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### Author Topic: What is the accepted value of g?  (Read 7333 times)

#### jeffreyH

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##### What is the accepted value of g?
« on: 17/03/2014 02:42:18 »
I have seen g stated as 9.78 m/sē on wikipedia and 9.81 m/sē elsewhere. I know this value will vary with altitude but what is the best value to use? Also on a related note, has there been any experiments on gravitational acceleration in space between masses. I doubt it but I thought I'd ask.

#### CliffordK

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##### Re: What is the accepted value of g?
« Reply #1 on: 17/03/2014 04:00:13 »
Here is a list of different gravitational acceleration based on different locations around the world.

http://en.wikipedia.org/wiki/Gravity_of_Earth#Local_topography_and_geology

Personally I would only consider the acceleration due to gravity to be accurate to two significant figures (9.8 m/sē).

If one needs a more accurate estimate, then one would need to know the location.  No doubt they know the acceleration due to gravity at and around Cape Canaveral down to several significant figures.

I also typically see G-Force represented to 1 or 2 significant figures.  While acceleration in m/sē might be represented to a dozen significant figures, G-Force acceleration typically isn't.

#### evan_au

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##### Re: What is the accepted value of g?
« Reply #2 on: 17/03/2014 10:28:29 »
There have been several specialised satellites constructed to study gravitational fields in space, with the goal of studying Einstein's general relativity (Gravity Probe B) and the internal structure of the Moon (GRAIL).

General-purpose satellites orbiting Saturn and Jupiter have been able to make deductions about the internal structure of some gas-giant moons by studying the gravitational effects they have on the space probe.

There are tentative plans to put a sensitive gravity wave detector in space, looking at distant astronomical events like black hole mergers.

#### jeffreyH

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##### Re: What is the accepted value of g?
« Reply #3 on: 17/03/2014 13:26:14 »
I read that Gravity Probe B had verified the distortions due to the vortex around the earth which was a step forward. My problem at the moment is the uncertainty in various values. We currently do not have an accurately determined mass with an equivalent value for g. Any mathematics will suffer too much uncertainty. Values for g can be out by a large margin with only a slight deviation in G. BTW how accurate is the value of the Planck constant? I have found no information on this. I know it relates to frequency and wavelength.

#### CliffordK

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##### Re: What is the accepted value of g?
« Reply #4 on: 17/03/2014 19:06:00 »
My problem at the moment is the uncertainty in various values.

I think it is not as much uncertainty as variation in values.

If you measured the gravitational constant at London, and Cambridge, undoubtedly you'd find variation in the 3rd, or perhaps 4th sig fig.  Measure it again in Cairo as well as AmundsenScott, and it would be off by quite a bit.

Other values such as air pressure varies by both location and time.

1 ATM is defined as exactly 760 Torr (which is apparently slightly off from 760 mm hg).

Ahhhh, found the Wiki reference: [1g] is defined by standard as exactly 9.80665 m/sē, or about 35.30394 (km/h)/s (≈32.174 ft/s2 or ≈21.937 mph/s). This value was established by the 3rd CGPM (1901, CR 70).  I have no idea why they didn't define it as 9.80m/sē????

#### jeffreyH

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##### Re: What is the accepted value of g?
« Reply #5 on: 17/03/2014 20:05:57 »
My problem at the moment is the uncertainty in various values.

I think it is not as much uncertainty as variation in values.

If you measured the gravitational constant at London, and Cambridge, undoubtedly you'd find variation in the 3rd, or perhaps 4th sig fig.  Measure it again in Cairo as well as AmundsenScott, and it would be off by quite a bit.

Other values such as air pressure varies by both location and time.

1 ATM is defined as exactly 760 Torr (which is apparently slightly off from 760 mm hg).

Ahhhh, found the Wiki reference: [1g] is defined by standard as exactly 9.80665 m/sē, or about 35.30394 (km/h)/s (≈32.174 ft/s2 or ≈21.937 mph/s). This value was established by the 3rd CGPM (1901, CR 70).  I have no idea why they didn't define it as 9.80m/sē????

