How to Calculate Mass of Binary Star Systems Using Kepler's Law and Iteration?

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Homework Help Overview

The discussion revolves around calculating the mass of an astrometric binary star system using Kepler's laws and iterative methods. The original poster presents a problem involving specific parameters such as the period, semi-major axis, and parallax, while noting that luminosity is neglected.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the interpretation of the problem, particularly whether it refers to the total mass of the system. There are attempts to express the mass ratio and concerns about the lack of knowledge regarding one of the masses. Some participants suggest using iterative methods to solve a cubic equation derived from the mass ratio.

Discussion Status

The discussion is ongoing, with participants exploring various interpretations and approaches to the problem. Some guidance has been offered regarding the use of mass ratios and iterative methods, though there is still uncertainty about the implementation of these methods.

Contextual Notes

Participants note the absence of certain information, such as the second semi-major axis, and the implications of homework constraints that may affect the approach to the problem.

quasarLie
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Homework Statement


I have to calculate the mass of an astrometric binaries with P=10 years, and a1=15mas, parallax w=64mas
the luminosity is neglected

Homework Equations

The Attempt at a Solution


i used this equation:
M_1 + M_2 = \frac{(a/w)^3}{p^2}<br />
but the problem is taht i don't have M1
 
Last edited:
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I suspect when the problem asks you to calculate the mass, they mean the total mass of the system, i.e. M1+M2.
 
No finally, i think that i have to use q =M2/M1= a1/a2 replace in the equation but then i will get a 3 dgree equation which i have to solve it with iterative methode (i don't know how yet)
 
quasarLie said:
No finally, i think that i have to use q =M2/M1= a1/a2 replace in the equation but then i will get a 3 dgree equation which i have to solve it with iterative methode (i don't know how yet)

How will you know a1 and a2?
 
I have a1 i will use Kepler law, it will become
\frac{a_1}{p^2}= M_1\frac{q^3}{(1+q)^2} w^3
the resolution will give a 3rd degree equation which can be solved using:
q_i = (1+q_{i-1})^{2/3} q_0
Until it converge but i don't know how to use this part (to solve this equation with iteration)
 

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