# Completing satellite's state vector by given info

1. Apr 19, 2015

1. The problem statement, all variables and given/known data
A satellite is orbiting earth with a period time of T=110 min.
At the ascending node, the state vector of the satellite is rAN =[4500 7100 ???]T km
At the northernmost latitude, the state vector of the satellite is rn=[1700 ??? 7000]T km. The question marks imply that the information is missing.

The question asks to complete the vectors, and find orbit's elements: a, e, i, ω, Ω
2. Relevant equations
Given a state vector of a satellite, rAN =[x y z]T km
the latitude is:

there is also the following Kepler rule:

and the 2 body problem generalized solution:

where:

though i don't think the last two would help solving the missing vector.

3. The attempt at a solution
Well completing the rAN is quite easy as it's known that the ascending node is at the equator plane, thus: rAN =[4500 7100 0]T km.

It is also known that the latitude of the northernmost point is the inclination angle (i).

Finding a (the semi major axis) is possible by knowing period time:

was trying to use cross product of rAN and rn and thought that the angle between them is the latitude, but then i figured out i was completely wrong.

I think there's some vector calculus to be done but not sure what exactly.
Your help is appreciated.

2. Apr 19, 2015