Why is a standard g exactly 9.80665m/s/s?

For the discussion of the sciences. Physics problems, chemistry equations, biology weirdness, it all goes here.

Moderators: gmalivuk, Moderators General, Prelates

User avatar
skeptical scientist
closed-minded spiritualist
Posts: 6141
Joined: Tue Nov 28, 2006 6:09 am UTC
Location: San Francisco

Why is a standard g exactly 9.80665m/s/s?

Postby skeptical scientist » Wed Mar 17, 2010 12:44 pm UTC

I've wondered this for a while, but was reminded of it recently by this thread in Logic Puzzles. The strength of gravity varies over the surface of the Earth - not by a lot, but by as much as .04m/s2, or about one part in 200. So why is a standard gravity defined to be a precise value whose significant digits would indicate a precision of one part in a million? Is the quantity 9.80665m/s2 somehow more physically meaningful than 9.8 or 9.81 would be? If not, what quirk of history caused it to be this bizarre value rather than something rounder?

On a related note, it also bothers me when people use that exact number to compute a trajectory, since the added "precision" it imparts is wholly imagined.

In the thread that prompted this one, phlip and I had the following exchange:
skeptical scientist wrote:While we're on the subject, does anyone know why standard gravity is defined to be exactly 9.80665? Is this precise value in any way physically meaningful? If it isn't, why don't we use the much simpler value of 9.8 for standard gravity?

phlip wrote:Probably for the same reason that the speed of light isn't quite 3e8 m/s, and standard atmospheric pressure is over 1e5 Pa... and, for that matter, why an inch isn't 2.5cm... inertia, and the desire not to change a value too much when it gets redefined in terms of something else.

Presumably, when they decided to define standard gravity as a specific value in m/s/s, they just took the previous value for g, however that was defined, rounded it off to more digits than you'd ever really need, and used that.

I don't buy this argument, especially the comparison to the speed of light. Yes, the meter is now defined to be exactly 1/299,792,458 of the distance light travels in vacuum in one second, so one could say that the speed of light is 299,792,458 by definition, and one could rather have defined it to be 300,000,000. But before this was the definition of the meter, the length of a meter was defined by the length of a particular platinum bar held at the International Bureau of Weights and Measures. Also before the speed-of-light-definition of the meter, the speed of light in vacuum had been measured to 4 parts per billion, and was known to be 299,792,458±1 times the length of that platinum bar in a second. So when the meter was defined by a prototype meter bar, the speed of light really was 299,792,458 m/s, and that precise number had physical meaning. When the meter was redefined from the speed of light as opposed to from a prototype, it made sense to keep the same value, so as not to change the length of the meter.

I don't see how a similar argument can be made for a standard gravity. I understand how the number 299,792,458 used for the speed of light is physically meaningful, but I don't understand the physical significance of 9.80665 m/s2. Moreover, I don't see how it can be physically significant. It can't possibly be the exact force of gravity on the surface of the Earth, since that value varies between 9.78 m/s2 and 9.82 m/s2 based on location. So what, if anything, does it measure?
I'm looking forward to the day when the SNES emulator on my computer works by emulating the elementary particles in an actual, physical box with Nintendo stamped on the side.

"With math, all things are possible." —Rebecca Watson

User avatar
Charlie!
Posts: 2033
Joined: Sat Jan 12, 2008 8:20 pm UTC

Re: Why is a standard g exactly 9.80665m/s/s?

Postby Charlie! » Wed Mar 17, 2010 5:45 pm UTC

Perhaps it's an average over a long time interval, over the surface of the earth.
Some people tell me I laugh too much. To them I say, "ha ha ha!"

User avatar
gmalivuk
GNU Terry Pratchett
Posts: 25399
Joined: Wed Feb 28, 2007 6:02 pm UTC
Location: Here and There
Contact:

Re: Why is a standard g exactly 9.80665m/s/s?

Postby gmalivuk » Wed Mar 17, 2010 6:13 pm UTC

Wikipedia is, as usual, your friend:
The article on standard gravity wrote:The value of g0 defined above is a nominal midrange value on Earth, representing the acceleration of a body in free fall at sea level at a geodetic latitude of about 45.5°.


