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Just wondering if there is any relationship between the two, i don't see how there can be but it is a bit strange, is it coincidence?

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- Thread starter bmcgann
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Just wondering if there is any relationship between the two, i don't see how there can be but it is a bit strange, is it coincidence?

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DaveC426913

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Just wondering if there is any relationship between the two, i don't see how there can be but it is a bit strange, is it coincidence?

Coincidence. Get enough numbers, perform enough arbitrary operations on them, with a large enough margin of error, and it would be a miracle if you

In case there's any doubt, note that the number you use to define gravity on Earth is based on metres and seconds. In feet, g is closer to 30. In furlongs per fortnight^2 you'll get a different number again. Pi is unitless (it works in feet and metres and furlongs).

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If you were correct, the gravitational constant would be equal to (pi^2*(radius)^2)/(mass)

The actuall equation for calculating the gravitational constant is (pi^2*(r)^2*d*s)/(M*T*L)

(page 6 from link provided at bottom)

G is the gravitational constant;

r is the distance between the center of the small sphere and its nearest large sphere;

d = 0.05 m, is the half the distance between the centers of the small spheres;

M is the mass of the large spheres;

T is the undamped period of oscillation;

L is the perpendicular distance from the mirror to the wall; and

S is the distance on the wall between positions of the spots of light associated with the equilibrium positions of the small spheres-rod-mirror assembly if the large spheres are fully clockwise to the equilibrium position, and if the large spheres are fully counterclockwise position.

http://www.physics.arizona.edu/~haar/ADV_LAB/BIG_G.pdf

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In case there's any doubt, note that the number you use to define gravity on Earth is based on feet and seconds. In metres, g is closer to 30. In furlongs per fortnight^2 you'll get a different number again. Pi is unitless (it works in feet and metres and furlongs).

You've got that backwards. It is 32.2 ft/s^2 or 9.81 m/s^2

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DaveC426913

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Good catch. S'what I get for doing too much editing and not enough proofing. Fixed.You've got that backwards. It is 32.2 ft/s^2 or 9.81 m/s^2

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The period of a pendulum is approximately T = 2π(L/g)^1/2

If you set T=2 and L=1 the acceleration due to gravity is π^2

That doesn't seem like a coincidence.

http://godplaysdice.blogspot.com/2007/09/why-g-2.html

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Good catch. S'what I get for doing too much editing and not enough proofing. Fixed.

Probably also related to the time of the post. I find I make a lot more errors of logic and typos when I post closer to when I wake up in the morning. If I don't wait at least an hour to really wake up, there is no telling what I might post.

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Not nearly as coincidental as you think. It is coincidental thatCoincidence.

This happy coincidence led many to propose a definition of the meter that would have made

However, the French revolutionaries also happened to be the very first aficionados of political correctness. Defining the meter to be the length of a seconds pendulum at 45

So yes, you are correct that this is a happy circumstance, but only thanks to human stupidity.

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Vanadium 50

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I didn't look past DaveC's post. Honest!

There was an immense amount of play in the standards of length that preceded the meter. By sheer dumb luck, those definitions coupled with the already well-defined value for the second (well-defined by the standards of the late 1700s) happened to more or less be such that

Two coincidences just happened to nearly coincide, and this was just coincidence. Of course the PC (and they were very PC) revolutionary council picked the dumbest but most politically correct of the three alternatives for defining the meter. A lot of French scientists who still had heads on their shoulders were quite POed at the choice. It made Poincare resign from the council.

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1790 May 8 – The French National Assembly decides that the length of the new metre would be equal to the length of a pendulum with a half-period of one second.

http://en.wikipedia.org/wiki/Metre

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Vanadium 50

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First of all, the acceleration due to gravity has DIMENSION [length]×[time]^(-2). Therefore, the **numerical value** depends on the choice of the system of units. If you want to compare numbers, you must form a DIMENSIONLESS quantity.

