The G spot

[peter]

Not that one you bad people but as you're here........

What I'd like a quick re-run on is 'G' [as in the Gravitational constant], 'g' as in acceleration due to gravity], the relatinship between them [ie how do you get from an experimental derivation of g {9.8 m/s iirc} to a value of G, is g also a constant right throughout the Universe (and if so why do we need G) [constants are normally introduced to eliminate 'proportional to' signs in equations aren't they), if g is not constant (ie varies depending on the place/speed/ color of your hair, whatever) what are these variarions and why do they occur. Not much then.

(Sometimes it helps me to think in terms of the momentum of bodies and how force is required to change momentum, Thus [even though it is wrong] I might view an object being acted on by gravity as being pushed toward the earth in the same way I might push a heavy supermarket trolley, taking effort to get it moving and speeded up, but little to keep it going at the same velocity.)

This started one day when as a thought experiment I decided to see how far I could get along Newtons path leading to his formation of the Laws of Motion and the Universal Law of Gravitation. re Supermarket trollies and my experience of them, I can come up with a rough approximation of F being proportional to Mass x Acceleration. ie it takes twice as much 'push' to get twice the speed from a trolly of mass M. Turn this situation vertically and consider what it tells us about gravity. We know that things of equal mass fall at the same rate by experiment and even if we didn't logic would tell us that they did. (Take two bricks, tie them together; if rate of falling was dependant on mass then they would fall twice as fast as each individual brick would alone. Loosen the string so they were then not so tightly bound, what happens - they fall a bit slower? Tie them together with a fooot of string sepparating them - slower still? Rubbish, and you can see it as such). So if all things accelerate toward the earth at the same rate irrespective of their mass, then twice the force must be required to accelerate the two bricks as the one. (but then I'm back to my string connondrum) Help me sort out this mess and if possible show me how far Newton could have got by thinking about apples?

[I'm Murrin]

G is the gravitational constant, which is universal.

g is a variable that depends on the mass and positions of the bodies involved.

G is the coefficient used to determine gravitational force at a point in a particular system. g is the acceleration due to that force.

[Hashi Lebwohl]

Well, Scienceworld by WolframAlpha is always a good place to start.

[High Lord Tolkien]

"The G spot"......science and math......???

[Vraith]

So if all things accelerate toward the earth at the same rate irrespective of their mass, then twice the force must be required to accelerate the two bricks as the one. (but then I'm back to my string connondrum)

Keeping in mind the previous responses [big G/little g and such]

A single brick and 2 bricks mortared together will fall at the same rate.

HOWEVER: imagine the landing.
The single brick will strike your head, transfer less force/energy into cracking your skull, than the two bricks cemented together. [though beyond a certain starting elevation, whether there was one or two will only be of interest to folk investigating your death]
Or, for instance...most African Swallows can attain a velocity of nearly 25Miles per hour [as long as unladen by coconuts] Would you rather get run over by one of them...or by the London Big Bus [avec ou sans tourists] traveling at the same speed?
So, reverse that.
The energy lost at the end of the fall is the energy needed to raise it up again.
[this response may have inspired me to twist things oddly and create a work dealing with our fall from the garden, and what it takes to rise again. Are there local and universal variables/constants? What is the mass of Sin? Does it have any? If not, is there a constant for its velocity in a vacuum? Heh...what if the Higgs is a "false-God particle."]

[peter]

Well they do talk about the 'burden of guilt' Vraith . Of course g is different at different places - how could I be so stupid! It's approx one sixth on the moon as it is here. I know this; fool! Bandersnatch! The 'force' of gravity cannot be a constant at one spot - it is the acceleration due to gravity that is the same for all objects in a given place. the force required to produce this given value of g must be proportional to the mass of the object being acted on. As in my wife and I walking across the supermarket carpark and my trolly being half the weight of hers, she has to push twice as hard to keep the one step distance behind me that propriety demands - now I understand!

Thing is - how do you get from here to the attractive force between two objects being proportional to the square root of the product of theitr masses divided by the distace of sepparation between them. Well if Soloman couldn't understand the 'ways of a man with a maid' there's no reason why I should be able to!

[I'm Murrin]

F = G(m[1]m[2]/r^2)

That formula's how G was determined in the first place. The attractive force is equal to the product of the masses divided by the square of their separation, multiplied by the gravitational constant.

