Find the distance from the sun to the planet known the orbital period problem

[subopolois]

Homework Statement

the problem asks to find the distance from the sun to a planet. the only information the question gives the the orbital period of 27 years and asks for the answer in km.

Homework Equations

c= (2)(pi)(r)

The Attempt at a Solution

assuming the planet revolves around the sun, i was assuming this is a simple problem using the circumference of a circle and solver for r to get the radius which is also the distance to the sun. here's my attempt.
c=(2)(pi)(r)
27=(2)(pi)(r)
r= 27/(2)(pi)
r= 4.29

thats my solution, but is seems really close to the sun, 4.29 km. have i done something wrong? can someone help?

 

[Borek]

Take a look at units - your result is 4.29 years, not kilometers. So obviously there is something wrong.

This is either application of Kepler's third law (but then you need infomation about some other planet distance and period) or of Newton's law of universal gravitation combined with equations of motion (but then you need mass of the Sun). Not knowing in what context this question has been asked it is not possible to decide which approach will be correct (although they will both give the same result, as Kepler's laws can be derived from Newton's law).

 

[the pro]

yup it is calculatet in years not in km