I don't know either. Must be for convenience. I'll keep thinking about the problem but at the moment I am going to look into what Zvi Bern is doing with supergravity.

https://www.simonsfoundation.org/quanta/20140314-betting-on-the-future-of-quantum-gravity/

Of course this work may fall over soon as a lot of other attempts have. He seems to be getting some interesting results.

#### Bored chemist

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##### Re: What is the accepted value of g?
« Reply #6 on: 18/03/2014 20:39:05 »
My guess is they chose that value because it's the "right answer"
Specifically, I think it's the right answer for a rotating spherical Earth or some such "ideal" from which the local value can be calculated if you know the altitude and latitude.

#### jeffreyH

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##### Re: What is the accepted value of g?
« Reply #7 on: 18/03/2014 20:57:59 »
My guess is they chose that value because it's the "right answer"
Specifically, I think it's the right answer for a rotating spherical Earth or some such "ideal" from which the local value can be calculated if you know the altitude and latitude.

Then I assume what you are saying is it is the the mean value. If that is correct then it is the value to use in any calculations. It all depends upon how accurately we know the mass of the earth. That I don't know. Of course the other method would be to determine the range of possible values and produce data over this range. Again this depends upon the accuracy of the determination of the mass of the earth. I wonder if calculating over this range could be used to determine the mass to a high degree of accuracy. Satellite data could be used to determine a more or less accurate radius value. The variations over the surface could be catered for using elevation data. Ocean volume could be determined the same way.
« Last Edit: 18/03/2014 21:05:11 by jeffreyH »

#### jeffreyH

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##### Re: What is the accepted value of g?
« Reply #8 on: 18/03/2014 21:11:25 »
Because of the bulge at the equator Mount Chimborazo in Ecuador has been determined to be the highest point. That is furthest from the centre of the planet. A determination of g on the summit would be a very useful measurement. Extremely difficult I would imagine.

#### jeffreyH

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##### Re: What is the accepted value of g?
« Reply #9 on: 18/03/2014 21:25:09 »
This was actually done slightly differently. Quite an interesting read.

http://www.michaelbeeson.com/interests/GreatMoments/Chimborazo.pdf

#### Bored chemist

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##### Re: What is the accepted value of g?
« Reply #10 on: 18/03/2014 22:04:12 »
"A determination of g on the summit would be a very useful measurement. Extremely difficult I would imagine."
Nope, trivial.
http://en.wikipedia.org/wiki/Gravimeter
(OK tricky if you want 12 digit accuracy, but otherwise, no great challenge.)

#### jeffreyH

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##### Re: What is the accepted value of g?
« Reply #11 on: 18/03/2014 22:27:53 »
"A determination of g on the summit would be a very useful measurement. Extremely difficult I would imagine."
Nope, trivial.
http://en.wikipedia.org/wiki/Gravimeter
(OK tricky if you want 12 digit accuracy, but otherwise, no great challenge.)

I wonder why it hasn't been done then. The scientific community appears to have taken this area of research for granted!
« Last Edit: 18/03/2014 22:42:14 by jeffreyH »

#### Bored chemist

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##### Re: What is the accepted value of g?
« Reply #12 on: 19/03/2014 19:54:45 »
"A determination of g on the summit would be a very useful measurement. Extremely difficult I would imagine."
Nope, trivial.
http://en.wikipedia.org/wiki/Gravimeter
(OK tricky if you want 12 digit accuracy, but otherwise, no great challenge.)

I wonder why it hasn't been done then. The scientific community appears to have taken this area of research for granted!
Why do you think it hasn't been done?
It has.
The results were pretty much what was expected.

#### jeffreyH

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##### Re: What is the accepted value of g?
« Reply #13 on: 19/03/2014 20:36:08 »
"A determination of g on the summit would be a very useful measurement. Extremely difficult I would imagine."
Nope, trivial.
http://en.wikipedia.org/wiki/Gravimeter
(OK tricky if you want 12 digit accuracy, but otherwise, no great challenge.)

