Answer to Question #246146 in Molecular Physics | Thermodynamics for Kelani

Question

A comet has a period of 80.8 years and moves in an elliptical orbit in which its perihelion (closest approach to the Sun) is 0.670 AU. Find the semimajor axis of the comet and an estimate of the comet's maximum distance from the Sun, both in astronomical units.

(a) the semimajor axis of the comet (in AU)

__ AU

(b) an estimate of the comet's maximum distance (in AU) from the Sun

 ___AU

Answer 1

a)

$T^2=a^3,\implies$ $a=18.69~\text {AU},$

b)

$q=a(1-e),\implies$

$e=1-\frac qa=0.964,$

$Q=a(1+e)=36.71~\text{AU}.$