Physicists Find More Precise Gravity Number 143
DM writes "Physicists establish the most precise measurement ever achieved of Isaac Newton's gravitational constant and use this information to recalculate the mass of the earth. Check out the article at ScienceDaily." Now if they could only recalibrate to make me really buff, that would be nice.
Females (Score:5)
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CAIMLAS
This is Great News (Score:2)
Would it be... (Score:2)
And the new gravitational constant is... (Score:1)
Wishful thinking (Score:2)
Sorry, Emmett. They're scientists, not miracle workers.
Re:And the new gravitational constant is... (Score:1)
Interesting.. (Score:2)
""That is a huge embarrassment for modern physics, where we think we know everything so well and other constants are defined to many, many digits," Gundlach said. "
Hmm.. well it's great that they have recalculated Newton's Gravity Number, but.. in what will we gain with knowing the mass of Earth?
"Gundlach acknowledged that the more precise calculation probably won't mean much to the average person."
Ahh here we go.. not much to us, hrmm..
What will many different Earth Scientists/Chemists learn from this then? The article doesn't seem to mention anything.. Wow, we know the Earth's mass, lets move on to the next operation to waste money..
How really important is the value of 'G'?
If this is going to make teleportation devices and enhance lightspeed development, I'm all for it! I can't wait to teleport to China and back within seconds, wouldn't anyone love that?
""Gravity is the most important large-scale interaction in the universe, there's no doubt about it," Gundlach said. "It is largely responsible for the fate of the universe. Yet it is relatively little understood.""
What? I'm sure every student in every High School does *many* things concerning gravity, and different sorts of energy and how gravity affects them.. at least *I* did..
Gravity the most important part of this world? I thought it was evading black holes.. Oh wait, that does deal with gravity!
Ah well, anything new about our Earth to help to explain it is worth it to me. Good work Gundlach!
so....what is it? (Score:1)
"There are no shortcuts to any place worth going."
Do you realy want to be "Buff" ? (Score:1)
In this case the various stages of Bufness are on a scale similar to the various levels of Bufness the way emmett probably meant it. Therefore by being "really buff" would make you attractive to Heterosexual men. The same kind who get mad when the realize they are dating a man in disguise.
So emmett. Next time be more careful what you wish for. A larger more muscular body is more accurate.
Silly physicists... (Score:1)
"I always used Pi Squared for g, the math seemed to come out right", said local physicist Fred Flintstone.
However, his assistant Barney Rubble disagreed, saying "Gee, Fred, I thought Pi was somewhere between 2 and 5. That doesn't sound very precise to me!"
Apparently the tried-and-true method of waiting for an apple to fall from a tree and counting "One Mississippi, Two Mississippi..." doesn't offer significant resolution to reliably yield a better approximation for g, either. Scientists are now experimenting with coconuts, and early results look optimistic.
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pb Reply or e-mail; don't vaguely moderate [ncsu.edu].
That screws up Wednesday's test (Score:1)
Cheers to Ep = -GMm/d
amnesty
Grand Unified Theory (Score:1)
"Sorry, but you know all that research you guys threw out. Well bring it back out we have a new G for you guys."
is this retroactive? (Score:4)
Q: What do you think about American Culture?
A: I think it's a good idea.
Gravity stinks ... (Score:1)
Think (Score:1)
Re:And the new gravitational constant is... (Score:2)
The analysis of our first set of measurements gives us an uncertainty of only about 0.0015%
So it makes sense that they are not publishing the number until it is confirmed. But apparently they are sure enough about it in the sense that "[they] are already confident that [they] know the mass of
amnesty
Re:so....what is it? (Score:1)
I wish I could find where they mention the real number itself, or at least offer a link to where one may find it.
The lay person's version [aps.org] of the paper in question says "we are still running a number of tests in order to confirm our final number". So I guess you can't get the number just yet, but hopefully soon enough will be able to..
Re:Silly physicists... (Score:1)
Re:Silly physicists... (Score:1)
However they are having this big debate on what size of coconut to use and if it is better to leave the hairs on or shave them off.
Re:Think (Score:1)
UPDATE: /. effect weighs heavily on gravity site (Score:3)
G (Score:2)
6.67259 x 10 ^ -11 m^3/km/s^2
and the standard uncertaintity is
0.00085 x 10 ^ -11 m^3/kg/s^2
which is quite high when comparing to other fundamental consants
Wrong number. (Score:2)
What they are referring to here is the gravitational constant, used to calculate the force of attraction between two masses.
