-parameter: p=a(1-e2) . 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?


Okay, so you haven't found any glaring reason why the analysis would not be correct. You should confirm that the given position vector is consistent with the given inclination (it looks like it should be, given the "k" component of the position vector).

Now, if everything looks okay with the analysis you are faced with finding a location for the periapsis. If you have a true anomaly for the given position vector then you should be able to "locate" the periapsis.
Thank you for the help!

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