Question

If the Sun were orbited by a star of 1.8 solar masses at Jupiter's distance of 5.2 AU (or, more precisely, the Sun and the other star were orbiting each other 5.2 AU apart), what would be the orbital period of the system?

Answer 1

Based in the question you have given me, you will need to study Kepler's third law.

M=mass

a= average distance of the object

P= period of the orbit (EXPRESSED IN TIME UNITS)

Kepler's third law shows the relationship between the period of and objects orbit and the average distance that it is from the thing it orbits.

This means that in our problem we have mass (1.8 solar masses) and distance (5.2 AU).

Orbital period of the system (P)=?

We have a formula that states:

P ^2= k a^3

k is a constant which has various values depending upon what the situation is (depends upon a and P)

So, in order to answer this question, we will need to calculate k.

It is important to understand this key point: "astronomical unit: The mean distance from the Earth to the Sun (the semi-major axis of Earth’s orbit), approximately 149,600,000 kilometres (symbol AU), used to measure distances in the solar system". Because this is needed to calculate k.

We have that " The value of this constant is equal to 4 * pi^2 / G * M where G = 6.67 x 10^-11 Nm^2/kg^2 and M is the mass of the orbited body such as the sun".

With this in mind you can be able to get k, because you have every value. Once you obtain k, you can use the first formula that I worte here in the Answer tab, in order to get P.