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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.

  • $\begingroup$ Hint: en.wikipedia.org/wiki/… Also, there's missing information about velocity (you've been given only the amplitude) $\endgroup$ – DrLRX Feb 20 '18 at 22:43
  • $\begingroup$ 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? $\endgroup$ – Eoghan O Callaghan Feb 20 '18 at 22:54
  • $\begingroup$ 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. $\endgroup$ – cms Feb 21 '18 at 0:36

Your intuition is correct: you need to know the distance and velocity (velocity = speed and direction) in order to calculate the eccentricity. The speed is minimum at aphelion and maximum at perihelion. There are an infinite number of possible orbits that have a given distance and speed. If you want to calculate the range of possible eccentricities, let the direction vary between straight toward the Sun, to perpendicular to the sun-satellite line, to straight away from the sun.

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