Question

A comet orbits the Sun with a period of 72.0 yr.

(a) Find the semimajor axis of the orbit of the comet in astronomical units (1 AU is equal to the semimajor axis of the Earth's orbit).
(b) If the comet is 0.60 AU from the Sun at perihelion, what is its maximum distance from the Sun and what is the eccentricity of its orbit?

The answers are (a) 17.3 AU and (b) 34 AU; 0.965. I've forgotten how to solve for these answers. Any help is appreciated.

Answer 1

(a) Kepler's Third law for objects orbiting the sun says:
a^3 = P^2, where P is the period in years and a is the semimajor axis in a.u. .

Since P = 72.0 y,

a = 17.31 a.u.

(b) 2a = (perihelion distance)+ (aphelion distance)

Therefore
aphelion (greatest) distance = 34.0 a.u.

The perihelion distance is
0.6 au = (1 - e) a , so
1 - e = 0.6/17.3 = 0.0347
e = 0.9653

=