Suppose you are observing spec

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


The wavelength of H alpha line is 656.28 nm.

For a binary system of two stars, they will be rotating withtheir 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 comingtowards him.

The relative motion will cause a red shift to one light and ablue 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 (solarmass)

and G = 6.67*10-11

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