Rotating binary star system & three star system

In summary, two equal mass stars with a mass twice the sun's were discovered in a binary star system with a period of 90 days. The stars rotate about the center of mass at the midpoint between them. For the second problem, three stars each with a mass of our sun form an equilateral triangle with sides 1*10^12 m long and must rotate to prevent collision. The period of rotation can be calculated by finding the force acting on one star and using trigonometry to find the radius, angular velocity, and finally the period.
  • #1
bcjochim07
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0

Homework Statement


1) Astronomers discover a binary star system that has period of 90 days. The binary star system consists of two equal mass stars each with a mass twice the sun's. They rotate about the center of mass at the midpoint between them. How far apart are the two stars?

2) Three stars each with a mass of our sun, form an equilateral triangle with sides 1* 10^12 m long. The triangle has to rotate because otherwise the stars would collide. What is the period of rotation?


Homework Equations





The Attempt at a Solution



For #1,

There doesn't seem to me to be any clear pivot or mass around which the stars orbit, and that's what baffles me. I thought about pretending they were connected by a massless string and calculating the moment of inertia, and then using rotational kinetic energy, but I'm not sure how to start

#2 I think I'll have a better grasp on this after figuring out #1
 
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  • #2
Hi bcjochimo07,

Draw a force diagram for one of the stars. What is the only force that acts on it? The stars are moving in a circle, so you also know a formula for the acceleration.

Be careful when you assign distances--the distance that is used in the force formula is not the distance that is used in the acceleration formula.
 
  • #3
Thanks! I got the first problem right. Now for the second one... I would have to choose one of the stars and sum the force components. Next I would use trigonometry to find the radius & then I would solve for angular velocity & then the period.
 

1. What is a rotating binary star system?

A rotating binary star system is a system in which two stars orbit around a common center of mass. This type of system is also known as a binary star or a double star system.

2. How do rotating binary star systems form?

Rotating binary star systems form when a large cloud of gas and dust collapses under its own gravity. As the cloud collapses, it begins to spin, forming a disk of material. Eventually, the disk breaks up into smaller clumps, which become the two stars in the system.

3. How do the stars in a rotating binary star system affect each other?

The stars in a rotating binary star system affect each other through their gravitational pull. As they orbit around each other, they can cause one another to wobble or distort their shapes. They may also exchange mass and energy, which can impact their evolution.

4. What is a three star system?

A three star system is a system in which three stars orbit around a common center of mass. This type of system is also known as a triple star system.

5. How common are rotating binary star systems and three star systems?

Rotating binary star systems and three star systems are relatively common in the universe. In fact, it is estimated that about half of all stars are part of a multiple star system. However, these systems can be difficult to detect and study, so our understanding of them is still limited.

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