# Question about gravitational force(Binary star)

• Clara Chung
In summary, in a binary star system, if the two centres of rotation and mass do not coincide, there will be a net moment and the system will collapse. The book's approach involves using the sum of moments about the centre of mass to determine the mass of each star in a circular orbit.
Clara Chung

## Homework Statement

In a binary star system, the centre of rotation of the system coincides with its centre of mass. If the two centres do not coincide, there arises a net moment and the system will collapse.

## The Attempt at a Solution

But refer to the photo, isn't
Fh = Fh , so there is no net moment?

Clara Chung said:
If the two centres do not coincide, there arises a net moment and the system will collapse.
That's a very odd statement. First, "centre of rotation" implies circular orbits, whereas in general each will follow an elliptical orbit, the common mass centre being at a focus of each. Secondly, if circular, I do not understand how the centres might not coincide.
Clara Chung said:
Fh = Fh
I think the author is referring to angular momentum rather than moments of forces, but I could be wrong.

haruspex said:
That's a very odd statement. First, "centre of rotation" implies circular orbits, whereas in general each will follow an elliptical orbit, the common mass centre being at a focus of each. Secondly, if circular, I do not understand how the centres might not coincide.

I think the author is referring to angular momentum rather than moments of forces, but I could be wrong.

Yes. It is a circular orbit. The question originally ask for the mass of each star if the radius of orbit P is twice that of Q. P and Q are the stars in a binary system. My approach is listing out an equation with equal force and angular velocity. However my book approach is :
Sum of moments about center of mass is zero.
Mp r = Mq 2r
So the mass of p is half of that q.
I don't understand the statement of sum of moments about cg is zero

Clara Chung said:
I don't understand the statement of sum of moments about cg is zero
Clara Chung said:
Mp r = Mq 2r
Ok, I see. The book is using "moment" to refer to the first moment of mass, i.e product of mass and displacement from axis. When the chosen axis is the common mass centre, the sum of the first moments of mass is zero.

Clara Chung

## 1. What is gravitational force in a binary star system?

Gravitational force in a binary star system is the force of attraction between the two stars due to their masses and distance from each other. It is responsible for keeping the stars in orbit around each other.

## 2. How does the distance between the two stars affect the gravitational force in a binary star system?

The gravitational force between two stars in a binary system is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. This means that the closer the stars are to each other, the stronger the gravitational force between them.

## 3. What determines the orbital period of a binary star system?

The orbital period of a binary star system is determined by the masses of the two stars and the distance between them. The larger the masses and the smaller the distance, the shorter the orbital period will be.

## 4. Can the gravitational force in a binary star system cause one star to "steal" mass from the other?

Yes, in some cases, the gravitational force between two stars can cause one star to pull matter from the other. This is known as mass transfer and can result in changes to the orbits and characteristics of the stars.

## 5. How does the study of binary star systems contribute to our understanding of gravity?

Binary star systems provide a unique opportunity to study the effects of gravitational force on celestial objects. By analyzing the orbital characteristics of binary stars, scientists can gain a better understanding of the laws of gravity and how it influences the movements and interactions of objects in space.

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