(a) Use Fig. 12.19 to show that the sun-planet distance at perihelion is (1 - e) a, the sun-planet distance at aphelion is (1 + e la, and therefore the sum of these two distances is Za.
(b) When the dwarf planet Pluto was at perihelion in 1989, it was almost 100 million km closer to the sun than Neptune. The semi major axes of the orbits of Pluto and Neptune are 5.92 X 1012 m and 4.50 X 1012 m, respectively, and the eccentricities are 0.248 and 0.010. Find Pluto's closest distance and Neptune's farthest distance from the sun.
(c) How many years after being at perihelion in 1989 will Pluto again are at perihelion?