In this problem we will make use of the fact that for closed orbits the latus rectum a of the orbit is equal to a gm where g is the universal gravitational constant, / is the angular momentum per unit mass of the orbiting body, and mis the (much larger) mass of the body at one focus of the orbit the following questions refer to the shuttlecraft orbit shown in problem 1 above use your knowledge of kepler's laws and your results in problem 1 to determine expressions for (i) the shuttle's speed vp at perigee, and (ii the shuttle's speed va at apogee. write each expression in terms of g, m e, and the corresponding distance (rp or ra) a. b. use your results from part a of this problem to calculate the quantities listed below. in your work, assume that the planet has approximately the same radius and mass as earth (ie., rplanet re 6.38 x 10° m, and gms gme 3.98 x 10 n-m-/kg). in addition, suppose that the orbit of the shuttle has perigee rp = 2re and apogee ra = 8re. 14 = = i. the eccentricity e of the original (elliptical) orbit ii. the latus rectum a of the orbit iii. the speed vp at perigee in the orbit iv. the speed va at apogee in the orbit the minimum speed your shuttlecraft must attain at point p (e. g., by quickly firing your thrusters as you pass that point) in order to leave the planet v. (hint: what minimum value of eccentricity e is required for the shuttle's orbit in this case? )