Gravitation problem -- Binary star system

[gneill]

Point C is the center of mass of the system. It's the fixed point around which both bodies orbit.

 

[Angie Tom]

I meant Is there a body at point C? star...planet?

 

[Angie Tom]

Point C is the center of mass of the system. It's the fixed point around which both bodies orbit.

View attachment 92177

I meant is there a body at point c?

 

[gneill]

I meant is there a body at point c?

No, it's empty space.

The center of mass of two spherical masses lies along the line joining them, but there's no object associated with that center of mass: it's a mathematical point.

 

[Angie Tom]

Okay

No, it's empty space.

The center of mass of two spherical masses lies along the line joining them, but there's no object associated with that center of mass: it's a mathematical point.

Okay, so this means that the gravitational force is between the 2 masses and the centripetal force is directed from each mass to c right?

 

[gneill]

Okay

Okay, so this means that the gravitational force is between the 2 masses and the centripetal force is directed from each mass to c right?

Correct.

 

[Angie Tom]

Correct.

THANKS A MILLON

 

[Angie Tom]

Why does the normal on a mass have different values at the pole and at the equator?

 

[gneill]

Why does the normal on a mass have different values at the pole and at the equator?

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[haruspex]

Okay

Okay, so this means that the gravitational force is between the 2 masses and the centripetal force is directed from each mass to c right?

I wouldn't word it that way. The mass centres and c are in a straight line, so a direction 'towards c' is the same as 'towards the other star's centre'. Besides, it is important to remember that centripetal force is a resultant force. Your wording might give the false impression that each star is somehow attracted to the common mass centre.

If two stars are on parallel and opposite courses, at right angles to the line joining them at some instant, each experiences attraction towards the other star so accelerates in that direction. Since that is at right angles to their directions of motion, that results in a change of direction, not a change in speed. That is, it will lead them to start to revolve around some points (not necessarily the same point) on the line joining them.
This situation may be transient; a moment later their arrangement no longer matches those conditions.

If the distance between them, their speeds and their masses are in the right relationship to each other, that point will be, for both, the common mass centre. If so, the arrangement is dynamically stable, i.e. they will continue to satisfy all thes conditions and continue to orbit around that common mass centre. But the attaction is always to the mass centre of the other star.

One more point, just to be clear. That each star is attracted to the mass centre of the other is a special feature of spherically symmetric bodies. In reality, each atom of each star is attracted to each atom of the other. But if each star is made of concentric spherical shells, each of uniform mass density, it turns out that the net attraction of each atom of one star is towards the mass centre of the other. The situation would be far more complex with two amorphous lumps of rock orbiting each other.

 

[Angie Tom]

I wouldn't word it that way. The mass centres and c are in a straight line, so a direction 'towards c' is the same as 'towards the other star's centre'. Besides, it is important to remember that centripetal force is a resultant force. Your wording might give the false impression that each star is somehow attracted to the common mass centre.

If two stars are on parallel and opposite courses, at right angles to the line joining them at some instant, each experiences attraction towards the other star so accelerates in that direction. Since that is at right angles to their directions of motion, that results in a change of direction, not a change in speed. That is, it will lead them to start to revolve around some points (not necessarily the same point) on the line joining them.
This situation may be transient; a moment later their arrangement no longer matches those conditions.

If the distance between them, their speeds and their masses are in the right relationship to each other, that point will be, for both, the common mass centre. If so, the arrangement is dynamically stable, i.e. they will continue to satisfy all thes conditions and continue to orbit around that common mass centre. But the attaction is always to the mass centre of the other star.

One more point, just to be clear. That each star is attracted to the mass centre of the other is a special feature of spherically symmetric bodies. In reality, each atom of each star is attracted to each atom of the other. But if each star is made of concentric spherical shells, each of uniform mass density, it turns out that the net attraction of each atom of one star is towards the mass centre of the other. The situation would be far more complex with two amorphous lumps of rock orbiting each other.

This is really helpful! Thanks a lot :D