View Full Version : Question about math?

bigsplit

2005-Jan-11, 02:12 PM

If you have a circle with a circumferance of 3 and divide into three equal arcs of one, each arch would be 1. Take the archs and begin moving them simultaniously towards the center point of the circle with the archs maintaining a circle by overlap, the overlaps would be added cumulatively. Could this concept be applicable to gravity?

antoniseb

2005-Jan-11, 02:36 PM

Originally posted by rousejohnny@Jan 11 2005, 02:12 PM

Could this concept be applicable to gravity?

I'm not sure how, gravity is three-dimensional [at least], and circles and arcs are two dimensional. These arcs will increase in "depth according inversely proportional to the radius, whereas gravity goes as the inverse square.

Where did you see some kind of connection between this and gravity?

bigsplit

2005-Jan-11, 03:13 PM

Originally posted by antoniseb+Jan 11 2005, 02:36 PM--></div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td>QUOTE (antoniseb @ Jan 11 2005, 02:36 PM)</td></tr><tr><td id='QUOTE'> <!--QuoteBegin-rousejohnny@Jan 11 2005, 02:12 PM

Could this concept be applicable to gravity?

I'm not sure how, gravity is three-dimensional [at least], and circles and arcs are two dimensional. These arcs will increase in "depth according inversely proportional to the radius, whereas gravity goes as the inverse square.

Where did you see some kind of connection between this and gravity? [/b][/quote]

I understand a sphere is 3D, I was just simplifying for conceptual purposes. I do not necessarily see any connection, it was mostly one of those random brainstorms that caught my attention for more than a few seconds. If gravity propagates at the speed of light from a source in a shereical manner, can the weakening of gravity and spacetime curvature be correlated with the "spreading out" of the area through which the gravity propetuates? It could be concluded that for this reason as bodies move towards one another the overlap generates vectoring yeilding the conceptual curvature of spacetime. Certainly there are an infinate number of circles around a sphere, the particular circle or circles a body settles into would be the result of the angle and velocity at which the body entered the sphere of gravitational potential of the dominate body. The shape and composition of both bodies would have an effect as well. An irregular shaped body would have a more irregular field of gravitational potential (bent circles) that would also render more irregular orbits.

antoniseb

2005-Jan-11, 04:05 PM

Originally posted by rousejohnny@Jan 11 2005, 03:13 PM

can the weakening of gravity and spacetime curvature be correlated with the "spreading out" of the area through which the gravity propetuates?

The notion that started this thread, with the three equal arc segments was tough to connect to gravity, but you statements in the second post are a nice conceptual way to think about it. It may not work with general relativity, or with brane theory, ultimately, but it is a good way to picture Newtonian gravity, which is really close enough to reality for anything going on in the solar system that we needn't think about the more complex ideas.

BTW, You should note that an irregularly shaped object has nearly spherical gravity at a large distance. It is only close up that it has oddly shaped gravity. Look at the NEAR website for some details about a close orbit to a large shoe-shaped rock.

bigsplit

2005-Jan-11, 04:54 PM

Originally posted by antoniseb+Jan 11 2005, 04:05 PM--></div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td>QUOTE (antoniseb @ Jan 11 2005, 04:05 PM)</td></tr><tr><td id='QUOTE'> <!--QuoteBegin-rousejohnny@Jan 11 2005, 03:13 PM

can the weakening of gravity and spacetime curvature be correlated with the "spreading out" of the area through which the gravity propetuates?

The notion that started this thread, with the three equal arc segments was tough to connect to gravity, but you statements in the second post are a nice conceptual way to think about it. It may not work with general relativity, or with brane theory, ultimately, but it is a good way to picture Newtonian gravity, which is really close enough to reality for anything going on in the solar system that we needn't think about the more complex ideas.

BTW, You should note that an irregularly shaped object has nearly spherical gravity at a large distance. It is only close up that it has oddly shaped gravity. Look at the NEAR website for some details about a close orbit to a large shoe-shaped rock. [/b][/quote]

Why not GR?

antoniseb

2005-Jan-11, 05:23 PM

Originally posted by rousejohnny@Jan 11 2005, 04:54 PM

Why not GR?

Does your model account for Frame-Dragging? [among other things]

bigsplit

2005-Jan-11, 08:40 PM

I do not know if you could classify this as a model, but I do not see frame dragging as a problem. Since gravity is not instantanious there would be a slight drag produced by rotation. I think more than anything this is just another way to view GR, the question is by generating an alternative conceptualization, could new tools be generated to help solve the quantum problems with GR, a subject matter of which I know little about.

Could someone sum up these problems of GR and QM in a quick paragraph?

antoniseb

2005-Jan-11, 10:13 PM

Originally posted by rousejohnny@Jan 11 2005, 08:40 PM

Since gravity is not instantanious there would be a slight drag produced by rotation.

Neither your first, nor second post made any mention of speed of gravity, and so I had to assume you were describing a static field. If you think you can apply math to your model and make it come out looking like GR, you might have a good teaching tool on your hands.

ferg.c.

