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.