Re:so....what is it? (Score:1)
Not to be obnoxious, but 9.8N is not G...that's Earth's gravity. Big G is a universal constant, which was (before this article, anyhow) accepted to be:
6.672 x 10^-11 Nm^2/kg^2
Between that and the error information in the article, you could probably figure out what the new number is...which I would do if I wasn't already wasting time better spent studying for tomorrow's exam reading slashdot...
*sigh*
Dibs! (Score:2)
weight of all plant and animal life on the Earth's surface."
I call all the plant & animal life!!!!! (I know, I know, I'm gonna have to pay somebody rent, sigh).
It's all relative... (Score:1)
moving the world on hold (Score:5)
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www.chowda.net [chowda.net]
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Final Exams (Score:1)
Re:Would it be... (Score:1)
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Nothing is a constant (Score:1)
Problem with Measuring G (Score:3)
As the article said, G is very vague in its defination. Some new calculations have acutally put G at 6.64x10^-11 to 6.69x10^-11 which is quite a huge range. Whereas the two other constants, h [planck's contant] and c [speed of light in vaccum] is more well defined and had gotten more accurate.
The biggest problem with measuring big G [what we are discussion here, instead of little g which is 9.81m/s^2] is the influence of other objects. We did the experiement for our class in a basement labratory and I was able to predict based on minute changes in the data I was getting that people were moving their desks around. I was 4 floors down from the top floor and when I went upstairs, the professor [I was able to predict where in the building from the measurements and the fact that he was the only one up there in that section] admitted he was moving around to re-orient his new desk.
Also, another time, a huge pickup truck came to the parking lot in front of the physics building. I noticed right away my measurements go askew cause of it.
As I said, G is very sensitve to tiny changes in the enviorment, much more then h [planck's constant] and c [speed of light]. Often, to measure the constant G, people has to work when there is no activity going [either at night] or somewhere remote. In fact, one of the recent measurements was taken in the middle of the Nevada Desert.
You fools that didn't use mass (Score:1)
Re:Interesting.. (Score:3)
Newton's Universal Law of gravitation tells us that F = GMm/d^2. That means that any two objects in the universe apply an equal gravitation force to each other proportional to the product of the two masses and inversely proportional to the distance of the two objects squared.
So to find a geosynchronous orbit for a satellite, we would equate centripetal force with gravitation and get 4(pi)^2mr/T^2 = GMm/r^2 which would isolate to T^2 = 4(pi)^2R^3/GM, where T was the period of rotation of the planet.
It takes three satellites in geosynchronous orbit to cover the entire Earth, allowing a communication from any two points in the world in up to 0.5 seconds (limited by the speed of light). We have two satellites locked into place, but we have and failed over numerous attempts at putting the third one up, missing the target. Speculation suggests that perhaps an inaccurate value of G could have attributed to some of the failure here?
Even simple energy problems are affected by G. Ep=mgh is only useful for problems close to the Earth's surface. Since g (acceleration of gravity) is an inverse square proportion to the radius from the centre, that means that as the distance changes, so does g. So we must use energy wells. They come from the integration of our F=GMm/d^2, becoming E=-GMm/d (as integral of F-d is work, being energy). So even energy calculations need G.
I could go on forever, but the point is that all masses in the universe are related with constant G, so it therefore is important for us to get a precise value of this constant.
Re:so....what is it? (Score:2)
G is 6.67259x10-11
Another Article (Score:2)
Re:It's all relative... (Score:1)
As a side note, presuming you could survive at the centre of the earth, wouldn't you be weightless since the gravitational effect of the mass of earth would be pulling on you from all sides?
Re:Gravity stinks ... (Score:1)
The earth gains weight (Score:1)
Uh-oh. We're doomed. (Score:2)
WHY, oh WHY, couldn't they have left well enough alone?
"The map calling the territory black."
Re:Problem with Measuring G (Score:1)
Hint: the speed of light in vacuum c in m/s is an integer. So there is no need to get it more exact because it is already exact. Nice move to redefine the meter appropriately, isn't it?
