Question

A newly discovered comet orbits the sun at an average distance of 18.9 AU with an eccentricity of e = 0.38.

Calculate the comet's aphelion distance in AU using the equation:

                         aphelion = a (1 + e).

Give your answer to one decimal place.

You will need to show your work, including units, in E1.36d.

Answer 1

Recall that P² = a^3, where

P=The orbital period (in earth years), and

a=The length of the semi-major axis in astronomical units (AU) (also known as the average distance from the orbiter and orbital, in this case the star and the planet)

An astronomical unit is equal to the semi-major axis of the Earth-sun system, more precisely it's 149,597,871km (I usually round this off to 150 million km to make calculations easier)

Now to solve for the equation...

p² = a³

we take the square of both sides to get...

p = sqrt(a³ )

or

p = a^3/2

Now we plug in our known value for a of 18.9 AU to get

p=18.9^3/2= 82.166 earth years

Aphelion distance (in au) = a(1+e)

Where a is the semi-major axis, and e is the eccentricity. From here it is fairly straightforward to solve.

Aphelion distance (in au) = (18.9)(1+(0.38))= 26.082 AU