Find Pluto's year length using Kepler's third law.

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Homework Help Overview

The problem involves determining the length of a year on Pluto using Kepler's third law of planetary motion. The original poster states that Pluto is 40 times further from the Sun than Earth and seeks to find Pluto's orbital period based on this information.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to apply Kepler's third law by relating the orbital periods and distances of Earth and Pluto, but expresses uncertainty about the next steps. Some participants question the understanding of the constant relationship in Kepler's law and the implications of the distance ratio.

Discussion Status

The discussion is ongoing, with participants providing hints and prompting further exploration of the concepts involved. There is a focus on clarifying the relationship between the distances and periods of the planets, but no consensus or resolution has been reached yet.

Contextual Notes

Participants note the importance of understanding the constant ratio of R^3/T^2 for planets orbiting the same star, as well as the specific distance relationship between Earth and Pluto. There is an indication that the original poster may have misunderstood some aspects of the problem setup.

D.J Falcon
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Homework Statement



Pluto is 40 times further from the Sun than we are. How long is a year on Pluto? (Use Kepler's third law.)


Homework Equations



4∏^2/Gm=T^2/r^3


The Attempt at a Solution



Te^2(Earth period)=x*r^3

Tp^2(Pluto period)=x*(40r)^3


I don't know what to do exactly from here. I'm not even entirely sure that I'm going about this the right way.

Any help would be appreciated.
 
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Hint: For every planet [which goes around the sun] in our solar system R^3/T^2=constant.
Why?
 
estro said:
Hint: For every planet [which goes around the sun] in our solar system R^3/T^2=constant.
Why?

I've already made x a constant (T^2/r^3), in the attempt at a solution. I just don't realize what to do from there.
 
I don't know what you mean by:
D.J Falcon said:
I've already made x a constant (T^2/r^3), in the attempt at a solution.
...

First of all you need to understand why for every planet which goes around the same star R^3/T^2 is constant.
Then don't forget what you already know about the difference in R between Earth and Pluto.

I'm already gave you the answer, actually...
 

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