Apparently, though, the specifics are somewhat of a QWERTY-style phenomenon, where several countries happened to already have that value in their laws when it was made official.
Unless stated otherwise, I do not care whether a statement, by itself, constitutes a persuasive political argument. I care whether it's true.
---
If this post has math that doesn't work for you, use TeX the World for Firefox or Chrome

(he/him/his)

User avatar
skeptical scientist
closed-minded spiritualist
Posts: 6141
Joined: Tue Nov 28, 2006 6:09 am UTC
Location: San Francisco

Re: Why is a standard g exactly 9.80665m/s/s?

Postby skeptical scientist » Wed Mar 17, 2010 9:24 pm UTC

gmalivuk wrote:Wikipedia is, as usual, your friend:
The article on standard gravity wrote:The value of g0 defined above is a nominal midrange value on Earth, representing the acceleration of a body in free fall at sea level at a geodetic latitude of about 45.5°.


Apparently, though, the specifics are somewhat of a QWERTY-style phenomenon, where several countries happened to already have that value in their laws when it was made official.

Yeah, I saw that when I tried to google the answer for myself, but it doesn't really answer the question. It's a nominal midrange, but 9.8 would serve that purpose just as well, and I fail to see what's special about a latitude of "about 45.5º". I also found out when it was chosen: the 1901 meeting of the General Conference of Weights and Measures.
CGPM, 3rd meeting wrote:The value adopted in the International Service of Weights and Measures for the standard acceleration due to gravity is 980.665 cm/s2, value already stated in the laws of some countries.

However, this rather vague statement doesn't explain why it was chosen, just that it was "already stated in the laws of some countries" with no mention of which countries, or why they had adopted it.
I'm looking forward to the day when the SNES emulator on my computer works by emulating the elementary particles in an actual, physical box with Nintendo stamped on the side.

"With math, all things are possible." —Rebecca Watson

User avatar
gmalivuk
GNU Terry Pratchett
Posts: 25399
Joined: Wed Feb 28, 2007 6:02 pm UTC
Location: Here and There
Contact:

Re: Why is a standard g exactly 9.80665m/s/s?

Postby gmalivuk » Wed Mar 17, 2010 10:25 pm UTC

The 1930 International Gravity Formula gives 9.80635 as the average of its value at the equator and at the poles. So perhaps a prior formula gave .0003 more than this, and that's where they got the number?
Unless stated otherwise, I do not care whether a statement, by itself, constitutes a persuasive political argument. I care whether it's true.
---
If this post has math that doesn't work for you, use TeX the World for Firefox or Chrome

(he/him/his)

User avatar
You, sir, name?
Posts: 6966
Joined: Sun Apr 22, 2007 10:07 am UTC
Location: Chako Paul City
Contact:

Re: Why is a standard g exactly 9.80665m/s/s?

Postby You, sir, name? » Wed Mar 17, 2010 10:50 pm UTC

Its kind of ridiculous. With slightly varying g, what you do is not to designate a standard g with 6 significant digits, you express g with the appropriate uncertainty for the value to be correct everywhere. That is, g = 9.8(2) m/s2.
I edit my posts a lot and sometimes the words wrong order words appear in sentences get messed up.

User avatar
BlackSails
Posts: 5312
Joined: Thu Dec 20, 2007 5:48 am UTC

Re: Why is a standard g exactly 9.80665m/s/s?

Postby BlackSails » Wed Mar 17, 2010 10:56 pm UTC

Does NASA have to use a particular value of g, calculated/measured for their launch site for launches?

User avatar
gmalivuk
GNU Terry Pratchett
Posts: 25399
Joined: Wed Feb 28, 2007 6:02 pm UTC
Location: Here and There
Contact:

Re: Why is a standard g exactly 9.80665m/s/s?

Postby gmalivuk » Wed Mar 17, 2010 10:58 pm UTC

Probably, but the 1901 official value likely didn't take that into consideration...
Unless stated otherwise, I do not care whether a statement, by itself, constitutes a persuasive political argument. I care whether it's true.
---
If this post has math that doesn't work for you, use TeX the World for Firefox or Chrome

(he/him/his)

User avatar
You, sir, name?
Posts: 6966
Joined: Sun Apr 22, 2007 10:07 am UTC
Location: Chako Paul City
Contact:

Re: Why is a standard g exactly 9.80665m/s/s?

