Question

Ou discover a small body in space, a comet or asteroid, and after measuring its path through space, you find that it has an orbital period of 1 million years. Where does this object most likely reside?

Answer 1

A body with a period of a million years would be at a distance of 10,000AU.

Explanation:

Using Kepler's third law we can relate the period `T` to the semi-major axis distance `a`.

`T^2=a^3`

Given that `T=1,000,000` then:

`a^3=1,000,000,000,000`

Taking the cube root gives:

`a=10,000AU`

What is missing is the eccentricity of the orbit. If the orbit is nearly circular it would be at 10,000 AU which is way beyond the edge of the solar system. This area is where the Oort Cloud is thought to be and where long period comets come from.

Given that Neptune is 30AU from the Sun this would be 300 times as distant as Neptune. Even the projected planet 9 is only thought to be 700 AU from the Sun.

If the eccentricity of the orbit is high, like in a comet, then it could get quite close to the Sun, but it's aphelion would be much more distant. It would most likely be a comet originating in the Oort Cloud.