And of course F=ma, so F=mg

Therefore,
g[1] = F/m[1] = G(m[2]/r^2)

Which shows that g, acceleration due to gravity, for a given object is independant of the mass of that object and depends only on the mass of the object it is attracted towards. The same of course is true for the other object being attracted to the first.

[Wildling]

[peter]

If I'm right this is an expression of the inverse square law/rule (or at least it features in there somewhere). This mathematical relationship seems to feature large throughout physics - particularly in the relationships where energy and force play a role. what is it about the 'square of things sepparation' (or inverse of) that makes this so fundamental a relationship right across the board. (It always seemed to be cropping up at least [40 years ago] at school).

[I'm Murrin]

I think it's just a general form of force reducing over distance. Fields made up of waves from a point source reduce by the inverse-square law because the field lines are growing further apart as you move away from the source - I think that makes it an issue of geometry as much as anything.

[Hashi Lebwohl]

I think peter is trying to figure out how we go from first principles or observations to a formulation for an equation that describes gravity. Experiments with momentum can give us the formulas for F=ma--we can measure the mass, hit it with a set amount of force, then measure the time it takes to move through a distance, etc. From there, we move to dropping objects of known mass from various heights--our experiments would, with a sufficient data set of perhaps several hundred drops from different distances, show us that the object are being accelerated at the same rate regardless of their mass. This would show us that g is (for all intents and purposes) a constant as well as its approximate value.

How we would go from there to the gravitational constant...that I do not know right now. I know that astronomical observations could give us things such as the Moon's angular velocity but I can't see how it would be possible to estimate its mass or distance only by observation but that wouldn't help us get to attraction due to gravity.

Wildling, is that Pedro (or whatever his name was), the bellboy from Fawlty Towers?

[Wildling]

I think peter is trying to figure out how we go from first principles or observations to a formulation for an equation that describes gravity. Experiments with momentum can give us the formulas for F=ma--we can measure the mass, hit it with a set amount of force, then measure the time it takes to move through a distance, etc. From there, we move to dropping objects of known mass from various heights--our experiments would, with a sufficient data set of perhaps several hundred drops from different distances, show us that the object are being accelerated at the same rate regardless of their mass. This would show us that g is (for all intents and purposes) a constant as well as its approximate value.

How we would go from there to the gravitational constant...that I do not know right now. I know that astronomical observations could give us things such as the Moon's angular velocity but I can't see how it would be possible to estimate its mass or distance only by observation but that wouldn't help us get to attraction due to gravity.

Wildling, is that Pedro (or whatever his name was), the bellboy from Fawlty Towers?

Nah, it's a Gumby from Monty Python's Flying Circus.

Courtesy of Wikipedia ...

Gumbys
A character generally played by Michael Palin, though the first was played by Graham Chapman. All of the Pythons have played him at one time or another. Gumby is a character of limited intelligence and vocabulary. He speaks haltingly, in a loud, indistinct manner. He wears round wire glasses, a fair-isle pattern sweater-vest and wellington boots. His shirt sleeves and trouser legs are always rolled up, exposing his socks and his knees. Gumby stands stoop-shouldered, with his hands are permanently clenched in front of him, elbows slightly bent, and his feet turned to the outside. He wears a folded white handkerchief knotted at the corners on his head and sports a vaguely Hitler-esque moustache. His famous catchphrase is "my brain hurts."

[Hashi Lebwohl]

Nah, it's a Gumby from Monty Python's Flying Circus.

Wow--I completely dropped the ball on that one.

[Vraith]

If I'm right this is an expression of the inverse square law/rule (or at least it features in there somewhere). This mathematical relationship seems to feature large throughout physics - particularly in the relationships where energy and force play a role. what is it about the 'square of things sepparation' (or inverse of) that makes this so fundamental a relationship right across the board. (It always seemed to be cropping up at least [40 years ago] at school).

I'm not sure it is quite that fundamental.
It isn't true of magnetism [which varies as the cube, not the square]...UNLESS there really are monopoles, in which case it would sometimes apply? I think? [String theory has something to say about them...I don't know if it says they MUST exist or that they MIGHT, exist off the top of my head].
Neither the strong nor weak nuclear forces follow it [just starting with they have a precise and definite distance limit...IIRC, it's really a time limit due to decay of carrying particle in one case, and in the other because the carrying particle is massive instead of massless.
And their is the dark energy...I don't know enough about it...is it accelerating inflation because it is stronger? or just cuz there is more of it?

