# Binary Star system common period

• slft
In summary: Thus, they must have different masses.In summary, a binary star system consists of two stars orbiting around their common center of mass. The two stars are always diametrically opposite each other because of the direction of the gravitational force acting on them, which also explains why they have a common period. The inner star is more massive due to the conservation of momentum and the fact that the centripetal force acting on each star is the gravitational force.
slft

## Homework Statement

The questions are about binary star system.

## Homework Equations

Why the two stars in a binary star system are always diametrically opposite positions?
Why the two stars have common period?
Why the inner star is more massive?

## The Attempt at a Solution

For the period question, I'm thinking that they have same angular velocity, but I know that I should use force to explain why, but I don't know how to explain using gravitational force.
For the mass question, I think it's because of conservation of momentum, but don't know if it is right or how to explain.

Let us look at the definition of a binary star system: "a star system consisting of two stars orbiting around their common center of mass" according to Wikipedia. This succinct description in fact encodes all that you need to know to solve the question.
1. If the two stars are not diametrically opposite each other, what is the direction of the gravitational force acting on each of them? Can it possibly allow them to undergo circular motion?
2. This is linked to the first question. If they do not have the same period, then they would not always be diametrically opposite each other.
3. Based on the above two ideas, you can easily prove this using the fact that centripetal force acting on each is the gravitational force acting on it.

I would like to provide a response to the questions about binary star systems. Firstly, the two stars in a binary star system are always in diametrically opposite positions due to gravitational forces. Just like the Earth and Moon, the two stars in a binary system are attracted to each other by the force of gravity. This force acts in a straight line between the two stars, causing them to orbit around their common center of mass. This results in the two stars being in opposite positions at all times.

Secondly, the two stars in a binary system have a common period because they are in a stable orbit around each other. This means that the gravitational force between the two stars is balanced by their centrifugal force, resulting in a circular orbit. This circular orbit has a specific period, which is determined by the masses and distances of the two stars. As long as the masses and distances remain constant, the period of the orbit will also remain constant.

Lastly, the inner star in a binary system is usually more massive because of the conservation of angular momentum. When a binary system forms, the two stars are formed from the same cloud of gas and dust. As they are forming, they start to rotate due to the conservation of angular momentum. The inner star, being closer to the center of mass, has a shorter distance to travel in the same amount of time, resulting in a higher angular velocity. This higher angular velocity requires a larger mass to balance out the forces and maintain a stable orbit. Therefore, the inner star tends to be more massive than the outer star in a binary system.

I hope this explanation helps to clarify the concepts of binary star systems. If you have any further questions, please feel free to ask.

## 1. What is a binary star system?

A binary star system is a system of two stars that orbit around a common center of mass due to their gravitational attraction.

## 2. What is the common period in a binary star system?

The common period in a binary star system refers to the time it takes for both stars to complete one orbit around their center of mass. It is also known as the orbital period.

## 3. How is the common period in a binary star system calculated?

The common period in a binary star system can be calculated using Kepler's third law, which states that the square of the orbital period is proportional to the cube of the semi-major axis of the orbit. This can be expressed as P^2 = a^3, where P is the orbital period and a is the semi-major axis.

## 4. Why is the common period important in binary star systems?

The common period is important in binary star systems because it provides information about the masses and distances of the stars. It also affects the stability of the system and can influence the evolution of the stars.

## 5. Can the common period change in a binary star system?

Yes, the common period in a binary star system can change over time. This can be caused by interactions with other stars or planets, or by changes in the internal structure of the stars. However, these changes are usually small and occur over long periods of time.

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