1. The problem statement, all variables and given/known data Hey, I need to find whether an asteroid is in a "bound orbit" around the Sun. Furthermore, describe the shape of the orbit (elliptical or circular). The only information I have been given is its velocity and position at a random point. v_o=61m/s r_o=13.75AU=2.06E12m I also need to find its orbital energy. 2. Relevant equations vis-viva eqn: v^2=GM((2/r)-(1/a)) angular momentum L=mvr r_p=a(1-e) position at perihelion 3. The attempt at a solution First i used the vis-viva eqn with my v_o and r_o but a (semi-major axis) is an unknown. so a=((2/r_o)-(v_o^2)/GM)^-1 a=1.03E12m Then i used momentum conservation with the observed position and the position at perihelion (where velocity is a maximum) m(v_o)(r_o)=m(v_p)(r_p) r_p=(v_o)(r_o)/(v_p) call this eqn 1 I computed the vis-viva eqn at perihelion, and i subbed in eqn 1 and a=1.03E12m so i got a quadratic: v_p^2=GM[((2v_p)/(v_o)(r_o))-(1/a) (v_p)^2 - 2.11E6(v_p)+1.29E8=0 The solutions are 61m/s or 2.11E6m/s. I used assumed 2.11E6m/s =v_p since it is larger.. and 61m/s is my original velocity. then i found r_p using eqn 1 r_p=5.9E7m finally i used the eccentricity eqn e=1-(r_p/a) however r_p is of order 10^7 and a is of order 10^12, therefore i got e~1. that implies my orbit is a straight line.... so where did i go wrong? also, this feels like ALOT of steps so am i over thinking it?? Oh and for orbital energy I think the equation is E=-GM/2a. is that correct?