I wonder why it hasn't been done then. The scientific community appears to have taken this area of research for granted!
Why do you think it hasn't been done?
It has.
The results were pretty much what was expected.

Where is the data for that measurement?

#### CliffordK

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##### Re: What is the accepted value of g?
« Reply #14 on: 20/03/2014 18:17:34 »
My guess is they chose that value because it's the "right answer"
Specifically, I think it's the right answer for a rotating spherical Earth or some such "ideal" from which the local value can be calculated if you know the altitude and latitude.
You would need the altitude, latitude, and LOCAL CRUST DENSITY.

Won't the surface gravity also vary with the time of day, lunar phase, and perhaps even the month of the year.

#### JP

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##### Re: What is the accepted value of g?
« Reply #15 on: 20/03/2014 18:31:40 »
My guess is they chose that value because it's the "right answer"
Specifically, I think it's the right answer for a rotating spherical Earth or some such "ideal" from which the local value can be calculated if you know the altitude and latitude.
You would need the altitude, latitude, and LOCAL CRUST DENSITY.

Won't the surface gravity also vary with the time of day, lunar phase, and perhaps even the month of the year.

Yes, see:
http://en.wikipedia.org/wiki/Gravity_Recovery_and_Climate_Experiment

#### jeffreyH

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##### Re: What is the accepted value of g?
« Reply #16 on: 21/03/2014 03:26:34 »
My guess is they chose that value because it's the "right answer"
Specifically, I think it's the right answer for a rotating spherical Earth or some such "ideal" from which the local value can be calculated if you know the altitude and latitude.
You would need the altitude, latitude, and LOCAL CRUST DENSITY.

Won't the surface gravity also vary with the time of day, lunar phase, and perhaps even the month of the year.

Yes, see:
http://en.wikipedia.org/wiki/Gravity_Recovery_and_Climate_Experiment

Well that seems to rule out a determination of exact mass for the earth. Obvious really I suppose.

#### Bored chemist

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##### Re: What is the accepted value of g?
« Reply #17 on: 22/03/2014 20:43:09 »
My guess is they chose that value because it's the "right answer"
Specifically, I think it's the right answer for a rotating spherical Earth or some such "ideal" from which the local value can be calculated if you know the altitude and latitude.
You would need the altitude, latitude, and LOCAL CRUST DENSITY.

Won't the surface gravity also vary with the time of day, lunar phase, and perhaps even the month of the year.

Yes, see:
http://en.wikipedia.org/wiki/Gravity_Recovery_and_Climate_Experiment

Well that seems to rule out a determination of exact mass for the earth. Obvious really I suppose.

How "exact" do you want?
You can measure the local value of g all over the world, and they have.
You can get an average and then use that to calculate the mass of the earth.
You need the value of G and that's not very accurately known at the moment.

#### jeffreyH

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##### Re: What is the accepted value of g?
« Reply #18 on: 22/03/2014 21:15:53 »
My guess is they chose that value because it's the "right answer"
Specifically, I think it's the right answer for a rotating spherical Earth or some such "ideal" from which the local value can be calculated if you know the altitude and latitude.
You would need the altitude, latitude, and LOCAL CRUST DENSITY.

Won't the surface gravity also vary with the time of day, lunar phase, and perhaps even the month of the year.

Yes, see:
http://en.wikipedia.org/wiki/Gravity_Recovery_and_Climate_Experiment

Well that seems to rule out a determination of exact mass for the earth. Obvious really I suppose.

How "exact" do you want?
You can measure the local value of g all over the world, and they have.
You can get an average and then use that to calculate the mass of the earth.
You need the value of G and that's not very accurately known at the moment.