Go here [metric.org]
Re:so....what is it? (Score:1)
Re:Gravity stinks ... (Score:1)
Well, I think your problem is that you're going about it the wrong way. From the Hitchiker's Guide to the Galaxy: "There is an art, or rather a knack, to flying. The knack involves the ability to throw yourself at the ground very hard, and miss." (I'm quoting that from memory, so I probably mangled the actual quote, but that's the gist of it.) You'll never fly if you just stand there flapping your arms. You have to throw yourself at the ground without actually hitting it. The key to doing that is to completely forget about gravity, the ground, and how much it's going to hurt when you land. It might help to jump off a high cliff, so as to give yourself more time to forget about falling and thus achieve flight. Good luck!
Re:Big G (Score:1)
Using more accurate values and your logic, GM=G'M', thus G' = (6.67259x10^-11)(5.9736x10^24)/(5.792x10^24)
Which gives G' = 6.8818x10^-11. That gives a -3.04 % error.
However I'm not sure if we can arbitrarily equate the two.
actually... (Score:1)
no, but the cosmological constant was measured to be 42 a couple of years back, in whatever units it's usually reporte in (like nanometers of red-shift per megaparsec of space, or something like that). i thought that was pretty cool
cheers,
sh_
Re:Problem with Measuring G (Score:3)
Hehe - you know you're talking to a physics major when they claim, in a serious vein, that
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Gravitational life (Score:4)
Strong forces hold together the nuclei of all atoms more complex than hydrogen. Suppose a proton some 10^-13cm in size travelling at speed of 1000kilometers per second (average speed for a proton) at temperature of 1million K. It would cover a distance of 2 meters in 10^-21 of a second. Human would cover this distance in about a second. So for a proton 10^-21 second means the same as 1 second for a human.
Collisions of many elementary particles on a neutron star could produce massive nuclei, each made of thousands and tens of thousands, of elementary particles. They would last for 10^-15 of a second and then decay. In other words, a massive nucleus might have a million different collisions or other interactions before it decayed.
So if these particles could produce some equivalent of a structure capable of storing information and of replication by selective copying (like the DNA or RNA) star might produce forms of life. Individuals that interact with their environment and with other individuals in an organized way.
If this really happened, the development of life would happen much faster than what we observe in our solar system.. 10^-21 second is one billion-billionth of the thousandth of a second then the origin of life would require not about 1 billion years (our planet: ~600million years) but about 1/billionth of a year, of 1/13 of a second! It may seem short to us but it might exist on the surface of a neutron star. (too bad we could not interact with them)
On the other extreme end of this is the type of life we could call a "Gravitational Life" based on Gravitational forces. A typical subunit of life would be so large that gravity would be the dominant force for it, not electromagnetic force, a star would work in this case as a base unit. Individual stars would play the role of atoms (or molecules) on Earth. An organism so large that its basic building units are stars and galaxies (maybe even multiple universes) could in principle be possible. Would you like to think about yourself as of basicly microorganisms living in a huge super organism? Of-course star and galaxy interactions are upon scale of millionth of years, so if life originated from repeated effects of such interactions (like molecule interactions) then there is a long way to go before a living organism based on this interactions could develop.
And you think the mass of earth is important
Re:It's all relative... (Score:1)
But anyway the concern is not about 9.8m/s^2 (surface gravity of Earth). We're looking for G, one of the big three universal constants of nature (with Plank's constant and speed of light).
Relative Gravity (Score:1)
There is something called the Free Air Anomaly (FAA). This is the change is relative gravity if one moves in the vertical direction while neglecting the affect of "local" gravitational masses. You may want to review Gauss's Law. The FAA is about 0.31 milligals per meter (most students could measure to at least 1 mgal precision). We used to do a lab experiment that required one to measure the height of the tallest building on campus by measuring relative gravity. Neglect (which is to the 1st order isokay) the mass of the building. The measurements turned out to be relatively very good. One such measurement was performed on a structure that recently housed a relatively large Tetris game.
Old relative gravity measurements were made using submarines and pendulums. Remember 1st year physic classes/labs. This cyclic motion (period) of a pendulum is not based on the mass, but is a function of the length of the pendulum and gravity (sqrt(length/g). The subs provided a stable platform.
Re:Problem with Measuring G (Score:3)
Re:The earth gains weight (Score:1)
We probably lose a good deal of atmosphere too, though. Who knows.