Postby You, sir, name? » Wed Mar 17, 2010 11:04 pm UTC

BlackSails wrote:Does NASA have to use a particular value of g, calculated/measured for their launch site for launches?


Since they travel far enough from the surface for error to be small albeit significant, I doubt they use small g at all.
Last edited by You, sir, name? on Wed Mar 17, 2010 11:05 pm UTC, edited 1 time in total.
I edit my posts a lot and sometimes the words wrong order words appear in sentences get messed up.

User avatar
skeptical scientist
closed-minded spiritualist
Posts: 6141
Joined: Tue Nov 28, 2006 6:09 am UTC
Location: San Francisco

Re: Why is a standard g exactly 9.80665m/s/s?

Postby skeptical scientist » Wed Mar 17, 2010 11:04 pm UTC

It does make sense to define a standard gravity, for the same reason as you define standard pressure - it is important to have a reference. It is often used as a unit of acceleration, so it is obviously important that it has a standard value. But giving the standard value 6 digits when none but the first two are physically meaningful makes no sense to me.
I'm looking forward to the day when the SNES emulator on my computer works by emulating the elementary particles in an actual, physical box with Nintendo stamped on the side.

"With math, all things are possible." —Rebecca Watson

User avatar
gmalivuk
GNU Terry Pratchett
Posts: 25399
Joined: Wed Feb 28, 2007 6:02 pm UTC
Location: Here and There
Contact:

Postby gmalivuk » Wed Mar 17, 2010 11:23 pm UTC

Incidentally, this is wrong:
In the other thread, skeptical scientist wrote:the centrifugal acceleration at the equator...is less than .001 m/s2.

Acceleration around a circle is not radius/period^2. It's v^2/r, which works out to 4pi^2 times the figure you quoted.
Unless stated otherwise, I do not care whether a statement, by itself, constitutes a persuasive political argument. I care whether it's true.
---
If this post has math that doesn't work for you, use TeX the World for Firefox or Chrome

(he/him/his)

User avatar
skeptical scientist
closed-minded spiritualist
Posts: 6141
Joined: Tue Nov 28, 2006 6:09 am UTC
Location: San Francisco

Re: Why is a standard g exactly 9.80665m/s/s?

Postby skeptical scientist » Wed Mar 17, 2010 11:48 pm UTC

Doh! Actually the formula I used was [imath]\omega^2r[/imath]; I just forgot that angular velocity has units of radians per second, not rotations per second.
I'm looking forward to the day when the SNES emulator on my computer works by emulating the elementary particles in an actual, physical box with Nintendo stamped on the side.

"With math, all things are possible." —Rebecca Watson

MallowTheCloud
Posts: 21
Joined: Sun Mar 14, 2010 9:13 pm UTC
Location: Portland, Oregon, US

Re: Why is a standard g exactly 9.80665m/s/s?

Postby MallowTheCloud » Thu Mar 18, 2010 2:16 am UTC

skeptical scientist wrote:It does make sense to define a standard gravity, for the same reason as you define standard pressure - it is important to have a reference. It is often used as a unit of acceleration, so it is obviously important that it has a standard value. But giving the standard value 6 digits when none but the first two are physically meaningful makes no sense to me.


http://discovermagazine.com/2007/mar/gr ... ld-700.jpg

1 mGal = 1x10-5 m/s2

Most areas on Earth (at a given elevation) seem to have gravitational anomalies of -40 to +40 mGal, or on the order of 1x10-4 m/s2... so precision out to five decimals (or at least four) seems pretty reasonable to me.

Carnildo
Posts: 2023
Joined: Fri Jul 18, 2008 8:43 am UTC

Re: Why is a standard g exactly 9.80665m/s/s?

Postby Carnildo » Thu Mar 18, 2010 2:58 am UTC

You, sir, name? wrote:Its kind of ridiculous. With slightly varying g, what you do is not to designate a standard g with 6 significant digits, you express g with the appropriate uncertainty for the value to be correct everywhere. That is, g = 9.8(2) m/s2.

No. Standard gravity is not a measured quantity, it is a defined quantity. Expressing it to six digits is simply a shorthand; the actual value is exactly 9.8066500000000000000...m/s/s.

User avatar
phlip
Restorer of Worlds
Posts: 7535
Joined: Sat Sep 23, 2006 3:56 am UTC
Location: Australia
Contact:

Re: Why is a standard g exactly 9.80665m/s/s?

