Exploring the Gravitational Constant: Insights from Lunar Missions

[Blenton]

Has the gravitational constant been measured elsewhere than Earth? Perhaps during the lunar missions?

I ask this because I'm wondering whether the gravitational constant is indeed constant throughout space, or at least something that can verify that.

 

[Jonathan Scott]

Has the gravitational constant been measured elsewhere than Earth? Perhaps during the lunar missions?

I ask this because I'm wondering whether the gravitational constant is indeed constant throughout space, or at least something that can verify that.

As we can observe gravitational effects of bodies within the solar system to very high accuracy, we know that its value is effectively constant within the whole solar system.

We also know from various experiments (such as lunar laser ranging) that if it is varying with time, any variation must be very small (less than with the age of the universe or its inverse).

Such experiments actually typically prove that the product of the gravitational constant and a quantity of mass, Gm, is constant, but it is usually assumed that mass itself is constant.

We cannot directly measure G accurately outside the solar system. However, General Theory of Relativity matches experimental results very accurately within the solar system and seems to provide a reasonable explanation of more distant gravitational effects (although not entirely satisfactory, as it needs to be supplemented by dark matter and dark energy on large scales), and in that theory G is a universal constant.

In alternative theories of gravity based on Mach's Principle, G is a function of the distribution of the masses in the universe, so would be expected to vary near a substantial mass such as the sun. However, in such theories it is possible that the main variation simply manifests as the Newtonian potential, and that the G we calculate is the effect due to all other masses in the universe, which is effectively constant in our vicinity.

 

[Chronos]

Extrasolar tests of variations in G over time have been conducted. No evidence of any significant variation has been detected. See, for example

arXiv:0911.0190
Constraining a possible time-variation of the gravitational constant through "gravitochemical heating" of neutron stars

arXiv:1001.4704
Precision timing of PSR J1012+5307 and strong-field GR tests

 

[Blenton]

But compared to the what 14 billion years age of the universe is it not probable that we are simply measuring it on too small of a time scale?

 

[Chronos]

The science involved in these papers goes very deep into the nature of reality and time. It is not easily absorbed, but, compelling, IMO. I agree, however, these studies do not confirm properties of the universe all the way back to the big event.

 

[Vanadium 50]

If G varied, the energy produced in Type 1A supernovae would vary as well. It turns out this is a rather strong function of G, so we know that across space and time G doesn't vary by more than a few percent.

 

[Orion1]

Einstein field equations and gravitational constant.


The Einstein field equations in General Relativity are also based upon $$G$$, which agrees with experiments.

Einstein field equations:
$$G_{\mu \nu} + \Lambda g_{\mu \nu}= {8\pi G\over c^4} T_{\mu \nu}$$

Reference:
http://en.wikipedia.org/wiki/Einstein_field_equations#Mathematical_form"

 

[yogi]

If G varied, the energy produced in Type 1A supernovae would vary as well. It turns out this is a rather strong function of G, so we know that across space and time G doesn't vary by more than a few percent.

Alternatively, if G were stronger in the past, the 1a supernova data can be explained alternatively - without concluding the cosmos is accelerating - the distances appear to be greater because the 1a events occur with a stronger G and less mass - but don't bet to heavily upon it.

 

[Vanadium 50]

There is more evidence for dark energy than supernovae. You can't get around this constraint so easily.

 

[Chronos]

See also:

Confirmation of general relativity on large scales from weak lensing and galaxy velocities
Arxiv 1003.2185