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Suppose you are observing spectroscopic binary system of two stars, each with M = 1 solar...

Suppose you are observing spectroscopic binary system of two stars, each with M = 1 solar mass and T = 5770K. How far apart would the stars have to be for you to distinguish seperate Halpha lines?

Solutions

Expert Solution

The wavelength of H alpha line is 656.28 nm.

For a binary system of two stars, they will be rotating with their common center of mass as the center.

According to an observed far away from the system

when one star is moving away from him, the other will be coming towards him.

The relative motion will cause a red shift to one light and a blue shift to another light.

This shift depends on the relative velocity of the system

The gravitational force between the system is

F = Gm^2/d^2

The centrifugal force is F = mv^2/(d/2)

Equating the both

This is the velocity of one star.

So, the relative velocity between the two stars as seen by earth =

According to Doppler shift,

In terms of wavelength,

The least count of H alpha filter is 0.07 nm

Taking the shift as twice this least count,

Using this in the equation, with M = 2*10³⁰ kg (solar mass)

and G = 6.67*10^-11

genius_generous answered 1 year ago

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