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CAIMLAS
Re:Problem with Measuring G (Score:1)
All the planets have to be recalculated? (Score:1)
And on a lighter note, my calculator's now obsolete. The press of a button gives me G and mass of the Earth, which have since both changed.
What the hell? (Score:1)
Anyway, that affects little g (the gravitational attraction between anything and earth), not big G (the gravitational attraction between any two objects, depending on mass and distance). Big G stays the same everywhere.
Make you buff. (Score:1)
What you need is a device that will dynamically adjust gravity. It will increase gravity on you, so that you get a continual and constant workout during the day. But, then when you need to lift things or jump (and land too) it will reduce gravity.
This would use the increased gravity to build and tone muscle. Then the reduced gravity to lift the car, jump over buildings. And of course, increase gravity between your fist and the bully's face so, when you punch him/her you get a gravity assist.
Now if it can be done for less than $6,000,000 it's a deal. :)
Re:Grand Unified Theory (Score:1)
When I first read this article I was thinking along similar lines. How will this change all the calculations that rely on G? I think it's time to do some recrunching of numbers. The area I think would be most interested is astronomy with the orbits of all the Potentially Hazardous Asteroids [harvard.edu]. My favorit PHA is AN10 which will pass .0026AU from earth or in other words closer than the moon. You have to wait till 2027 for that to happen. Other close pass bys [harvard.edu] will happen before then. May 7th is when EH26 will visit at only 0.0406AU.
Bzzt Wrong? (Score:2)
Gravity, or big G is constant everywhere, its used in a formula (that I cannot remember) to calculate the gravitational force between any two objects (along with there mass and distance (increases with mass, decreases with distance).
You aren't being pulled toward the center of earth, you are being pulled toward every particle in it. The average vector points to the earth's center of gravity. When you get closer to that point, more and more of the vectors would be pointing away from that. When you got to the center, the average vector would be (0,0,0), so it would seem that you were weightless. When you get farther away from earth, the distance to those particles would be less, so the effect of gravity would seem to be less. That's why don't fall into the sun (since it has more mass then earth)
Its one thing to be misinformed, like the author of the root comment. It's quite another thing to be wrong and insult people who are correct. The second thing makes you an idiot.
um (Score:1)
Re:The earth gains weight (Score:1)
we weigh ~6,000,000,000,000,000,000,000 metric tons, we gain ~200 metric tons per year.
That's really significant!
\end{sarcasm}
Where does the earth ever hide away these lbs?
Give up? Rosie O'Donnel
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I cannot agree (Score:2)
This of course has had it's ramifications in the modern view of the Universe. See this Slashdot Story [slashdot.org], and the recent developments which suggest that is it "flat".
What I say is, this is a good start, but we have a long way to go.
AND, does this also include the all ellusive, but ever present Dark Matter in the calculation?
It's 95% of the universe, you know....
*Carlos: Exit Stage Right*
"Geeks, Where would you be without them?"
Buff? (Score:1)
Re:Would it be... (Score:1)
I don't think so...because then we would know what the question is, and we all know what happens to the earth 5 minutes before the question is figured out. The accurate mass of the Earth would be useless after the Vogons demolish the planet.
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Shrinkage? Way OT (Score:1)
This was a great discussion related to a /. poll before the "need" for moderation. I have said it once and and must say it again. Ask the freaking question again: toliet paper, under or over? This was a great question as eventually the cat ppl came out in force.
Re:Problem with Measuring G (Score:1)
Re: It's all relative (Score:1)
No. They're talking about the universal constant G, not the average gravitational acceleration on earth (g). G, if it's anything like the other universal constants, is the same everywhere in the universe.
Now, wouldn't it throw the physicists for a loop if G turned out to be the first "universal constant" to have local variations?
Hmmm... only way I can think of to test that is to watch the orbit of some planet or double-star system for a few gazillion years.
Re:Silly physicists... (Score:1)
When taking a rather complicated astrophysics class, we commonly approximated pi as 1, and pi^2 as 10. Honestly, even if we used exact constants, many times the physical model we were using was so unrealistic that we'd be lucky if we our answer was within an order of magnitude.
