Challenging High School Planetary Mechanics Problem

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Homework Help Overview

The discussion revolves around a binary star system problem in planetary mechanics, focusing on the calculation of the common period of revolution for two stars with different masses and a specified distance between them.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to equate centripetal force and gravitational force to solve for the period of revolution but expresses uncertainty about the method. Participants discuss the distinction between the radius used in the centripetal force equation and the distance between the stars, raising questions about the center of mass and its relevance to the problem.

Discussion Status

Participants are exploring the relationship between the forces involved and the geometry of the system. Some guidance has been provided regarding the need to determine the center of mass, but there is no explicit consensus on the approach or the necessity of a sketch for visualization.

Contextual Notes

There is an indication of confusion regarding the definitions and calculations related to the center of mass, as well as the need for a visual representation of the problem setup.

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Homework Statement


A certain binary star system consists of two stars of masses m and 3m respectively separated by a distance of 1.5 * 10^12 m measured between their centres. These stars revolve in sync with each other around their common centre of mass. If the smaller star has a mass of 1.0 * 10^30 kg, what is their common period of revolution?

r = 1.5 * 10^12 m
m1 = 1.0*10^30 kg
m2 = 3.0*10^30 kg

Homework Equations



Fg = Gmm/r^2
Fc = 4mpi^2r/T^2

The Attempt at a Solution



Initially, I thought I could do Fc = Fg and solve for period, but I'm not sure if that's the right way to do it and it doesn't sound right either.
 
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Your method is correct in principle. A slight complication is that the r's in both equations are different. One is measured from the center of revolution, another is the distance between the bodies. Which one is which and how are they related?
 
Oh, so the r in Fc is different. Center of revolution means I need to know my center of mass, right? Another problem I'm having is I'm not sure exactly how the sketch for this works, if that's needed at all?
 
Yes, you need to find out the C. M. I am not sure what your problem with the sketch is.
 
Do I need a sketch (to know visualize/see the diagram of the problem) to find the C.M.? I'm not sure how to find it.
 
What is the definition of the C. M.?
 

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