# The Naked Scientists Forum

### Author Topic: Is the equivalence principle correct  (Read 1792 times)

#### jeffreyH

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##### Is the equivalence principle correct
« on: 24/04/2014 02:19:52 »
If mass has no affect on acceleration then why when an object is condensed g goes up. The radius is reduced but the mass is the same. A neutron star has the same mass as an equivalent uncompressed object but exerts a greater pull. Therefore shouldn't a condensed object falling in the gravitational field of the earth exert a greater force and therefore a different g?

#### evan_au

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##### Re: Is the equivalence principle correct
« Reply #1 on: 24/04/2014 10:17:58 »
Quote
why when an object is condensed g [the acceleration due to that object's gravity] goes up

It is important to measure g under the same circumstances, ie measured at the same distance between the centers of the two objects.
• The Sun's gravitational acceleration at a distance of 150 million km (center-to-center) pulls the Earth into an orbit of 365 days.
• If you now compress the Sun into a neutron star 10km across, the Sun's gravitational acceleration at a distance of 150 million km (center-to-center) still pulls the Earth into an orbit of 365 days. ie the Sun's "g" is unchanged.
• If you now compress the Sun into an even smaller black hole, the Sun's gravitational acceleration at a distance of 150 million km (center-to-center) still pulls the Earth into an orbit of 365 days. ie the Sun's "g" is still unchanged, despite the fact that it is now a condensed object.
• The Sun's surface gravity is about 27 times that of Earth. This applies at a radius of 700,000km from the center of the Sun.
• If you compress the Sun into a neutron star or black hole, the gravitational attraction at a distance of 700,000km is still 27 times that of Earth.

I think that the OP may be asking about why the surface gravity of a neutron star is greater than the surface gravity of the original star. This is because it is possible to orbit to within 10km of the center of a compact neutron star, but you can't approach closer than 700,000 km to the center of the original, more diffuse star.

Newton's inverse square law says that the gravitational force is much stronger at 10km than at 700,000 km.

#### jeffreyH

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##### Re: Is the equivalence principle correct
« Reply #2 on: 25/04/2014 01:06:29 »
That still leaves the question unanswered. If we were able to manoeuvre two planetary sized masses together each with a g of around 9 so that they started falling towards each other (impossible yes I know) then from an outside observers perspective (s)he would see each moving toward the other at 4.5 g (to preserve equivalence). They would then meet at a point halfway between the starting position. This shows that mass size is irrelevant. However in a condensed object mass size hasn't changed. It is surface area that has changed. This means mass size is not the critical factor. Equivalence breaks down with change in density.

The surface of a mass is the interface between internal gravitation and external gravitation. The area of the surface and therefore the density determine how equivalence is interpreted.
« Last Edit: 25/04/2014 01:09:37 by jeffreyH »

#### jeffreyH

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##### Re: Is the equivalence principle correct
« Reply #3 on: 25/04/2014 01:13:54 »
If we now take the same situation as above and start with both masses at the same distances so the centres of gravity are in the same starting position but one mass is condensed. The midway point is now different and so more distance needs to be covered to bring them together, If they both start at 4.5 g then equivalence will be broken when they meet as this will now exceed the force in the first example. When they meet the velocity will have increased but the mass sizes will not have changed.
« Last Edit: 25/04/2014 01:16:46 by jeffreyH »

#### jeffreyH

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##### Re: Is the equivalence principle correct
« Reply #4 on: 25/04/2014 01:30:38 »
BTW (and this is not a new theory just an observation) the equivalence principle is preserved if the gravitional force is inversely proportional to density.

#### JP

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##### Re: Is the equivalence principle correct
« Reply #5 on: 25/04/2014 03:08:57 »
I'm not sure what this has to do with the equivalence principle.  Can you be more specific about which equivalence principle you're talking about and how it is violated by this example?
http://en.wikipedia.org/wiki/Equivalence_principle#Modern_usage

#### jeffreyH

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##### Re: Is the equivalence principle correct
« Reply #6 on: 25/04/2014 04:56:04 »
I'm not sure what this has to do with the equivalence principle.  Can you be more specific about which equivalence principle you're talking about and how it is violated by this example?
http://en.wikipedia.org/wiki/Equivalence_principle#Modern_usage

It's OK the equivalence principle isn't violated at all. I had a light bulb go on. Also density has nothing to do with gravitation so I have just binned months of work. I was looking at things the wrong way. A collapsed object will in fact maintain the same orbitals and all the gravitational equations are correct. Now that I have sorted the issue I'm moving on. At least I now know why it has taken almost 100 years to sort gravitation. I am waiting to see what happens to G2 as it encounters sag A*. If I am right then physics has been making a wrong assumption since Newton.

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##### Re: Is the equivalence principle correct
« Reply #6 on: 25/04/2014 04:56:04 »