Question

Astronomist using the most advanced telescope have only recently seen evidence of planets orbiting nearby stars. These are called extra-solar planets. Suppose a planet is observed to have a 1200 day period as it orbits a star at the same distance that Jupiter is from the sun. What is the mass of the star in solar masses.(SOLAR MASS IS DEFINED TO BE THE MASS OF THE SUN)

Answer 1

You will want to use Keplers law here. Keplers law states that the square of the orbital period \(T\) of a body about a central mass is proportional to the cube of the distance \(R\) of the object from the mass it is orbiting. Here I will assume circular orbits (but it applies to the more general elliptical orbit if radius is replaced with semi-major axis.)
In equation form, this law is \[T^{2} = \frac{4\pi^{2}}{GM}R^{3}\]
It is trivial then to work out the mass of the star, since we know \(T\), and we know what the Jupiter-Sun Distance is 5.2 AU (where 1 AU is the mean distance from the earth to the sun = \(1.496 \times10^{8})\) Km). Remember though to use appropriate units. If in any doubt, always convert to SI units. If you use the AU values, then make sure you calculate in units of years, so 1200/365.25 would be the period of the exo-planet in years.

Answer 2

If you want to join in on the hunt for extrasolar planets and make a real contribution to the advancement of scientific knowledge go to http://www.planethunters.org/ or the parent site www.zooniverse.org