# B What constitutes a body of mass?

1. Mar 5, 2016

### cjs94

How close do objects have to be to be considered a single mass? On Earth, with solid objects, the answer would seem to be intuitive: if an object can't fall any further then it is 'connected' to, or part of Earth's mass. But what about something like a gas giant, or a star?

I started thinking about this after learning of the Chandrasekhar limit. If there was a stable white dwarf whose mass was right on the limit and I threw an object at it, how close would it have to get before the star becomes unstable?

Chris

2. Mar 5, 2016

### Simon Bridge

When is a composite body a single mass?
Depends on the equipment you are using to do the measurement ... if the composite object is close enough that the equipment sees a point source within accuracy, it's a single mass. From an optical telescope, solar systems about other stars are a single mass.

Another way of looking at it: an object is a single mass if single-mass models are more useful at predicting it's behaviour than multimass models.
For instance, all solids are collections of atoms vibrating in a lattice: however the multi-atom model of the solid (requires quantum mechanics) is a lot less convenient for designing a go-cart than Newton's laws applied to rigid bodies.

For the chandrasakar limit dwarf .. it is already unstable: it is like a pin balanced on it's point.
Try looking more at two stars approaching each other ... see what happens.

3. Mar 5, 2016

### cjs94

Thanks, but I was asking more about the natural effects of mass rather than its perception by an observer. My understanding of the Chandrasekhar limit is that if a star is below the limit then it will remain a white dwarf indefinitely, but if it is over the limit then it will start to collapse. My question is, if I throw at a star below the limit an object of sufficient mass to make it exceed the limit, how close does the object have to get to the star before it is considered 'part of' it and causes it to start collapsing?

4. Mar 5, 2016

### Staff: Mentor

The derivation of the Chandrasekhar limit assumes spherical symmetry and stability. So you couldn't just throw a mass, you have to wait until the system becomes spherically symmetric and stable.