What does momentum conservation reveal about period and mass of binary systems?

In summary, a binary star is composed of two stars orbiting a common center, with the only force acting on them being the gravitational force along the line connecting them. The total momentum of the binary is constant due to the conservation of momentum, as there are no external forces acting on the system. The two stars are always in a diametrically opposite position in order for their velocity vectors to have opposite directions and maintain a constant net momentum. This also explains why the two stars have a common period of rotation and the inner star is more massive, as the outer star must have a longer distance to travel in order to maintain the same period. No equations are needed for this explanation.
  • #1
FelixISF
23
0

Homework Statement


A binary star consists of two stars that are orbiting a common centre. The only force acting on the stars is the gravitational force of attraction in a direction along the line joining the stars.

a) Explain carefully why the total momentum of the binary is constant.

b) Explain why the two stars are always in a diametrically opposite position.

c) Hence explain why the two stars have a common period of rotation and why the inner star is the more massive of the two.


Homework Equations



No equations needed.



The Attempt at a Solution



a) The total momentum p = m1 x v1 + m2 x v2. Since there are no external forces acting on the binary system, momentum is by definition conserved.

--> Does that also imply that the momentum is constant? Because I think that the momentum could vary during one complete revolution and still be conserved right?

b) They must be in a diametrically opposite position in order for their velocity vectors to have opposite directions. If the were not diametrically opposite, the net momentum would not be constant.

c) I have no clue here..
 
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  • #2
A quick hint'd suffice..
 

Related to What does momentum conservation reveal about period and mass of binary systems?

1. What is momentum conservation and how does it relate to binary systems?

Momentum conservation is a fundamental principle in physics that states that the total momentum of a closed system remains constant over time. In binary systems, this means that the total momentum of the two objects orbiting each other will remain constant as they move around their common center of mass.

2. How does momentum conservation reveal information about the period of a binary system?

According to Newton's second law of motion, the period of a binary system is directly proportional to the square root of the distance between the two objects and inversely proportional to the square root of their combined mass. Therefore, by observing the conservation of momentum, we can determine the period of the binary system.

3. Can momentum conservation tell us anything about the individual masses of the objects in a binary system?

Yes, momentum conservation can reveal the ratio of the masses of the two objects in a binary system. This is because the total momentum of the system is equal to the product of the individual masses and their velocity. By solving for the ratio of the masses, we can determine the individual masses if we know the total momentum and velocity.

4. How does the law of conservation of energy relate to momentum conservation in binary systems?

The law of conservation of energy states that in a closed system, energy cannot be created or destroyed, only transferred from one form to another. In binary systems, this means that the total kinetic energy of the two objects will remain constant as they orbit each other, which is directly related to the conservation of momentum.

5. Can momentum conservation reveal any information about the orbits of the objects in a binary system?

Yes, by observing the conservation of momentum, we can determine the shape and orientation of the orbits of the objects in a binary system. This is because the change in momentum is related to the force acting on the objects, which is dependent on the distance and angle between the objects.

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