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,

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

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##