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I've been tasked with computing binary star orbits based on their initial parameters, positions and velocities.

In this problem everything must be expressed in terms of the masses, but I am struggling to define positions and velocities in terms of mass.

It is assumed that the stars are in circular orbits around a common center of mass at the origin (0,0) and the stars are on the x-axis (y=0) at time t=0. The primary star is on the negative x-axis and the secondary is on the positive x axis.

Using the relevant dimensionless properties:

Mass

_{primary}≡ Mass

_{primary}/M

Mass

_{secondary}≡ Mass

_{secondary}/M

where M = Mass

_{primary}+ Mass

_{secondary}

Distance = X

_{primary}≡ X

_{primary}/a

X

_{secondary}≡ X

_{secondary}/a

where, a = initial binary separation

Time = t ≡ t/(sqrt(a^3/GM))

## The Attempt at a Solution

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I got as far as determining the masses of the stars: Primary = 4/5, Secondary = 1/5.

I cannot even begin to express the initial positions and velocities in terms of mass.

Any help would be very much appreciated.