Total energy ofa closed two-body system in this problem we calculate the total energy of a system consisting of one body (mass m) orbiting another body (mass m» m) along a closed elliptical orbit in so doing we will make more general the result we found in tutorial for a circular orbit of radius ro 1. gmm ent (circular orbits only) 2r, highly eccentric orbit. let the center of the consider a comet (mass m) orbiting a star (mass m) star be located at the origin (r=0) of a polar coordinate system in a 2 recall that the angular momentum per unit mass (of the comet can be written / = r*0, and also that the latus rectum a of the orbit is related to / according to: /= (gma)1. 1/2 we first need to express the kinetic energy of the comet. to do this we note that the velocity of the comet can be written in polar coordinates as follows: = rê, +rô e, a. starting with this expression for velocity, write two expressions for the kinetic energy of the comet: ( one that is written in terms of r, f, and 0, and then (ii) eliminate 0 from your expression so that it is written instead in terms ofr, f, and /. clearly show al1 work. b. now express the total energy (etot) of the comet-star system, and do this in two ways: (i) write expression in terms ofr, f, i, and given constant parameters, and then (ii) eliminate / from clearly show all work one your expression so that it is written instead in terms ofr, r, and a you result in part b is valid for all points along the orbit of the comet, although in its present form it may not appear very useful. however, your expression can be simplified when considering the distances of closet approach (perihelion) and farthest approach (aphelion) of the comet c. what simplification can be made for perihelion and aphelion? explain 1. ii. show that your expression for eot simplifies to the same expression for both perihelion (p a/(1e)) and aphelion (ra = a/(1 e). your final expression will be in terms of just the semi-major axis a of the comet's orbit, the masses m and m of the comet and star, and g an be expressed in terms of a and e as follows: a a(1 - 2)