Postby phlip » Thu Mar 18, 2010 4:19 am UTC

Carnildo wrote:No. Standard gravity is not a measured quantity, it is a defined quantity. Expressing it to six digits is simply a shorthand; the actual value is exactly 9.8066500000000000000...m/s/s.

Sure, but the question is why it was defined as that, and not 9.800000000000... m/s/s. Since that value is much easier to remember, and is just as good an approximation for the actual gravity in any given place on the Earth as the actual value.

Code: Select all

enum ಠ_ಠ {°□°╰=1, °Д°╰, ಠ益ಠ╰};
void ┻━┻︵​╰(ಠ_ಠ ⚠) {exit((int)⚠);}
[he/him/his]

Fume Troll
Posts: 254
Joined: Wed Jan 13, 2010 8:06 am UTC
Location: Scotland / Norway mainly

Re: Why is a standard g exactly 9.80665m/s/s?

Postby Fume Troll » Thu Mar 18, 2010 12:33 pm UTC

I guess because the "standard" it was based on was the average between the poles and the equator - albeit a bit out by modern reckoning.

Rounding it off wouldn't make it relevant to any particular physical phenomenon, and seems rather unscientific.

User avatar
phlip
Restorer of Worlds
Posts: 7535
Joined: Sat Sep 23, 2006 3:56 am UTC
Location: Australia
Contact:

Re: Why is a standard g exactly 9.80665m/s/s?

Postby phlip » Thu Mar 18, 2010 1:42 pm UTC

Fume Troll wrote:Rounding it off wouldn't make it relevant to any particular physical phenomenon, and seems rather unscientific.
But leaving it at the rather random number it's at doesn't make it any more relevant to any physical phenomena, and isn't any more scientific...

Code: Select all

enum ಠ_ಠ {°□°╰=1, °Д°╰, ಠ益ಠ╰};
void ┻━┻︵​╰(ಠ_ಠ ⚠) {exit((int)⚠);}
[he/him/his]

User avatar
gmalivuk
GNU Terry Pratchett
Posts: 25399
Joined: Wed Feb 28, 2007 6:02 pm UTC
Location: Here and There
Contact:

Re: Why is a standard g exactly 9.80665m/s/s?

Postby gmalivuk » Thu Mar 18, 2010 2:02 pm UTC

Fume Troll wrote:I guess because the "standard" it was based on was the average between the poles and the equator - albeit a bit out by modern reckoning.

That's still only a guess as far as this thread is concerned, unless someone else has come across actual references to that fact.

phlip wrote:But leaving it at the rather random number it's at doesn't make it any more relevant to any physical phenomena, and isn't any more scientific...

Well sure, but I don't see how rounding it off outweighs the disadvantages of fucking with an international standard that's been in place for over a century.
Unless stated otherwise, I do not care whether a statement, by itself, constitutes a persuasive political argument. I care whether it's true.
---
If this post has math that doesn't work for you, use TeX the World for Firefox or Chrome

(he/him/his)

User avatar
Zamfir
I built a novelty castle, the irony was lost on some.
Posts: 7210
Joined: Wed Aug 27, 2008 2:43 pm UTC
Location: Nederland

Re: Why is a standard g exactly 9.80665m/s/s?

Postby Zamfir » Thu Mar 18, 2010 2:50 pm UTC

Just a thought: an exactly defined g is important for laws and standards (and contracts!) that for some reason define quantities of matter as a weight. You want to be able to buy so many tonnes or pounds without having to worry whether those are polar tonnes or equatorial tonnes, or going into discussing whether those tonnes were intended really as a mass or a weight. So under those circumstances I can imagine that countries defined a fixed g before an international standard was chosen.

Also, "9.8" is only simple in a metric system. I can imagine that our beloved inchy friends across the waters thought that if they were going to get a weird number, so was everyone else.

User avatar
gmalivuk
GNU Terry Pratchett
Posts: 25399
Joined: Wed Feb 28, 2007 6:02 pm UTC
Location: Here and There
Contact:

Re: Why is a standard g exactly 9.80665m/s/s?

