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knowlewj01

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## Homework Statement

The spectral lines in a low mass main sequence star show sinusodal velocity variations with an amplitude of 500 km/s and a time period of 10 hours

calculate a lower limit to the mass of the unseen binary companion

## Homework Equations

M

_{1}+ M

_{2}= [tex]\frac{4\pi^2a^3}{GP^2}[/tex]

M

_{1}r

_{1}= M

_{2}r

_{2}

a = r

_{1}+ r

_{2}

## The Attempt at a Solution

The redshifted and blueshifted spectral lines show that the star is traveling at 500km/s

in a time period of 10 hoiurs (= 36 000 seconds)

Distance traveled in 1 orbit = 18 000 000 km

radius of orbit = [tex]\frac{18 000 000}{2\pi}[/tex] = 28274334 km

assume that the hidden object is much more massive.

so a = radius of this orbit = 28274334000 m

M

_{1}>> M

_{2}therefore r

_{1}<< r

_{2}

M

_{1}= [tex]\frac{4\pi^2r^3}{GP^2}[/tex]

M

_{1}= 1.30x10^13 kg

this is wrong,

think i may have made a mistake when i said that the hidden object is much more massive, can this be solved without making an assumption?