# The Naked Scientists Forum

### Author Topic: Is the equivalence principle valid?  (Read 2186 times)

#### jeffreyH

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##### Is the equivalence principle valid?
« on: 27/06/2015 13:50:35 »
Consider an object at rest at the Lagrange point between two large but unequal masses. Then consider that the two masses are moving towards each other due to mutual gravitational attraction. As the masses move together the central object should tend towards the smaller mass as the Lagrange point moves due to the change in the intersecting fields. It would appear to an observer at this point that the field of the smaller mass is greater than that of the larger. Thus violating the equivalence principle. If another particle is situated away from the Lagrange point by a small closer to the larger mass then it would tend towards that mass. Giving the impression to an observer that the field strengths must somehow be equivalent although the masses are diferent.

#### PmbPhy

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##### Re: Is the equivalence principle valid?
« Reply #1 on: 27/06/2015 22:45:23 »
Quote from: jeffreyH
Consider an object at rest at the Lagrange point between two large but unequal masses. Then consider that the two masses are moving towards each other due to mutual gravitational attraction. As the masses move together the central object...
What is this "central object" that you're talking about?

Quote from: jeffreyH
... should tend towards the smaller mass as the Lagrange point moves due to the change in the intersecting fields.
Actually the distance to both masses is decreasing.

Quote from: jeffreyH
It would appear to an observer at this point that the field of the smaller mass is greater than that of the larger.
I don't see how. Why would you suggest a thing?

Quote from: jeffreyH
Thus violating the equivalence principle.
That doesn't do anything of the kind. The equivalence principle has nothing to do with the strength of a gravitational field.

#### jeffreyH

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##### Re: Is the equivalence principle valid?
« Reply #2 on: 28/06/2015 10:22:50 »
OK let's put it another way. Say you have a speck of dust with the same mass as 1 Plank mass and also a Planck mass black hole. take these as both a set distance above a celestial object with nil atmosphere and with the horizon of the black hole aligned with the bottom of the dust speck. As they approach the surface which one will touch it first? If the black hole beats the dust speck then an increase in density must violate the equivalence principle.

#### alancalverd

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##### Re: Is the equivalence principle valid?
« Reply #3 on: 28/06/2015 11:24:45 »
If you are dealing with point masses, the three will collide at the same time. There is no discontinuity in the classical gravitational equations.

If you are dealing with bodies of finite radius at short distances compared with the radii, the simple gravitational equations don't apply, and the Lagrange Point is not fully defined by the centers of mass. You need to know the density distribution of the bodies.

#### jeffreyH

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##### Re: Is the equivalence principle valid?
« Reply #4 on: 28/06/2015 12:15:56 »
If you are dealing with point masses, the three will collide at the same time. There is no discontinuity in the classical gravitational equations.

If you are dealing with bodies of finite radius at short distances compared with the radii, the simple gravitational equations don't apply, and the Lagrange Point is not fully defined by the centers of mass. You need to know the density distribution of the bodies.

I'm still thinking about this. If I come to any other conclusions I will post them here.

#### evan_au

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##### Re: Is the equivalence principle valid?
« Reply #5 on: 28/06/2015 13:14:13 »
An aside: I think the question may have been using the term "Lagrangian point" rather loosely.

Even though an arbitrary 3-body problem cannot be solved in closed form, Euler and Lagrange managed to find 5 solutions where a small mass would remain in a stable orbit, providing the other 2 objects were in a circular orbit.

If the larger objects are in a circular orbit, then they cannot come closer together.

#### jeffreyH

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##### Re: Is the equivalence principle valid?
« Reply #6 on: 28/06/2015 14:31:09 »
An aside: I think the question may have been using the term "Lagrangian point" rather loosely.

Even though an arbitrary 3-body problem cannot be solved in closed form, Euler and Lagrange managed to find 5 solutions where a small mass would remain in a stable orbit, providing the other 2 objects were in a circular orbit.

If the larger objects are in a circular orbit, then they cannot come closer together.

It's a fair cop. I put my hands up.

#### PmbPhy

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##### Re: Is the equivalence principle valid?
« Reply #7 on: 28/06/2015 16:59:18 »
OK let's put it another way. Say you have a speck of dust with the same mass as 1 Plank mass and also a Planck mass black hole. take these as both a set distance above a celestial object with nil atmosphere and with the horizon of the black hole aligned with the bottom of the dust speck. As they approach the surface which one will touch it first? If the black hole beats the dust speck then an increase in density must violate the equivalence principle.
Sorry, Jeff. I still don't see what you're getting at. All that Plank mass stuff belongs in a quantum theory of gravity and as you know, no such theory exists. Whenever I see those terms I skip over whatever it is that contains it and I move on to the next thing that may be of interest.

#### jeffreyH

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##### Re: Is the equivalence principle valid?
« Reply #8 on: 28/06/2015 20:19:30 »
That's fair enough Pete. I sometimes just throw out ideas.

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##### Re: Is the equivalence principle valid?
« Reply #8 on: 28/06/2015 20:19:30 »