2005-Jan-12, 12:22 PM

I'd like to simplify things a bit by pointing out that The idea of the overlapping lines (however dimensions are involved) does not represent even the intensity of gravity correctly. To start with I'll rearrange the dimensions of you circle a bit. A circle with radius if 1 has a circumference of 2pi. So if gravity is correct here (lets assume that this is where we start the experiment) then to represent gravity as a sum of the parts of this circumference on a circle with a smaller radius in flawed because we know from previous experiment that the total gravity will be more. This can be calculated thus:

for a circle of say .25 the actual circumference will be 1/2 pi but we expect the gravity to be to be a factor of 16 different from the r=1 circle by the inverse square law and not just 4 as would be derived from the overlapping lines idea.

So out of the water goes that one!

Cheers

Ferg :)

bigsplit

2005-Jan-12, 12:47 PM

Originally posted by ferg.c.@Jan 12 2005, 12:22 PM

I'd like to simplify things a bit by pointing out that The idea of the overlapping lines (however dimensions are involved) does not represent even the intensity of gravity correctly. To start with I'll rearrange the dimensions of you circle a bit. A circle with radius if 1 has a circumference of 2pi. So if gravity is correct here (lets assume that this is where we start the experiment) then to represent gravity as a sum of the parts of this circumference on a circle with a smaller radius in flawed because we know from previous experiment that the total gravity will be more. This can be calculated thus:

for a circle of say .25 the actual circumference will be 1/2 pi but we expect the gravity to be to be a factor of 16 different from the r=1 circle by the inverse square law and not just 4 as would be derived from the overlapping lines idea.

So out of the water goes that one!

Cheers

Ferg :)

Thanks Ferg, never thought about actually applying the math, but 4 sq is 16 I wonder if this would be a consistant, I have a feeling it would be and is just a restating of the already known equation. I am more concerned with the concept and answering the unanswered questions. But you are probable right about tossing it, but I just love the brainwork.

ferg.c.

2005-Jan-12, 12:57 PM

Don't give up on this one just yet. Look, if the lines had a finite thickness and this was to increase somehow as they approached the centre of gravity then there might be a way round my sticking point. Of course there isn't but you should have come up with some thing like this before chucking ths lot in the trash. Don't just get more self critical about your thoughts get more cunning about how to get out from under the self criticism too!

Cheers

Ferg :)

bigsplit

2005-Jan-12, 02:52 PM

Originally posted by ferg.c.@Jan 12 2005, 12:57 PM

Look, if the lines had a finite thickness and this was to increase somehow as they approached the centre of gravity then there might be a way round my sticking point.

Ferg :)

Here is from where the concept comes. A gravity wave is produced spherically outward from the center of gravity. Any two lines from the center point outward that intersects the gravitational sphere (single wave of gravity) perpendicularily would generate an arch. The curvature of this arch would generate a circle, depending on the shape of the mass and distance from the center, the perfection of this "circle" would vary.

You have a consistent pull from (some prefer a push towards) a center of gravity. In order for the arch to maintain the circle and conserve energy, its magnitude must be maintain resulting in an increase in gravitational "density" per any given area as you move towards the center.

It is the speed, angle and mass of a body that enter an area of greater gravitational potential that determines the geometry of its path. The gravity acts linearly and any "curvature" of spacetime is the result of the linear forces influence and its sphereical propagation at the speed of light upon the mass entering the system.

bigsplit

2005-Jan-12, 05:55 PM

I have a thought experiment that could disprove this concept. If you could isolate a mass outside the influence of any external effect. The mass is a perfect sphere and cannot be spinning. Take a similar (like charged) but smaller sphere and move it on a path where their center of gravities are moving together in a staight line, if my concept of only apparrent curvature is correct there will be no deviation in the direct linear path of the little sphere. Inversly, if the space is indeed "curved" the tiny sphere will begin to arch on its dissent. Does GR account for this?

filrabat

2005-Jan-15, 03:32 PM

Question about Newton’s Harmonic Law Based on Kepler’s Third Law of Planetary Motion.

I searched site after site for this formula. My goal is to figure out the semi-major axis (mean distance from the sun) for a planet with the following characteristics:

Same mass as Earth

180 earth day orbital period

The star mass is 0.85 Sols

It’s bad enough that I found formulas on two sites that contradicted each other (one site listed the numerator in the middle term as 4p2 , the other as 4Π2 !). What’s even worse is that they never gave ANY specifics as to which denominations of measurement to use in the formula:

mass (the page drafter could have meant anything from metric tons down to micrograms as far as I’m concerned)

time (similarly, could have been femtoseconds, eons, or anything in between -- and then some)

distance (yes, you can predict the commentary I'd write here -- and chances are extraordinarily high you’d be correct!!!<groans!!!>)

Is there anyone who can clear all this up for me? I’d greatly appreciate it.

ferg.c.

2005-Jan-19, 02:55 PM

Google search "Titius Bode"

Cheers

Ferg :)

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