Postby gmalivuk » Thu Mar 18, 2010 3:04 pm UTC

No, because it's still only a terminating value in metric, and not in inches or feet.
Unless stated otherwise, I do not care whether a statement, by itself, constitutes a persuasive political argument. I care whether it's true.
---
If this post has math that doesn't work for you, use TeX the World for Firefox or Chrome

(he/him/his)

MallowTheCloud
Posts: 21
Joined: Sun Mar 14, 2010 9:13 pm UTC
Location: Portland, Oregon, US

Re: Why is a standard g exactly 9.80665m/s/s?

Postby MallowTheCloud » Thu Mar 18, 2010 5:11 pm UTC

phlip wrote:Sure, but the question is why it was defined as that, and not 9.800000000000... m/s/s. Since that value is much easier to remember, and is just as good an approximation for the actual gravity in any given place on the Earth as the actual value.


And the answer is that it's not just as good an approximation.

The OP was incorrect about the variability of gravity at a given elevation over the Earth's surface.

MallowTheCloud wrote:http://discovermagazine.com/2007/mar/grace-in-space/world-700.jpg

1 mGal = 1x10-5 m/s2

Most areas on Earth (at a given elevation) seem to have gravitational anomalies of -40 to +40 mGal, or on the order of 1x10-4 m/s2... so precision out to five decimals (or at least four) seems pretty reasonable to me.



Yes, elevation plays a much larger role, but there's a precise equation to get the force of gravity given standard g and your elevation, so that doesn't fly either. Standard g should have at least 5 significant digits, and 6 seems reasonable as well.


EDIT: Latitude also plays a significant role (due to "centrifugal force"), but again, this can be calculated precisely.

So, basically, a "standard gravity" will generally be accurate to at least four decimal places after you take latitude and altitude into consideration.

User avatar
scarecrovv
It's pronounced 'double u'
Posts: 674
Joined: Wed Jul 30, 2008 4:09 pm UTC
Location: California

Re: Why is a standard g exactly 9.80665m/s/s?

Postby scarecrovv » Thu Mar 18, 2010 8:00 pm UTC

gmalivuk wrote:No, because it's still only a terminating value in metric, and not in inches or feet.


That's not actually correct. 1 inch is exactly 2.54 cm, and I get this in clisp:

Code: Select all

[20]> (format t "~10,100F" (/ (/ (* 980665/100000 100) 254/100) 12))
32.1740500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
NIL
[21]>


fractions in lisp are exact, and I only converted to floats during printing.

User avatar
You, sir, name?
Posts: 6966
Joined: Sun Apr 22, 2007 10:07 am UTC
Location: Chako Paul City
Contact:

Re: Why is a standard g exactly 9.80665m/s/s?

Postby You, sir, name? » Thu Mar 18, 2010 9:00 pm UTC

MallowTheCloud wrote:
Spoiler:
phlip wrote:Sure, but the question is why it was defined as that, and not 9.800000000000... m/s/s. Since that value is much easier to remember, and is just as good an approximation for the actual gravity in any given place on the Earth as the actual value.


And the answer is that it's not just as good an approximation.

The OP was incorrect about the variability of gravity at a given elevation over the Earth's surface.

MallowTheCloud wrote:http://discovermagazine.com/2007/mar/grace-in-space/world-700.jpg

1 mGal = 1x10-5 m/s2

Most areas on Earth (at a given elevation) seem to have gravitational anomalies of -40 to +40 mGal, or on the order of 1x10-4 m/s2... so precision out to five decimals (or at least four) seems pretty reasonable to me.



Yes, elevation plays a much larger role, but there's a precise equation to get the force of gravity given standard g and your elevation, so that doesn't fly either. Standard g should have at least 5 significant digits, and 6 seems reasonable as well.


EDIT: Latitude also plays a significant role (due to "centrifugal force"), but again, this can be calculated precisely.


So, basically, a "standard gravity" will generally be accurate to at least four decimal places after you take latitude and altitude into consideration.


If you take latitude and altitude into consideration, you are no longer using standard gravity.
I edit my posts a lot and sometimes the words wrong order words appear in sentences get messed up.

User avatar
gmalivuk
GNU Terry Pratchett
Posts: 25399
Joined: Wed Feb 28, 2007 6:02 pm UTC
Location: Here and There
Contact:

Re: Why is a standard g exactly 9.80665m/s/s?

