A certain triple-star system consists of two stars, each of mass \( m = 6.7 \times 10^{30} \, \text{kg} \), revolving in the same circular orbit of radius \( r = 3.9 \times 10^{11} \, \text{m} \) about a central star of mass \( M = 4.4 \times 10^{33} \, \text{kg} \) (see the figure). The two orbiting stars are always at opposite ends of a diameter of the orbit. Calculate the period of revolution of the stars.**Diagram Explanation:**- The diagram shows a circular orbit with a central star of mass \( M \) located at the center.- Two smaller stars, each with mass \( m \), are positioned on the orbit at opposite ends of a diameter.- The distance from the center to the orbit is marked as \( r \).- Arrows indicate the direction of the stars' motion along the orbit.

As force between the orbiting stars is very less than the force between the central star and the orbiting star then we only have to consider the central force on one star and calculate the time period and it will be same for both orbiting stars. As in circular orbit Fc=mv2R=GMmR2thenv2=GMRorv=GMRAlso v=2πRT (here, T is the period)then 2πRT=GMRorT=2πRRGM=2πR3GMNow, T=2πR3GM=2π(3.9×1011)3(6.67×10-11)(4.4×1033)orT=2.021×1011=4.5×105s =5.21 days

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A certain triple-star system consists of two stars, each of mass m = 6.7×1030 kg, revolving in the same circular orbit of radius r = 3.9×10¹¹ m about a central star of mass M = 4.4x1033 kg (the figure). The two orbiting stars are always at opposite ends of a diameter of the orbit. Calculate the period of revolution of the stars. m M m

A certain triple-star system consists of two stars, each of mass m = 6.7×1030 kg, revolving in the same circular orbit of radius r = 3.9×10¹¹ m about a central star of mass M = 4.4x1033 kg (the figure). The two orbiting stars are always at opposite ends of a diameter of the orbit. Calculate the period of revolution of the stars. m M m

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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