Calculating a Planetary Year for Krau?

AI Thread Summary
To calculate the orbital period of planet Krau, Kepler's Third Law is applied, which states that the square of the orbital period (T) is proportional to the cube of the average orbital radius (R). Given that planet Rool has an orbital radius 1.6 times that of Krau and orbits in 2.9 Earth years, the relationship can be expressed as T_Rool^2/R_Rool^3 = T_Krau^2/R_Krau^3. The challenge lies in rearranging the equation to isolate T_Krau and substituting the known values. It is clarified that T does not increase linearly with R; instead, it increases with the cube root of R, emphasizing the need for proper application of Kepler's Law. The solution requires careful manipulation of the equation to derive Krau's orbital period in Earth years.
omgitsmonica
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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...
 
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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?
 
omgitsmonica said:

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 = kT2/3, where k is the constant of proportionality. When R increases by 1.6, by what factor does T increase?
 
Last edited:
Does T increase by 1.6, too?
 
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.
 
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