Rotating binary star system & three star system

Click For Summary
SUMMARY

The discussion centers on solving two problems related to binary and three-star systems in astrophysics. The first problem involves a binary star system with a 90-day orbital period and two stars, each with a mass of twice that of the Sun, requiring the calculation of their separation distance. The second problem involves three solar-mass stars forming an equilateral triangle with sides of 1 x 1012 m, necessitating the determination of the period of rotation to prevent collisions. Key insights include the importance of force diagrams and the distinction between distances used in force and acceleration calculations.

PREREQUISITES
  • Understanding of Newton's laws of motion
  • Familiarity with circular motion and centripetal acceleration
  • Knowledge of gravitational forces and mass calculations
  • Basic trigonometry for calculating distances and angles
NEXT STEPS
  • Study Newton's law of gravitation and its application to binary star systems
  • Learn about centripetal force and its role in circular motion
  • Explore the concept of moment of inertia in rotating systems
  • Investigate angular velocity and its relationship to rotational period
USEFUL FOR

Astronomy students, astrophysicists, and educators seeking to deepen their understanding of binary and multi-star systems, particularly in the context of orbital mechanics and gravitational interactions.

bcjochim07
Messages
366
Reaction score
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
 
Physics news on Phys.org
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.
 
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.
 

Similar threads

High School Question: Orbital mechanics of a binary star system
  • · Replies 5 ·
Replies
5
Views
3K
What is the distance and mass of a binary star system with given parameters?
  • · Replies 5 ·
Replies
5
Views
2K
Binary system of stars (##\alpha## - centauri)
  • · Replies 5 ·
Replies
5
Views
2K
Question about gravitational force(Binary star)
  • · Replies 3 ·
Replies
3
Views
2K
Find Absolute Magnitude, distance and "T" of binary star system
  • · Replies 10 ·
Replies
10
Views
3K
Centre of mass of binary system calculation
  • · Replies 8 ·
Replies
8
Views
2K
Combined magnitudes of two solar-type stars
  • · Replies 6 ·
Replies
6
Views
2K
Finding the period of rotation of this system....
  • · Replies 8 ·
Replies
8
Views
3K
Finding the mass of a planet is a binary system
  • · Replies 2 ·
Replies
2
Views
6K
Binary Star Systems: Radial Velocities, Observations & Unresolved Eclipses
  • · Replies 1 ·
Replies
1
Views
2K