Author Topic: Gravitational constant and calculators  (Read 2922 times)

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Offline Maxlor

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Gravitational constant and calculators
« on: September 01, 2015, 09:52:45 pm »
I got a new calculator for my collection today, the HP 9g. It's an odd little thing, with its 35x23 pixel display used for graphing, and a tiny, separate result display. It also stores a couple of scientific constants, such as the newtonian constant of gravitation, G. It gives the value as 6.6725985e-11. It's curious that they give that much precision.

G may be a constant, but it's notoriously hard to measure, because gravity is the weakest of the fundamental forces, and it's impossible to remove the measurement apparatus from the influences of stars and planets or the material of the apparatus itself. Many different experiments have been conducted, from these the people at NIST build a weighted average and publish it as part of their CODATA set of constants. The CODATA values from different years are:

1969: 6.6732(31)
1973: 6.6720(41)    - note the increase in uncertainity!
1986: 6.67259(85)   - oh, large improvement in accuracy, maybe they were getting a bit cocky there?
1998: 6.673(10)   - experiments in the 90s must have been all over the map! Or it's a typo in their publication, which seems very unlikely.
2002: 6.6742(10)
2006: 6.67428(67)
2010: 6.67384(80)   - again, note the increase in uncertainity.
2014: 6.67408(31)   - published just a couple of months ago.

Btw, a recent study claims to have found a weird annomaly by statistical analysis: measurements of G increase and decrease by 1.6e-14 (so the 3rd place after the period in the values above) in a 5.9 year cycle. They suggest that G itself doesn't actually change, but that a yet unknown effect influences all measurements. Curious, huh.

A note about the syntax: 6.6732(31) means 6.6732+-0.0031. The two digits inside the parentheses have the same order of magnitude as the last two digits of the given value. If only one digit were given inside the parentheses, it'd have the same order of magnitude as the last digit of the given value.

And now I get to my calculators. By looking at what value they use for G, we get a small glimpse into the development, i.e. whether they took just old code, or went to the trouble of updating the constants. Here's a short list of calculators I tested with their values (just the mantissa, I left out the e-11 exponent)

HP 9g: 6.6725985 - Wtf. Seems the guy who created the table didn't know what the parentheses syntax meant! Otherwise it's the 1986 value.
HP 35s: 6.673 - 1998 value.
HP 48G: 6.67259 - 1986 value.
HP 50G: 6.67259 - 1986 value.
HP Prime: 6.67384 - 2010 value.

TI-85: 6.67259 - 1986 value.
TI-86: 6.67259 - 1986 value.
TI-89 (first gen): 6.67259 - 1986 value.
TI Voyage 200: 6.6742 - 2002 value.
TI-nspire CAS: 6.6742 - 2002 value.
TI-30X Pro: 6.67428 - 2006 value.

Casio fx-991EX: 6.67384 - 2010 value.

Anyway, that was my nerdgasm for today. Thought I'd share :)
« Last Edit: September 05, 2015, 01:32:28 pm by Maxlor »
 

Offline sarepairman2

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Re: Gravitational constant and calculators
« Reply #1 on: September 02, 2015, 02:08:52 am »
 

Offline alsetalokin4017

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Re: Gravitational constant and calculators
« Reply #2 on: September 02, 2015, 02:36:54 am »
Sharp EL-520W : 6.6742
The easiest person to fool is yourself. -- Richard Feynman
 

Offline wasyoungonce

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Re: Gravitational constant and calculators
« Reply #3 on: September 02, 2015, 10:07:31 am »
I thought the gravitational constant was now being measured by/against type 1A supernova...which are very specific in there nature...and can be measured in distance galaxies ...aka back and forth in time!   Aka the constant has not changed in billions of years.

http://arxiv.org/abs/1402.1534
http://www.swinburne.edu.au/media-centre/news/2014/03/exploding-stars-prove-newtons-law-of-gravity-unchanged-over-cosmic-time.html

To which I thought the Chandrasekhar limit was very specific and a defined known value thus the gravitational constant can be measured against.  Anyway I'd have to do more reading on this to get back up to scratch.  Anyway the discussion is very unique but welcome... FWIW!

edit:
probably what I should have said is that ...new methods of determining the gravitation constant like using the type 1a supernova have revealed that it has not changed.  Our understanding of this has.
« Last Edit: September 02, 2015, 11:58:51 am by wasyoungonce »
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Offline Maxlor

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Re: Gravitational constant and calculators
« Reply #4 on: September 02, 2015, 09:45:35 pm »
My understanding was that they were able to confirm that G hasn't changed by more than one billionth by observing those type Ia supernovas. It didn't help with actually improving the measurements of G. But, eh, I haven't read the papers, nor am I an astrophysicist. I figure though that if it was clear-cut, NIST would give G with a lot more precision.

Also: Casio fx-991ES: 6.673 (1998 value)
« Last Edit: September 02, 2015, 09:47:24 pm by Maxlor »
 

Offline wasyoungonce

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Re: Gravitational constant and calculators
« Reply #5 on: September 03, 2015, 01:49:35 am »
Interesting that its though earth's rotational oscillation have an effect on measurements

"....As a clue to what this "something else" is, the scientists note that the 5.9-year oscillatory period of the measured G values correlates almost perfectly with the 5.9-year oscillatory period of Earth's rotation rate....."

"Once a surprising 5.9-year periodicity is taken into account, most laboratory measurements of G are consistent, and are within one-sigma experimental error limits,"

http://phys.org/news/2015-04-gravitational-constant-vary.html#jCp

That said...that graph of their measurements looks a little all over the place.
I'd forget my Head if it wasn't screwed on!
 

Offline codeboy2k

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Re: Gravitational constant and calculators
« Reply #6 on: September 03, 2015, 03:30:13 am »
Android RealCalc : 6.67408  (2014 value)
 

Offline amyk

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Re: Gravitational constant and calculators
« Reply #7 on: September 03, 2015, 03:32:18 am »
Interesting that its though earth's rotational oscillation have an effect on measurements

"....As a clue to what this "something else" is, the scientists note that the 5.9-year oscillatory period of the measured G values correlates almost perfectly with the 5.9-year oscillatory period of Earth's rotation rate....."

"Once a surprising 5.9-year periodicity is taken into account, most laboratory measurements of G are consistent, and are within one-sigma experimental error limits,"

http://phys.org/news/2015-04-gravitational-constant-vary.html#jCp

That said...that graph of their measurements looks a little all over the place.
IMHO it's not so surprising, there are other planets around and they also contribute to the gravitational field, however tiny it is.
 


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