I am looking for ways of using known values to calculate G. The earth is a very bad choice but any two masses that are accurately determined could be used to work backwards to give G as long as a precise gravitational acceleration could be measured. For this you would not need G. It could be determined from direct observation. It is really an impossible task at the moment. We can zero in on a range of values that would narrow down the possibilities but can go no further. It has to be possible to determine mathematically under the right conditions.

#### jeffreyH

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##### Re: What is the accepted value of g?
« Reply #19 on: 22/03/2014 21:22:58 »
The way to achieve this is to construct two spherical masses of known size one significantly larger than the other and determine the acceleration of the smaller towards the larger. It could only be done in space where the gravitational influenced are lower. One reading would be taken with the larger mass nearer the sun in and another the other way round to balance out the effect of the sun's gravitation. This would not remove the effects of the planets. Any difference could be taken into consideration.

#### Bored chemist

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##### Re: What is the accepted value of g?
« Reply #20 on: 23/03/2014 17:52:06 »
" The earth is a very bad choice but any two masses that are accurately determined could be used to work backwards to give G as long as a precise gravitational acceleration could be measured. For this you would not need G. It could be determined from direct observation. It is really an impossible task at the moment. "
It was perfectly possible when Cavendish did it a couple of hundred years ago
http://en.wikipedia.org/wiki/Cavendish_experiment

Why do you think it's impossible?
Have you just not done any research?

#### jeffreyH

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##### Re: What is the accepted value of g?
« Reply #21 on: 23/03/2014 18:51:23 »
" The earth is a very bad choice but any two masses that are accurately determined could be used to work backwards to give G as long as a precise gravitational acceleration could be measured. For this you would not need G. It could be determined from direct observation. It is really an impossible task at the moment. "
It was perfectly possible when Cavendish did it a couple of hundred years ago
http://en.wikipedia.org/wiki/Cavendish_experiment

Why do you think it's impossible?
Have you just not done any research?

Just look at the latest measurements and the discrepancies between them. The gravitational field of the earth will always have an effect on the attraction of two bodies within its field. The pull towards the centre of the earth will change the momentum between the two masses being measured. You also have complex cancellation effects to take into account. It can never be a good idea to determine G inside a high gravitational field. Not when we have no reliable experimental results from a theory of gravitation to fall back on. Why we can't have reliable results is because we have not accurately determined G. This is a recursive situation.
« Last Edit: 23/03/2014 19:02:01 by jeffreyH »

#### JP

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##### Re: What is the accepted value of g?
« Reply #22 on: 25/03/2014 19:59:03 »
It's all a question of how many digits you want to know for G.  Because gravity hasn't been unified with the other forces and because it's incredibly weak compared to the other forces and because we always have to contend with earth's gravity when doing experiments, getting it to the extreme precision of other fundamental constants is going to be difficult unless you get funding for a Cavendish experiment in deep space.

This is a reason why there's so many open questions about gravity--doing experiments is tough!

On the other hand, we know G (and can measure g) with far better precision than is necessary for most engineering applications as Bored Chemist pointed out.

#### jeffreyH

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##### Re: What is the accepted value of g?
« Reply #23 on: 26/03/2014 00:45:26 »
It's all a question of how many digits you want to know for G.  Because gravity hasn't been unified with the other forces and because it's incredibly weak compared to the other forces and because we always have to contend with earth's gravity when doing experiments, getting it to the extreme precision of other fundamental constants is going to be difficult unless you get funding for a Cavendish experiment in deep space.

This is a reason why there's so many open questions about gravity--doing experiments is tough!

On the other hand, we know G (and can measure g) with far better precision than is necessary for most engineering applications as Bored Chemist pointed out.

The value we have for G does work for practical applications yes. For a theory of quantum gravity it is a different story. There must be some mathematical way of determining G even with earth as a reference point. There should also be an experiment to test it. We just haven't thought it up yet.

#### yor_on

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##### Re: What is the accepted value of g?
« Reply #24 on: 26/03/2014 16:22:44 »

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##### Re: What is the accepted value of g?
« Reply #24 on: 26/03/2014 16:22:44 »