Binary Star initial positions and velocities

[Astro_Husky]

Hi all,

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.

 

[gneill]

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

How? I don't see any given data in your problem statement from which such results could be derived.

I cannot even begin to express the initial positions and velocities in terms of mass.
Any help would be very much appreciated.

For circular orbits, what forces are always in balance?