Is This A Problem... (Score:2)
...or a solution waiting for a problem. Has anybody come up with any good applications yet? How expensive is this device? Could you use it to find, oh... trapped miners, people burried under earthquake debris, or gold veins? I mean, if you can tell that your professor is moving around upstairs, then you can presumeably tell that there is a tiger behind door number 2, but could it be made more precise and/or accurate than other techniques (e.g., ultrasound, cat scans, etc.).
Re:Gravity stinks ... (Score:1)
Re:Uh-oh. We're doomed. (Score:1)
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I'm not ashamed. It's the computer age, nerds are in.
They're still in, aren't they?
Re:Silly physicists... (Score:1)
Re:It's all relative... (Score:1)
Yes, but that assumes that people are simply points. Gravity actually depends entirely on how tall you are. That's why the tall presidential candidate always wins. (Unless the other guy has hair). The votes are pulled toward them.
The closer you get to the center of the earth, the more gravity there is going to be.
Now that's just ridiculous. Everybody knows that gravity comes out of the sun, and the Earth just reflects it onto us. Therefore, the closer you get to the sun the more gravity there is. It's just like the moon at night: It doesn't actually emit light, it just reflects it. That's why everything seems to have less gravity during the night.
Therefore making the number higher.
It's refreshing to know that English grammer teachers haven't invaded Slashdot yet. I'm not sure what to say about that bit.
If you were to stand on a tall mountian, however, that number would be less.
Well, if you consider the implications of Bell's theorum on quantum dynamics, you cannot stand on a tall mountain unless the tall mountain stands on you. Likewise, the mountain will not gravitate you unless you gravitate the mountain.
Doh! (Score:1)
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I'm not ashamed. It's the computer age, nerds are in.
They're still in, aren't they?
Re:Silly physicists... (Score:1)
(and Pi Squared is pretty close to g, actually...
So I guess my point is, who cares what g really is if no one uses it? Especially if it took them this long to find out they were wrong, they really weren't paying attention...
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pb Reply or e-mail; don't vaguely moderate [ncsu.edu].
Re:PRIMERO (Score:1)
-Mirando el juego, bibiendo un Bud.
-Verdad. Verdad.
-Oye, ?donde esta Duque?
-!Duque, recoja el teléfono!
-?Bien?
-**QUE PASAAAAAAAAAAAAAAAAA!!!***
-AAAAAAAAAAAAAAA
-AAAAAAAAAAAA
-AAAAAAAAAAAAAAA *el clic*
-Entonces, ?que pasa, muchacho?
-Mirando el juego, bibiendo un Bud.
-Verdad. Verdad.
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I'm falling around the sun (Score:1)
orbiting the sun (which, to paraphrase some of the
posts above, is basically "falling but missing")
Re:And? (Score:1)
Less weight, same mass, less droopy...
Gravity only affects weight, not mass. So there is exactly the same amount of cute buttocks there, it just weighs less.
Re:Would it be... (Score:1)
Re:Silly physicists... (Score:1)
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What about the force? (Score:1)
Drawing with gravity (Java) (Score:1)
http://www.snibbe.com/sc ott/dynamic/gravilux/gravilux.html [snibbe.com]
Kinda offtopic, but gravity-related and FUN! Try collecting a bunch of the stars into a small cluster, and then clicking right in the middle of it. BOOM!
- Isaac =)
G Spot (Score:2)
News for Nerds - stuff that matters??
David E. Weekly [weekly.org]
5.9763 e21 tons (Score:1)
Re:Problem with Measuring G (Score:1)
Well, if I measured your weight in Jupiter masses, you'd look pretty insignificant too.
That sort of re-scaling is the kind of thing that a PR group will do to make things look a certain way. Once, when I was on the board of an enviromental org. A nearby Shell gas station mentioned that they wanted to gass off leaked gasoline from their underground tanks into the neighbourhood. They said that they'd "only" be evaporating about 3.5 cubic metres of liquid.
Many members were willing to skip on it as minimal until I looked at the app, did some number crunching (habitual), and suddenly blurted out "Those bastards, that's almost a thousand gallons!".
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Re:The earth loses weight (Score:1)
Nathaniel P. Wilkerson
NPS Internet Solutions, LLC
www.npsis.com [npsis.com]
Re:Problem with Measuring G (Score:1)
As I said before, the experiemnt was done in the Nevada Desert. No people, completely automated. hundreads of miles away from any people or movement.
Re:Problem with Measuring G (Score:1)
In time, the meter got redefined in terms of speed of light. But nothing similar has happened to G.