Postby gmalivuk » Thu Mar 18, 2010 9:04 pm UTC

scarecrovv wrote:
gmalivuk wrote:No, because it's still only a terminating value in metric, and not in inches or feet.


That's not actually correct. 1 inch is exactly 2.54 cm, and I get this in clisp:

Code: Select all

[20]> (format t "~10,100F" (/ (/ (* 980665/100000 100) 254/100) 12))
32.1740500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
NIL
[21]>


fractions in lisp are exact, and I only converted to floats during printing.

What now?

Are you claiming that 980665/254 or 980665/3048 are terminating decimals? Because they're definitely not, and I'm furthermore not sure why you obfuscated that with your bit of code there when WolframAlpha would have told you quite easily.
Unless stated otherwise, I do not care whether a statement, by itself, constitutes a persuasive political argument. I care whether it's true.
---
If this post has math that doesn't work for you, use TeX the World for Firefox or Chrome

(he/him/his)

MallowTheCloud
Posts: 21
Joined: Sun Mar 14, 2010 9:13 pm UTC
Location: Portland, Oregon, US

Re: Why is a standard g exactly 9.80665m/s/s?

Postby MallowTheCloud » Thu Mar 18, 2010 11:33 pm UTC

You, sir, name? wrote:
MallowTheCloud wrote:
Spoiler:
phlip wrote:Sure, but the question is why it was defined as that, and not 9.800000000000... m/s/s. Since that value is much easier to remember, and is just as good an approximation for the actual gravity in any given place on the Earth as the actual value.


And the answer is that it's not just as good an approximation.

The OP was incorrect about the variability of gravity at a given elevation over the Earth's surface.

MallowTheCloud wrote:http://discovermagazine.com/2007/mar/grace-in-space/world-700.jpg

1 mGal = 1x10-5 m/s2

Most areas on Earth (at a given elevation) seem to have gravitational anomalies of -40 to +40 mGal, or on the order of 1x10-4 m/s2... so precision out to five decimals (or at least four) seems pretty reasonable to me.



Yes, elevation plays a much larger role, but there's a precise equation to get the force of gravity given standard g and your elevation, so that doesn't fly either. Standard g should have at least 5 significant digits, and 6 seems reasonable as well.


EDIT: Latitude also plays a significant role (due to "centrifugal force"), but again, this can be calculated precisely.


So, basically, a "standard gravity" will generally be accurate to at least four decimal places after you take latitude and altitude into consideration.


If you take latitude and altitude into consideration, you are no longer using standard gravity.


True. If there were equations which allowed you to use g to more simply calculate acceleration due to gravity at any latitude or altitude, then it would be worthwhile to keep the precision. However, it seems the equations to approximate the effects of latitude and altitude don't even involve "standard gravity", so I can't really defend the precision.

User avatar
scarecrovv
It's pronounced 'double u'
Posts: 674
Joined: Wed Jul 30, 2008 4:09 pm UTC
Location: California

Re: Why is a standard g exactly 9.80665m/s/s?

Postby scarecrovv » Thu Mar 18, 2010 11:48 pm UTC

gmalivuk wrote:
scarecrovv wrote:
gmalivuk wrote:No, because it's still only a terminating value in metric, and not in inches or feet.


That's not actually correct. 1 inch is exactly 2.54 cm, and I get this in clisp:

Code: Select all

[20]> (format t "~10,100F" (/ (/ (* 980665/100000 100) 254/100) 12))
32.1740500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
NIL
[21]>


fractions in lisp are exact, and I only converted to floats during printing.

What now?

Are you claiming that 980665/254 or 980665/3048 are terminating decimals? Because they're definitely not, and I'm furthermore not sure why you obfuscated that with your bit of code there when WolframAlpha would have told you quite easily.


Oh dear, it seems you're correct! I didn't think to use Wolfram Alpha, and I assumed format would print fractions as decimals with as much precision as I asked for. Oh well.

Never mind me.

Fume Troll
Posts: 254
Joined: Wed Jan 13, 2010 8:06 am UTC
Location: Scotland / Norway mainly

Re: Why is a standard g exactly 9.80665m/s/s?

Postby Fume Troll » Mon Mar 22, 2010 1:56 pm UTC

gmalivuk wrote:
Fume Troll wrote:I guess because the "standard" it was based on was the average bewteen the poles and the equator - albeit a bit out by modern reckoning.

