What is the concept of concentrated mass?

[DB]

A little confused, could someone explain what it means when it is said that "the point in a body or a system of bodies, at which the total mass of the body or system may be regarded as concentrated".(definition of Center of mass) What does it mean concentrated? I'm trying to understand the concept of Binary Stars and I can seem to put it all together.

 

[silverpig]

Balance a book on your finger. The centre of mass is a point in the book just above your finger. It's the point where the mass of the book seems to be located.

Now all binary systems have the bodies orbitting the common centre of mass. In the limit that one body is large (sun) and the other is small (small planet) it seems as though the sun is stationary and the planet revolves around it. This is usually a good approximation, however they do in fact both orbit around their combined centre of mass. Because of how the centre of mass is calculated, for this system it will be inside the large sun so it doesn't seem to move very much.

In a binary star system, you have two roughly equal masses. The centre of mass is therefore located about halfway between them, and they both revolve around it.

 

[DB]

Thanks, though wat is it that creates the stars to revolve around the center of mass?
Is it a mix of gravitational force from each star that creates this center of mass?

 

[Nereid]

Thanks, though wat is it that creates the stars to revolve around the center of mass?
Is it a mix of gravitational force from each star that creates this center of mass?

Conservation of angular momentum, gravity.

The details of how a binary star is formed are fascinating, intricate, and not yet fully understood. As a one sentence summary: as a gas cloud collapses under its own, self-gravity (losing energy through radiation), it fragments; if two of these fragments collapse to form stars, with relative motions in the 'right' range, they will form a gravitationally bound system - i.e. they will orbit a common centre of mass.

 

[DaveC426913]

"What does it mean concentrated"

I think, more to the point, what it is referring to, is this:

When considering the gravitational effect of any number of bodies upon a second body, it's effect can be treated as an equivalent gravitational mass concentrated at the gravitiational centre of the system.

In practice, examples:

1] The pull of the Earth/Moon system on Mars will be the same as a point-sized object whose mass is equal to the sum of the Earth and Moon, and located at the gravitational centre of the Earth/Moon system.

2] The pull of all the other planets in the Solar System upon the Earth is exactly equivalent to the pull of a single body with the mass of all those other planets, and located at their mutual centre of gravity.

i.e. the physical arrangement of a bunch of masses does not alter its gravititational effect on other bodies.


Unless - you are close enough to the system to experience *tides* (gravitiational gradient).