Re:Is This A Problem... (Score:1)
Re:Is This A Problem... (Score:1)
The experiments I did, I noticed things moving cause the values that we were getting was different from the normal values that we were getting. Something had to change during all the tests to signify something. That is hard to do in real life
Re:The earth gains weight (Score:1)
Re:so....what is it? (Score:1)
G unimportant for sattelites... (Score:1)
that is to say, for sattelite trajectories, gravitational potential energy, you get everything you need to know just by measuring little g right here.
I could go on forever[...]
but you didn't even start
cheers,
sh_
Re:It's all relative... (Score:1)
You're correct about G. It's the gravitational constant of the universe. It's empirical value is what is trying to be determined.
Re:Females (Score:3)
"Does this value of G make my butt look big in these pants? Well what if the value of G is this?"
Re:Gravitational life (Score:1)
The point is, I'm not sure you can have life if you don't have some sort of non-deterministic system, like particles colliding but not stars orbiting in a galaxy.
PS. Please don't flame me or some such. This theory is very much 'work in progress'. No doubt it will be revised and re-revised before toon long.
Possible in principal, but... (Score:2)
In principle I don't see a problem with this - my personal belief on the subject is that life *could* form wherever there is a system of sufficient complexity, no matter the exact details of that system. So if you had enough "macroatoms" or whatever, the gravitational force could cause this to happen.
But the real killer is the timescale. Bearing in mind how many times smaller than the electrmagnetic force gravity is, the timescale would be correspondingly larger - rather than a ~10^9 second lifespan like we have, an equivalent gravitational being's lifespan would be ~10^49 seconds long, but for it, that time would seem the same length as a human lifespan.
In that length of time, the structure of the Universe will change. Spacetime will expand, leading to increased delays for communication between different components of the entity, stars will die, galaxies will collide, black holes will form and entropy in general will increase. The lifespan of this entity would be so great that by the time it could have formed, either all protons in the Universe will have decayed, all matter will be in slowly evaporating black holes, or we'll have had the Big Crunch.
So I think it's possible in principal, but not in practice. Of course, I could be totally wrong here :)
Re:so....what is it? (Score:1)
....and they'd both be inaccurate by now.
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"This isn't the post you're looking for. Move along."
Science mag? (Score:2)
5.972 sextillions? What the hell is that? Oh, you mean 5.972 x 10^18. Is this mag for scientists or what?
Also, did I miss it or did they not tell us the new value? Yesterday, GPS is opened up to civilians, but today G becomes proprietary information. One step forward...
Re:G unimportant for sattelites... (Score:3)
You are right, if you know surface gravity and the mass of the planet then you can get around G. But wait -- we didn't know the mass of Earth correctly. If you read the article, as a result of finding the more accurate G now we have a different number for the mass of Earth. So how is it that G is unimportant?
In close orbit perhaps the significance of these numbers is smaller, but in geosynchronous orbits where the satellite has to be locked into place 4.215x10^7 m away you'd better be sure that your numbers are right so that you're not just throwing billions of dollars randomly into space.
We can't find the mass/density of planets and stars without G. We have to throw something into orbit above it. If we don't even know mass + density then it's obvious we can't use Mass + surface gravity to do calculations. The other way is to go on the surface and measure acceleration, but good luck on planets like Venus with acid rain up the wazoo.
Re:Gravitational life (Score:2)
Life based on Strong Force? Existing in an environment where the gravity and velocities tear atoms apart?
What kind of life would that be?
- You'd (literally) have to drag yourself out of bed in the morning.
- You'd eat photon pancakes for breakfast.
- Commuting to work, by more than a single Planck length, would be killer.
- Any attempt to "move up in the world" or to even "get a raise" would meet with complete failure; and due to the conditions, you could not even find a tall building to jump from to end your misery.
- Light and fluffy pastries would be but a dream.
- All your friends (the Harmoniums) would be down and out.
- You fell, and you can't get up.
- "Wazzzup!?" might actually be funny.
Dragon's Egg (Score:2)
Re:SPEED OF LIGHT [Re:Gravitational life] (Score:2)
"The Search For Life In The Universe" 2nd ed. by Donald Goldsmith & Tobias Owen, chapter: "How Strange Can Life Be?" pp 242/244
Enjoy