(a) Express the eccentricity of the elliptic orbit described by a satellite about a planet in...

Question:

(a) Express the eccentricity ε of the elliptic orbit described by a satellite about a planet in terms of the distances ances r0 and r1 corresponding, respectively, to the perigee and apogee of the orbit.

(b) Use the result obtained in part a and the data given in Prob. 12.113, where Rε=93.0×106 mi, to determine the appropriate maximum distance from the sun reached by comet Hyakutake. Problem 12.113: Based on observations made during the 1996 sighting of the comet Hyakutake, it was concluded that the trajectory of the comet is a highly elongated ellipse for which the eccentricity is approximately ε = 0.999887. Knowing that for the 1996 sighting the minimum distance between the comet and the sun was 0.230RE , where RE is the mean distance from the sun to the earth, determine the periodic time of the comet.