That's still only a guess as far as this thread is concerned, unless someone else has come across actual references to that fact.

Fair enough.

That's what's suggested here: http://en.wikipedia.org/wiki/Kilogram_force

and is here: http://mtp.jpl.nasa.gov/notes/altitude/altitude.html
edited for quotes.
Last edited by Fume Troll on Mon Mar 22, 2010 2:44 pm UTC, edited 1 time in total.

User avatar
skeptical scientist
closed-minded spiritualist
Posts: 6141
Joined: Tue Nov 28, 2006 6:09 am UTC
Location: San Francisco

Re: Why is a standard g exactly 9.80665m/s/s?

Postby skeptical scientist » Mon Mar 22, 2010 2:42 pm UTC

Fume Troll wrote:That's what's suggested here: http://en.wikipedia.org/wiki/Kilogram_force

To be fair, that only says that standard gravity is "a conventional value approximating the average magnitude of gravity on Earth". This is true of lots of other values, including 9.8.


Interestingly, that says "The original definition of \(\gamma_{45}\) was 9.8 m/s2; however, this was changed in the US in 1935 to the current value: \(\gamma_{45}\)=9.80665 m/s2. Finally, the earth's gravity model has been modified slightly since this most recent definition of \(\gamma_{45}\), so \(\gamma_{45}\) is now the gravity at 45.542 degrees instead of 45.0 degrees." So originally the US had the value which makes more sense to me, and then changed it to the one which makes less sense (presumably to bring it in line with the international standard, which leaves open the question of why the international standard was the strange value in the first place. It also suggests that even though 9.80665 m/s is now the gravity at 45.542º, at one point it may have been the gravity at 45º exactly. Unfortunately, it doesn't actually say this.
I'm looking forward to the day when the SNES emulator on my computer works by emulating the elementary particles in an actual, physical box with Nintendo stamped on the side.

"With math, all things are possible." —Rebecca Watson

Fume Troll
Posts: 254
Joined: Wed Jan 13, 2010 8:06 am UTC
Location: Scotland / Norway mainly

Re: Why is a standard g exactly 9.80665m/s/s?

Postby Fume Troll » Mon Mar 22, 2010 3:47 pm UTC

More here: http://www.numericana.com/answer/units.htm#g
Spoiler:
To an actual measurement of 9.80991 m/s2 in Paris, a theoretical correction factor of 1.0003322 was applied which gives a sea-level equivalent at 45° of latitude. The result (9.80665223...) was rounded to five decimals to obtain the value officially enacted by the third CGPM, in 1901.

The above includes a centrifugal component due to the rotation of the Earth, whereas the gravitational field at altitude zero has a slightly larger value, used when tracking satellites outside the atmosphere in nonrotating coordinates (9.82025048(2) m/s2 ) which is the ratio of the Earth's gravitational constant (3.986004415(8) 1014 m3/s2 ) to the square of the conventional radius of the Earth (R = 6371000 m).



Shame I can't find the conference proceedings.

User avatar
gmalivuk
GNU Terry Pratchett
Posts: 25399
Joined: Wed Feb 28, 2007 6:02 pm UTC
Location: Here and There
Contact:

Re: Why is a standard g exactly 9.80665m/s/s?

Postby gmalivuk » Mon Mar 22, 2010 3:54 pm UTC

Well even without conference proceedings, you did at least finally find something that said explicitly how the number was arrived at. So thanks for that.

I wonder why the Internet made this particular question so difficult to actually pin down...
Unless stated otherwise, I do not care whether a statement, by itself, constitutes a persuasive political argument. I care whether it's true.
---
If this post has math that doesn't work for you, use TeX the World for Firefox or Chrome

(he/him/his)

User avatar
skeptical scientist
closed-minded spiritualist
Posts: 6141
Joined: Tue Nov 28, 2006 6:09 am UTC
Location: San Francisco

Re: Why is a standard g exactly 9.80665m/s/s?

Postby skeptical scientist » Tue Mar 23, 2010 1:44 am UTC

Thanks, fume troll.
I'm looking forward to the day when the SNES emulator on my computer works by emulating the elementary particles in an actual, physical box with Nintendo stamped on the side.

"With math, all things are possible." —Rebecca Watson


Return to “Science”

Who is online

Users browsing this forum: No registered users and 4 guests