Question

What formula would be used to calculate the aphelion distance of Halley's Comet from the sun? Halley’s comet has a perihelion distance of 0.6 AU & an orbital period of 76 years,

Answer 1

Given the aphelion distance and period given the perihelion distance is 35.28AU.

Explanation:

Kepler's third law relates the orbit period T in years to the semi-major axis distance a in AU using the equation `T^2=a^3`. If `T=76` then `a=17.94`.

Given that the comet's orbit is an ellipse then the sum of the perihelion distance and the aphelion distance is twice the semi-major axis `d_a+d_p=2a` or `d_a=2a-d_p`. We have `d_p=0.6` and `a=17.94` then `d_a=2*17.94-0.6=35.28AU`.

A direct equation relating the three values would be: `d_a=2*T^(2/3)-d_p`