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Plat
2005-Mar-06, 01:12 AM
"In most studies of equivalence principle violation by solar system bodies, it is assumed that the ratio of gravitational to inertial mass for a given body deviates from unity by a parameter Delta which is proportional to its gravitational self-energy. Here we inquire what experimental constraints can be set on Delta for various solar system objects when this assumption is relaxed. Extending an analysis originally due to Nordtvedt, we obtain upper limits on linearly independent combinations of Delta for two or more bodies from Kepler's third law, the position of Lagrange libration points, and the phenomenon of orbital polarization. Combining our results, we extract numerical upper bounds on Delta for the Sun, Moon, Earth and Jupiter, using observational data on their orbits as well as those of the Trojan asteroids. These are applied as a test case to the theory of higher-dimensional (Kaluza-Klein) gravity. The results are three to six orders of magnitude stronger than previous constraints on the theory, confirming earlier suggestions that extra dimensions play a negligible role in solar systemdynamics and reinforcing the value of equivalence principle tests as a probe of nonstandard gravitational theories."

I dont fully understand what the author is trying to say

Russ
2005-Mar-06, 03:01 AM
Translation: I'm trying to impress you with how smart I am and how much I know by blowing all this Brovo Sierra at you. ;) :lol:

Gullible Jones
2005-Mar-06, 03:59 AM
In most studies of equivalence principle violation by solar system bodies,

Equivalence principle = effects of uniform acceleration are the same as those of gravitational fields. IIRC that's part of special relativity. I haven't a clue how or why an object would violate it; ask ATP about that.


it is assumed that the ratio of gravitational to inertial mass for a given body

No idea what gravitational and inertial mass refer to.


deviates from unity by a parameter Delta which is proportional to its gravitational self-energy.

I don't know what "unity" refers to, though I guess it might mean the point at which "gravitational mass" and "inertial mass" are the same, i.e. the ratio is equal to 1.

I suppose "gravitational self-energy" would be the strength of the body's gravitational field, though that would be a rather odd way of putting it.


Here we inquire what experimental constraints can be set on Delta for various solar system objects when this assumption is relaxed.

Not sure what's meant by "experimental constraints" here, but the rest is obvious enough.


Extending an analysis originally due to Nordtvedt, we obtain upper limits on linearly independent combinations of Delta for two or more bodies from Kepler's third law, the position of Lagrange libration points, and the phenomenon of orbital polarization.

I don't know what's meant by "due to Nordvedt" - maybe it's supposed to be "an unfinished analysis by Nordtvedt"?

No idea what "linearly independent" would mean in this sense.

I don't know what Kepler's Third Law or orbital polarization are... :oops: But I can give you the definition of a Lagrange point. (http://en.wikipedia.org/wiki/Lagrange_point)


Combining our results, we extract numerical upper bounds on Delta for the Sun, Moon, Earth and Jupiter, using observational data on their orbits as well as those of the Trojan asteroids. These are applied as a test case to the theory of higher-dimensional (Kaluza-Klein) gravity.

Again, seems fairly obvious. In case you don't know what Kaluza-Klein theory is, it was one of the precursors of string theory and current hyperspace theories. I think the idea here is that they were looking for the leakage of gravity out of our 4-dimensional space-time as predicted by brane theory.


The results are three to six orders of magnitude stronger than previous constraints on the theory, confirming earlier suggestions that extra dimensions play a negligible role in solar systemdynamics and reinforcing the value of equivalence principle tests as a probe of nonstandard gravitational theories.

The author is saying that equivalence principle tests should provide valid results according to this research, because higher dimensions (if there are any) don't play a significant role in gravitational phenomena on the scale of solar systems.

papageno
2005-Mar-07, 03:14 PM
In most studies of equivalence principle violation by solar system bodies,

Equivalence principle = effects of uniform acceleration are the same as those of gravitational fields. IIRC that's part of special relativity. I haven't a clue how or why an object would violate it; ask ATP about that.
Equivalence principle is one of the postulates of General Relativity.




it is assumed that the ratio of gravitational to inertial mass for a given body
No idea what gravitational and inertial mass refer to.
Gravitational mass = mass in Newton's formula for gravity (F = G *m*M/r^2).
Inertial mass = mass in Newton's second law (F = m*a).
The definitions of the masses are not equivalent.




deviates from unity by a parameter Delta which is proportional to its gravitational self-energy.
m(grav)/m(inert) = 1 if the equivalence principle is strictly valid.
If it is not, we can write:
m(grav)/m(inert) = 1 + delta, where delta = 0 if the equivalence principle is valid.
Experiments give a range of possible values for delta, and these values are consistent with 0 within the experimental errors.

"Gravitational self-energy": a mass in a gravitational field due to another body, has a potential energy.
The "self-energy" would be the potential energy of the mass that produces the gravitational field.
There is the same concept in electrodynamics.



I don't know what "unity" refers to, though I guess it might mean the point at which "gravitational mass" and "inertial mass" are the same, i.e. the ratio is equal to 1.
Yes, it is the 1 in the formula above.



I suppose "gravitational self-energy" would be the strength of the body's gravitational field, though that would be a rather odd way of putting it.


Here we inquire what experimental constraints can be set on Delta for various solar system objects when this assumption is relaxed.

Not sure what's meant by "experimental constraints" here, but the rest is obvious enough.
We expect delta to be zero.
Experiments give us delta = (0 +/- error): error is an constraint on delta, based on experiments.
It is called "constraint", because delta might be non-zero, but only within the range given by error.


About the rest of quote, :-k beats me.