Re: OK, Q... (Score: 2, Informative)
posted Wednesday, March 09, 2005 - 11:23 AM (
#25906)
In Response to jon (#25890):
Those of you allergic to math may wish to skip to the end, which is a nice bit and has Siobain in it.
Okay, Newton's Universal Law of Gravitation states that the force due to gravity (Fg) between two objects is equal to some constant (G, the Universal Gravitational Constant) times the product of their masses, divided by the distance between their centers (we'll assume all objects are spherical) squared:
Fg = G mM/R^2
Given that, on the surface of the earth, the force due to gravity is taken as an object's mass times the acceleration due to the local gravitational field (we'll disregard rotational effects):
Fg = mg
we can set:
mg = G mM/R^2
"m" is your mass. M is the mass of the earth, and R is the distance from the center of you (on the surface of the earth) to the center of the earth. The two "m" terms cancel each other out, thus acceleration due to the local gravitational field is:
g = GM/R^2
Per the
CRC Handbook of Chemistry and Physics, 65th Edition:
G = 6.670e-11 m^3/kg sec^2
M = 5.979e24 kg
R = 6378533 m (mean equatorial radius; bump it up by 1 meter to account for the distance from your feet to the center of your mass)
Plug it all in together, and you get:
6.67e-11 * 5.979e24/6378534^2 = (approximately) 9.8 m/sec^2
Now, if G is equal to 3, the acceleration due to gravity on the surface of the earth is going to go up by a factor of 3/6.67e-11, or (approximately) 4.497e10 (44.97e9 for you engineers out there).
So instead of gravity cruising along at the relatively sane 9.8 m/sec^2, it's now a somewhat oppresive 4.409e11 m/sec^2. Now then, weight: not the same thing as mass (which is inertial, and always the same regardless of gravity acting upon it). Weight = mass times the local gravitational field strength.
W = m g units: kg m/sec^2, or Newtons (N)
I've personally gone from a somewhat svelte 588 Newtons to a slightly blimpish 2.6454e13 (26 and a half trillion!) Newtons, or nearly as much as Kirstie Alley (and Ms Alley is tipping the scales with a number usually associated with globular superclusters). For the moment, Redwizz is correct: we weigh much, much more than we used to.
Now, to explain why Jon, Phillip, Fineas, and indeed the universe as a whole have not collapsed into a supermassive and supercompact black hole, we could explicate a complete Unified Field Theory, which would most likely require the strong nuclear force, weak nuclear force, and electromagnetic forces to precisely balance out the shift in G. Fortunately, Fineas's brain now contains all the knowledge of Stephen Hawking, so that's all right.
Or, more simply (cf: Occam's Razor), we could point out that Fineas merely said that G was now equal to "three",
with no mention of units of measure. Given that in Goatsland, it's well established that "three" has its own special
units [goats.com], we may take G's new value of "three" to be in units of "1/3 of the total of the Universal Gravitational Constant", and hey-presto, nobody's dead. Redwizz, by assuming that G is still measured in m^3/kg sec^2, instead of "units", has come to an incorrect conclusion. QED.
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