Since the meter was originally defined through the length of the Earth's meridian (such that the distance from the North Pole to the Equator is 10^7 m), and the second was defined through the Earth's rotation period (which is 24 × 60 × 60 = 86400 s). Thus, your*hypothesis* really is:

[tex]

\pi^2 = \frac{g \cdot 1 \, \mathrm{s}^2}{\mathrm{m}}

[/tex]

[tex]

\pi^2 = \frac{g \, \left( \frac{T}{86400} \right)^2}{\frac{\frac{R \, \pi}{2}}{10^7}}

[/tex]

Simplifying, we get:

[tex]

\frac{g \, T^2}{R} = \left( \frac{36 \, \pi}{5} \right)^3

[/tex]

Since the meter was originally defined through the length of the Earth's meridian (such that the distance from the North Pole to the Equator is 10^7 m), and the second was defined through the Earth's rotation period (which is 24 × 60 × 60 = 86400 s). Thus, your

[tex]

\pi^2 = \frac{g \cdot 1 \, \mathrm{s}^2}{\mathrm{m}}

[/tex]

[tex]

\pi^2 = \frac{g \, \left( \frac{T}{86400} \right)^2}{\frac{\frac{R \, \pi}{2}}{10^7}}

[/tex]

Simplifying, we get:

[tex]

\frac{g \, T^2}{R} = \left( \frac{36 \, \pi}{5} \right)^3

[/tex]

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AlephZero

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It was proposed in 1668 by Wilkins, it was adopted on May 8 1790 by the French National Assembly, it was changed only slightly March 30 1791 becuase the force of gravity varies slightly over the surface of the earth.

I would never question Wikipedia as an authority [/IRONY] but the early navigators knew very well that the length of a seconds pendulum varies with latitude. Finding an explanation for this was one of the major scientific questions of the time, given the importance of timekeeping for accurate navigation, and various experiments had been done on the subject. (One hypothesis was that gravity was a function of temperature). Newton summarised the experimental data in Principia, and modelled the effect in terms of gravitation and the earth's rotation.

Wren was a colleague of Newton (in fact Newton used Wren's the partly-built St Paul's Cathedral in London for some dynamics experiments on damping) so it seems rather odd that Wren would propose a "standard" that he most likely knew was poorly defined. But the French National Assembly may have had the same respect (i.e. not much) for Newton as Newton did for French scientists in general (again, reference Principia)....

But where Wilkins fits into all this, I don't know.

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The period of a pendulum is approximately T = 2π(L/g)^1/2

If you set T=2 and L=1 the acceleration due to gravity is π^2

That doesn't seem like a coincidence.

http://godplaysdice.blogspot.com/2007/09/why-g-2.html

Ok, then go and make a pendulum with length 1 and measure its period and tell us if it is 2. We eagerly await your answer.

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Ok, then go and make a pendulum with length 1 and measure its period and tell us if it is 2. We eagerly await your answer.

I was just quoting the blog, but the point was that length and time are both arbitrary measurements until you define them and correlate one with the other.

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I was just quoting the blog, but the point was that length and time are both arbitrary measurements until you define them and correlate one with the other.

No, that's not the point. The point is that g is a CONSTANT in that equation. Given the length, you cannot have arbitrary periods, but only one corresponding to the result obtained from that equation.

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No, that's not the point. The point is that g is a CONSTANT in that equation. Given the length, you cannot have arbitrary periods, but only one corresponding to the result obtained from that equation.

The length from the equator to the north pole they would have measure would have been:

(cirumfrence/4)=(radius*pi/2)

We can calculate that this would have been:

(6378100 meters * pi)/2

Which equals

10018696.05 meters which back in the day, since the meter was equal to the equivalent of 997 millimeter, the length they would have measured would have been 100488425.6 meters which is very close 10000000.

The question is, was the length from the equator to the north pole known before they chose to divide it by 10 million. If so, the relation between g and pi squared would have remained highly correlated. If not, and the division by 10 million was a random guess, then that would have been a coincident.

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lol.

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The seconds pendulum is a fluke of a convoluted time standard. One of the proposals to the French Academy was a decimal system for time with the unit of time being a day. A days pendulum would be a just bit on the long side. That the length of a seconds pendulum happens to be close to the length of a human's stride (a common standard for length prior to the meter) is sheer coincidence. That it happens to be close to one ten millionth of the distance from the equator to the north pole is also sheer coincidence.

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