Calculating a Planetary Year for Krau?

[omgitsmonica]

Homework Statement

"Yoda has just discovered planetary system consisting of star Dagobahr and its two planets: Rool and Krau. Planet Rool has average orbital radius 1.6 times as big as planet Krau. If planet Rool orbits Dagobahr in 2.9 Earth years, how long is a year for the resident of Krau? Give the answer in Earth years.

Homework Equations

Trool^2/rRool^3 = TKrau^2/rKrau^3

The Attempt at a Solution

TRool =?
rRool = 1.6*rKrau
Tkrau=2.9
rkrau=?

I have no idea where to go from here...

 

[Janus]

Try re-arranging your equation so that the orbital radii are on the same side. What happens if you substitute your values into the equation?

 

[horatio89]

Homework Statement

"Yoda has just discovered planetary system consisting of star Dagobahr and its two planets: Rool and Krau. Planet Rool has average orbital radius 1.6 times as big as planet Krau. If planet Rool orbits Dagobahr in 2.9 Earth years, how long is a year for the resident of Krau? Give the answer in Earth years.

Homework Equations

Trool^2/rRool^3 = TKrau^2/rKrau^3

The Attempt at a Solution

TRool =?
rRool = 1.6*rKrau
Tkrau=2.9
rkrau=?

I have no idea where to go from here...

Kepler's Third Law can be rewritten as R = kT^2/3, where k is the constant of proportionality. When R increases by 1.6, by what factor does T increase?

 

[omgitsmonica]

Does T increase by 1.6, too?

 

[horatio89]

That is incorrect. T would increase by 1.6 if T and R are directly proportional. However, according to Kepler's Law, R is proportional to T^2/3.