Calculating a Planetary Year for Krau?

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Homework Help Overview

The problem involves calculating the orbital period of planet Krau based on its relationship with planet Rool in a planetary system around the star Dagobahr. The context is rooted in celestial mechanics, specifically Kepler's Third Law of planetary motion.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the application of Kepler's Third Law, questioning how to manipulate the equation relating the orbital periods and radii of the two planets. There is an exploration of the relationship between the increase in orbital radius and the corresponding change in orbital period.

Discussion Status

The discussion is ongoing, with participants offering guidance on rearranging the equation and substituting known values. There is a mix of interpretations regarding the proportional relationships defined by Kepler's Law, with some participants questioning assumptions about direct proportionality.

Contextual Notes

There is a lack of clarity regarding the specific values for the orbital radius of Krau, which is necessary for further calculations. Participants are also navigating the implications of Kepler's Third Law in their reasoning.

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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