[sgt.null]

not what I was expecting at all from the title, very disappointed...

[peter]

( Allow me to point you toward a liitle site I know Sarge )

I once read an introduction (or history of, I forget which) to philosophy by Bryan Magee in which he somehow managed to put into words rather than numbers, how Newton had arrived at his Universal Law of Gravitation. The thing that struck me was that, although I had clearly not grasped it in the precise way that Newton had, I was however getting where it was coming from; I had the slightly odd sensation that I was close to something that I couldn't quite get but was pretty near to doing so. We tend to view figures like Newton, Einstein, Bhor, Hawking etc as giants whose thinking, whose intellect is so far above the ordinary as to put their minds into a different stratospheric level. The above example I think, showed me that this need not be the case. Yes, they have a clarity of thought, a gift for logical thinking that sets them appart - but not a million miles so. Those steps are small, not huge as they appear so from below.

Back to G and g however; was it Plato or Socratees who believed that all knowledge could be achieved by 'ratiocination'. Newton sat under his tree and with thought and observation came up with the goods. How close then can we just by thinking and general observation, come to the same place.

(edit; The book in question was The Story of Philosophy by Bryan Magee, pub Dorian Kindersly)

[Hashi Lebwohl]

Most of the people from history whom we term "geniuses" or "great intellects" were smart, yes, but typically not outside the realm of the ordinary. Instead, they merely came up with answers to questions that no one had found before or decided to think about something differently and uncovered some wonderful scientific principles. Sometimes scientists seem significantly smarter than the average person because their knowledge in a particular field surpasses everyone else's and not because they have a 185 IQ. (On a tangent, research seems to indicate that IQ over 150 suffers from the law of diminishing returns--170 is not significantly better than 160 and guarantees no increased real-world success.)

Newton's discoveries about gravity are amazing because they had not been formulated before, only observed, and because they involve something that cannot be seen, only tested. If we set out to "rediscover" gravity we will still be better off than he was because we already know about gravity and we cannot "unlearn" that knowledge to start from where he started.

[peter]

I am always amazed in reading about various scientific advances (the double helix is a case in point) how the most obvious (post-discovery) can prior to that discovery be shrouded in mystery to the point where it's uncovering seems almost impossible and takes years to achieve. As John Archibald Wheeler said "Behind it all is surely an idea so simple, so beautiful, that when we grasp it - in a decade, a century, a millenium - we will all say to each other, how could it have been otherwise?"

[Avatar]

Hindsight is 20/20.

--A

[peter]

Quick revision of relativity - or how I ain't getting it.

Guy on a train throws a ball in the air and catches it on the way down. To him the ball goes in a straight line up a distance x, back down the same distance x and the process takes a total time t. An observer on the embankment sees the balls motion as an arc and not a staight line up and down. The process takes time t for the observer as well as the 'thrower' on the train. The way they see the balls motion is relative to their position [or 'frame of reference' in technospeak] but other than this I see no 'relativity' at play here [ie no paradox]. In both cases the vertical component of the balls motion has covered the distance 2x in time t. In the throwers case there just is no horizontal component because he also is travelling in the same direction and same speed as the ball. So where does relativity come into this.

The observer hangs about untill nightfall approaches and a train approaches him in the dusk. [It's a fast train - in fact travelling just short of the speed of light.] As it does so the train driver decides to switch on the trains headlamps and the observer, having his equipment ready does a quick measurement of the speed of the light emmited from the lamps. He finds it to be 299, 792, 458 meters per second. The driver also decides he will jst check out the speed of light emerging from the lamps as well; lo and behold he also comes up with a speed of 299, 472, 458 meters per second and the fact that he is travelling forward at near the speed of light already makes not one jot or tittle of difference to the speed measured. Both observers measure exactly the same speed irrespective of their frame of reference. Now thats relativity. Considering both the train and the emerging light from the observers point of observation, he sees the train hurteling along and the light crawling out in front of it [relative to the trains motion, ie like one race car crawling past another as they both hurtle round the track at 200mph] but the driver measures this crawling as 299, 792, 458 meters per second. The only way to account for this paradox is to postulate that the passage of time is different at different frames of reference ie is dependant upon your position of ebservation. Hmm .... think that about sums up as far as you can get on that one without a pencil and paper.