Kepler’s Third Law states that the ratio T/a^3/2 is equal to a constant C for all planetary orbits around the sun, where T is the period (time for a complete orbit) and a is the semimajor axis.

(a) Compute C in units of days and kilometers, given that the semimajor axis of the earth’s orbit is 150 × 10⁶ km.

(b) Compute the period of Saturn’s orbit, given that its semimajor axis is approximately 1.43 × 10⁹ km.

(c) Saturn’s orbit has eccentricity e = 0.056. Find the perihelion and aphelion of Saturn (see Exercise 63).

Data From Exercise 63

Kepler’s First Law states that planetary orbits are ellipses with the sun at one focus. The orbit of Pluto has eccentricity e ≈ 0.25. Its perihelion (closest distance to the sun) is approximately 2.7 billion miles. Find the aphelion (farthest distance from the sun).