Binary Star initial positions and velocities

In summary, the conversation discusses computing binary star orbits based on initial parameters, positions, and velocities. The stars are assumed to be in circular orbits around a common center of mass at the origin and on the x-axis. The relevant dimensionless properties for mass, distance, and time are also introduced. The primary and secondary masses are determined to be 4/5 and 1/5, respectively. The conversation ends with a request for help in expressing initial positions and velocities in terms of mass for circular orbits.
  • #1
Astro_Husky
1
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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:
Massprimary ≡ Massprimary/M
Masssecondary ≡ Masssecondary/M
where M = Massprimary + Masssecondary

Distance = Xprimary ≡ Xprimary/a
Xsecondary ≡ Xsecondary/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.
 
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  • #2
Astro_Husky said:
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?
 

FAQ: Binary Star initial positions and velocities

1. What determines the initial positions and velocities of binary stars?

The initial positions and velocities of binary stars are determined by the conditions present at the time of their formation. This includes factors such as the mass of the stars, their distance from each other, and the environment in which they were formed.

2. How do scientists measure the positions and velocities of binary stars?

Scientists use various techniques such as spectroscopy, astrometry, and interferometry to measure the positions and velocities of binary stars. These methods involve analyzing the light emitted from the stars and using mathematical models to calculate their positions and velocities.

3. Can the initial positions and velocities of binary stars change over time?

Yes, the initial positions and velocities of binary stars can change over time due to various factors such as gravitational interactions with other stars, gas clouds, and planets. These changes can also be caused by the aging and evolution of the stars themselves.

4. Do all binary stars have the same initial positions and velocities?

No, not all binary stars have the same initial positions and velocities. The conditions present during their formation can vary, leading to differences in their initial positions and velocities. Additionally, the type of binary star (e.g. visual, spectroscopic, eclipsing) can also affect their initial properties.

5. Why is it important to study the initial positions and velocities of binary stars?

Studying the initial positions and velocities of binary stars can provide valuable information about their formation and evolution. It can also help scientists understand the dynamics of star systems and the effects of various factors on their movement and behavior. This knowledge can contribute to our overall understanding of the universe and its origins.

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