This means I'm gonna lose weight, right? (Gravity question)

Factual Questions
1

OK - cheap joke. This thread is about G, Newton’s Universal Gravitational Constant.

Without getting too technical, the idea is that if you have two masses a certain distance apart, and you multiply the masses by each other then divide the product by the square of that distance, you get a number that, when multiplied by a value, G, equals the force of gravitational attraction between the two masses.

So, if I hold a 10 kg bowling ball 5 meters away from a 100 kg weight I can, using algebra, figure how much gravity there is between them.

(Of course, that example is preposterous because it ignores the fact that both the ball and the weight are fairly close to the Earth, an object of some significant mass.)

Anyway, that’s the way I learned it in High School. The idea is that there is come constant number at the root of this Univeral force that pulls all masses in the Universe together.

So, a few days ago, I was re-reading Expanded Universes, a fantastic collection of essays by Robert Heinlein. In one, called “Paul Dirac, Anti-Matter and You,” Heinlein tells of the acheivements of Nobel Laureate Paul Dirac, the theoretical physicist (it’s an article that makes up the entry on Dirac in the Britannica).

Anyway, here’s what I want to ask about. Heinlein says that Dirac proved that G, Newton’s Gravitational Constant is a diminshing value over time. In other words, gravity is getting… um… less. Every day it’s a little more less. Heinlein writes:

**

So, I guess what I am asking is, is this true? If so, is anyone else worried? I mean, I know it’s just a little number, but still, the implication is significant!

2

Well, if you can make a bad joke, I can do a [blatant hijack]. I just wanted to say, I have that same book “Expanded Universe”, it was my first Heinlein (but not my last), got it when I was IIRC 11 years old, and it had a profound effect on me.

…
Oh yes…[/blatant hijack]

Carry on.

3

Only once, I promise.

I just can’t believe that nobody can answer this - I figure that it fell off the front page because of the old thread title.

One more time…

4

IIRC, “Big G” has not even been determined to more than a few decimal places. The current estimate may be off by as much as .01%. It certainly hasn’t been determined so precisely that we can measure a decrease of one billionth part per year.

5

No offense, but Heinlein and Dirac probably know what they’re talking about, doncha’ think?

Can anyone do better that “IIRC”?

6

Apparently not. From http://www.physics.mq.edu.au/~dalew/Cavendish.html:

So, depending on who you believe, the value for big G is either 6.6739 x 10^-11 or 6.6726 x 10^-11, a different of .02%, even greater than what I said. Even if one of these two values is accurate for all of its decimal places, this still makes it impossible to detect a decrease of 1 ten billionth of the total, which would require accuracy to 11 decimal places.

7

Try this NIST Fundamental Physical Constants page. Click on “Universal constants” then “Newtonian constant of gravitation.” It lists the official uncertainty of this constant as 1.5x10^-3, or 0.15 percent. I believe this uncertainty was increased a couple of years ago because of conflicting measurements.

Sometimes the rate of change ov something can be measured more accurately than the value itself - for example, it’s difficult to measure the distance to a distant galaxy, but it’s easy to measure the rate of change of distance (i.e. speed) by measuring the redshift. However, Dirac didn’t make such measurements. As I understand it, his claim of a changing gravitational constant is based on numerical coincidences, in an attempt to explain the expansion of the universe. Do a search for “Dirac large number hypothesis” and you’ll find a lot of info, like this page.

8

Here’s a Discover magazine article about the situation

http://www.discover.com , Big G, March, 1996

http://208.245.156.153/archive/output.cfm?ID=705

9

Don’t forget that the Earth is not a perfect circle. The fact that the Earth is an oblate spheroid (flatter on the top and bottom and bulkier at the equator) never seemed to fit into make it to anyone’s calculations, granted that when the same person does the same expirment twice, he’s probably in the same spot, but two different scientists probably are not…just making sure everyone thinks of this…

10

At least, that was true for a very long time–like, before 1666.

11

scr4 is right here, in that there are arguments which can rule out Dirac’s original hypothesis without you actually having to measure G. The most famous is probably that due to Edward Teller, back in 1948. Dirac was suggesting that G varies inversely with time. Teller pointed out that making G bigger in the past has serious consequences for whether life could have survived on the early Earth. Stronger gravity meant the Sun was denser and thus hotter. The Earth would also have been closer to it. He argued that a 1/t change in G means that the temperature on the Earth’s surface would falling relatively drastically. (Strictly, as 1/t to the power 9/4.) Conditions were therefore distinctly hotter here in the past. You don’t need to know G to make this comparison: just the temperature now, the age t now and the age then in order to work out the temperature then. And doing the details shows that it’d have been too hot for liquid water at times when we know life had already started. Thus one can rule out changes in G of one part in a billion per year now, without knowing the constant to this accuracy.

The big disadvantage of this compared to directly measuring G in the lab at different times is that there’s various assumptions built in. Perhaps it’s varying at that amount now, but not as fast in the past as Dirac suggested etc. There’s a substantial physics literature kicking variations on the basic case about. The references on the page src4 cited are a good starting point.

Incidentally, Dirac wasn’t trying to explain the expansion of the universe. Some of the “coincidences” he noticed involve the size of the universe and therefore only hold round about now in the age of the universe. To avoid our era being special, Dirac had to have something else change so that they were true at all times. His hypothesis that the coincidences were significant him forced into suggesting changes in a constant. The variation in G thus followed from the expansion and wasn’t an explanation of it. Post-Dicke’s anthropic explanation of the coincidences, most physicists accept that the coincidences actually only do hold round about now.

12

As I understand it, there’s other arguments for a constant G (or at least one not varying as quickly as Dirac claimed) which rely on fewer assumptions (for instance, no mention of life), but they also don’t put quite as stringent bounds on the rate of change.

To give you an idea of Dirac’s reasoning, he was relying on the fact that one is approximately equal to two thousand. We’re going out on a really shaky limb here, folks.

13

Hey! I submitted a great reply to this thread! It must have gotten wiped out in the Great Hack.

Well, no point in repeating the exercise since there are fine explanations here. Just wanted you all to know that some physical laws are constant, among them that Podkayne couldn’t possibly keep her nose out of a thread about Heinlein and astronomy.

14

That’s Van Flandern. He is no longer at USNO. He has a group he started called MetaResearch (http://www.metaresearch.org) which does wacky stuff like try to disprove the Big Bang, figure out if asteroids are from an exploded planet, show relativity is wrong, etc etc.

IMO, van Flandern is not correct in his beliefs. It’s a funny situation: he thinks everything known about physics today is wrong. I can understand someone having difficulties with the Big Bang or whatever, but he disagrees with everything! This makes him unlikely to be correct in all his assertions.

My point: take what he says with a chunk of salt big enough to cause a mass extinction.

15

Absolutely. Indeed, checking in Weinberg (Gravitation and Cosmology) throws up a limit derived from Shapiro’s radar ranging of Mercury and Venus. As in the Teller argument, a varying G would mean a change in the radius of their orbits. However, Sixties technology had reached the point where you could check such changes by measuring the distances with radar. The quoted limit is of order one part in a billion per year. There’ll no doubt be things like GR corrections folded into this answer, but, unlike the Teller argument, it’s a direct experimental result.

However, that was Weinberg writing back in 1972 and I’m sure the best current limits must be significantly better. But I don’t know what they are.

I agree about the “coincidences”. They were pretty piss-poor in the first place.