View Full Version : Calculating G using gravitational redshift

mkline55

2012-Nov-28, 02:36 PM

I've run across several instances in physics classes describing the gravitational constant as being considerably less accurate than other measured constants. They then go on to describe how torsion balances are used to determine the value of G, and how that process is limited in its ability to produce highly accurate results.

Since gravitational redshift is an accepted concept, have measurements of G been done using redshift in place of torsion balances?

According to this formula (hopefully the post syntax is right :confused:) http://upload.wikimedia.org/math/8/8/8/8880e3da1ad8883a30dac59ec153993a.png, an appropriate experiment should be able to utilize measured redshift, distance, mass and c to determine a value for G.

So, the question is, has this been done, and what were the results? If this has been previously proposed but never performed, then why not?

Hornblower

2012-Nov-28, 03:00 PM

I've run across several instances in physics classes describing the gravitational constant as being considerably less accurate than other measured constants. They then go on to describe how torsion balances are used to determine the value of G, and how that process is limited in its ability to produce highly accurate results.

Since gravitational redshift is an accepted concept, have measurements of G been done using redshift in place of torsion balances?

According to this formula (hopefully the post syntax is right :confused:) http://upload.wikimedia.org/math/8/8/8/8880e3da1ad8883a30dac59ec153993a.png, an appropriate experiment should be able to utilize measured redshift, distance, mass and c to determine a value for G.

So, the question is, has this been done, and what were the results? If this has been previously proposed but never performed, then why not?

How would you find M precisely for anything massive enough to cause a significant redshift?

mkline55

2012-Nov-28, 03:07 PM

How would you find M precisely for anything massive enough to cause a significant redshift?

Ar you saying it cannot be done because no one can find M with sufficient accuracy for anything massive enough to cause a significant redshift?

ShinAce

2012-Nov-28, 03:13 PM

This is close, but not the same measurement:

http://prl.aps.org/abstract/PRL/v100/i5/e050801

The classic maser experiment can be read here:

http://link.springer.com/article/10.1007%2FBF00653616?LI=true

http://www.nature.com/nature/journal/v463/n7283/full/nature08776.html (this one is a 'sister' article)

The idea was that with an atomic clock on a satellite, we measure what you're proposing, the redshift as light climbs out of earth's gravity. The problem, as I understand it, is that the gravity of the earth isn't very uniform. We have mountains, and tides, and etc... This limits the known precision of the distribution of earth's mass. The laser is simply too precise compared to our knowledge of M.

So we need a way to isolate the effects of mass distributions. That's where interferometry is useful. Experiments like:

http://prl.aps.org/abstract/PRL/v100/i5/e050801

edit: I wrote this before reading posts 2 and 3. It's not a reply to a reply, but a reply to the OP.

mkline55

2012-Nov-28, 03:41 PM

Thanks for the links, ShinAce. The proposals are interesting, but have any been carried out?

Grey

2012-Nov-28, 06:26 PM

The idea was that with an atomic clock on a satellite, we measure what you're proposing, the redshift as light climbs out of earth's gravity. The problem, as I understand it, is that the gravity of the earth isn't very uniform. We have mountains, and tides, and etc... This limits the known precision of the distribution of earth's mass. The laser is simply too precise compared to our knowledge of M.Those are pretty cool experiments. I think, though, that the issue Hornblower raises is still a problem. I can't think of any of the methods for calculating the mass of the Earth without first determining the value of G by some other method. The first two of those experiments appear to be comparing a measured redshift against a predicted one, but making that prediction assumes you already know GM for the Earth. Even if you went the other way and used this method to determine the value of GM, that won't help you split them apart to determine just G or just M. The last experiment is used to calculate G, but as far as I can tell from the abstract, they're using essentially the same principle as a torsion balance: taking a small known test mass and seeing how it affects the movement of other objects (in this case, individual Rubidium atoms).

ShinAce

2012-Nov-28, 07:46 PM

The last experiment is used to calculate G, but as far as I can tell from the abstract, they're using essentially the same principle as a torsion balance: taking a small known test mass and seeing how it affects the movement of other objects (in this case, individual Rubidium atoms).

Indeed.

But there is one more redshift experiment I know of, which involved a speaker with a radioactive source on the cone. Using the doppler effect and resonant coupling, they measured redshift over a height of some 10m. I'll try to find an abstract and edit that in.

edit: now that I found it, I feel like a rookie for forgetting the name (Pound-Rebka)

http://en.wikipedia.org/wiki/Pound%E2%80%93Rebka_experiment

Grey

2012-Nov-28, 11:23 PM

But there is one more redshift experiment I know of, which involved a speaker with a radioactive source on the cone. Using the doppler effect and resonant coupling, they measured redshift over a height of some 10m. I'll try to find an abstract and edit that in.

edit: now that I found it, I feel like a rookie for forgetting the name (Pound-Rebka)

http://en.wikipedia.org/wiki/Pound%E2%80%93Rebka_experimentPound-Rebka's pretty famous, being the first experimental verification of gravitational redshift. But measuring the redshift still only let's you calculate GM. To calculate G, you'd need some kind of independent way of measuring the mass of the Earth. I can't think of any realistic way to measure the mass of the Earth that doesn't involve first calculating G using small test masses.

Grey

2012-Nov-28, 11:24 PM

But there is one more redshift experiment I know of, which involved a speaker with a radioactive source on the cone. Using the doppler effect and resonant coupling, they measured redshift over a height of some 10m. I'll try to find an abstract and edit that in.

edit: now that I found it, I feel like a rookie for forgetting the name (Pound-Rebka)

http://en.wikipedia.org/wiki/Pound%E2%80%93Rebka_experimentPound-Rebka's pretty famous, being the first experimental verification of gravitational redshift. But measuring the redshift still only let's you calculate GM. To calculate G, you'd need some kind of independent way of measuring the mass of the Earth. I can't think of any realistic way to measure the mass of the Earth that doesn't involve first calculating G using small test masses.

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