Is the speed of an orbiting object at a given distance enough to uniquely classify an orbit's eccentricity? As in the title, I am having trouble with part ii and iii of the linked image. So far i have found the semi-major axis and the period of the orbit both using the vis-viva equation along with proving that it is elliptic.

I have found the eccentricity in terms of the semi major axis and the perihelion and aphelion but I cannot make further progress.

• Hint: en.wikipedia.org/wiki/… Also, there's missing information about velocity (you've been given only the amplitude) – DrLRX Feb 20 '18 at 22:43
• Does the fact that the question only give the speed and not the direction mean that the eccentricity is not uniquely determined? Could I find a range of possible eccentricities by considering two extreme cases: e.g. The velocity is parallel to its displacement from the sun and its velocity is perpendicular to its displacement? – Eoghan O Callaghan Feb 20 '18 at 22:54
• While you would indeed need both a position and velocity vector to fully describe the orbital state, the problem doesn’t ask for the full orbital state; e should be calculable from magnitudes alone. – cms Feb 21 '18 at 0:36