# Gravity Mathmatics

• May 2nd, 2009, 08:21 PM
Gravity Mathmatics
I was wondering if it has ever been done, I'm more than positive somebody would have done this already but theoretically if gravity is correct then it should be provable by math if you take the mass of each planet/sun/moon, the year for that planet (1 rotation around the sun/planet (incase of moon) and the distance between each object, then theoretically the numbers should match up, and a formula can be made using the variables, Gravity, Mass, and Distance. Anyone know if any test have been done that they can guide me too(web link)?
• May 2nd, 2009, 08:24 PM
drowsy turtle
It's not the strength of gravity that is unknown; it's what causes it.

So far there is no viable mechanism for gravity, excluding some rediculous and unproven theories like string theory.
• May 2nd, 2009, 08:28 PM
drowsy turtle
• May 2nd, 2009, 08:40 PM
Quote:

Originally Posted by drowsy turtle
excluding some rediculous and unproven theories like string theory.

you must mean dark matter, lol. I don't think I buy into that crap either, to be honest I would be thinking more along the line of a chemical bond of some kind, after all we don't have any way of knowing how super macro chemicals at that level react.

http://www.thescienceforum.com/Cosic...ule-18298t.php

I posted this here, it would tie into that, in my personal opinion.
• May 2nd, 2009, 09:29 PM
drowsy turtle
Except that gravity has an infinite range, whereas the other 3 fundamental forces do not.
• May 2nd, 2009, 09:39 PM
Quote:

Originally Posted by drowsy turtle
Except that gravity has an infinite range, whereas the other 3 fundamental forces do not.

yeah, or seemingly infinate. Either way, something that big would be foreign to us all together, I would think. What's weird is this brings up the question or possible micro chemicals, with potential micro chemical bonds (smaller than a microscope can see)

the craziest part of it all is how the universe is a web like structure. The molecules of people on a small enough scale aren't touching either. Almost like wondering if life can exist on an electron of an atom, at a scale so small we can't possibly see it at this current day and age.
• May 2nd, 2009, 11:38 PM
Arcane_Mathematician
I thought the other three just diminished to the point of being unmeasurable
• May 2nd, 2009, 11:52 PM
Janus
Quote:

Originally Posted by drowsy turtle
Except that gravity has an infinite range, whereas the other 3 fundamental forces do not.

Electromagnetic forces are also infinite in range.
• May 3rd, 2009, 04:28 AM
Dishmaster
Re: Gravity Mathmatics
Quote:

I was wondering if it has ever been done, I'm more than positive somebody would have done this already but theoretically if gravity is correct then it should be provable by math if you take the mass of each planet/sun/moon, the year for that planet (1 rotation around the sun/planet (incase of moon) and the distance between each object, then theoretically the numbers should match up, and a formula can be made using the variables, Gravity, Mass, and Distance. Anyone know if any test have been done that they can guide me too(web link)?

This has been done for only two bodies by Kepler and Newton. For more than two bodies, this is not so easy, and possibly not solvable. You are talking about a many-body problem, often also mathematically expressed as the n-body problem. Such a configuration of more than two particles interacting gravitationally cannot be solved by analytic math. The solutions can always only be approximated - although the results can be easily within the accuracy of the empirical measurement. If you allow for a sensible measurement accuracy, these laws have been proved many times. But the exact mathematical solution is impossible. Scientists that model the behaviour of ensembles of many gravitating particles (stellar clusters, galaxies) use numeric approximations.
• May 3rd, 2009, 10:46 AM
DrRocket
Re: Gravity Mathmatics
Quote:

Originally Posted by Dishmaster
Quote:

I was wondering if it has ever been done, I'm more than positive somebody would have done this already but theoretically if gravity is correct then it should be provable by math if you take the mass of each planet/sun/moon, the year for that planet (1 rotation around the sun/planet (incase of moon) and the distance between each object, then theoretically the numbers should match up, and a formula can be made using the variables, Gravity, Mass, and Distance. Anyone know if any test have been done that they can guide me too(web link)?

This has been done for only two bodies by Kepler and Newton. For more than two bodies, this is not so easy, and possibly not solvable. You are talking about a many-body problem, often also mathematically expressed as the n-body problem. Such a configuration of more than two particles interacting gravitationally cannot be solved by analytic math. The solutions can always only be approximated - although the results can be easily within the accuracy of the empirical measurement. If you allow for a sensible measurement accuracy, these laws have been proved many times. But the exact mathematical solution is impossible. Scientists that model the behaviour of ensembles of many gravitating particles (stellar clusters, galaxies) use numeric approximations.

While the n-body problem for n>2 is not solvable in closed form, the underlying theory of gravity has been verified by just the methods that you mention. The n-body problem can be solved numerically, and approximately, to a very high degree of accuracy and those solutions are based on the fundamental physical descriptions of gravity, both Newtonian gravity and general relativity.

So while the equations are not solvable in closed form, the available numerical methods are quite sufficient to act as confirmation of the underlying physical theories within reasonable domains of validity.
• May 3rd, 2009, 01:11 PM
MagiMaster
From what I understood, all forces are theoretically infinite range, but only gravity can be felt at a distance since all the others tend to cancel themselves out fairly quickly.
• May 3rd, 2009, 07:45 PM
DrRocket
Quote:

Originally Posted by MagiMaster
From what I understood, all forces are theoretically infinite range, but only gravity can be felt at a distance since all the others tend to cancel themselves out fairly quickly.

I think that the strong force actually has a finite range. And the force actually increases with distance until you have added so much energy by separating particles that the "bond" breaks and new particles are formed. That is why you don't often see free quarks.

The electromagnetic force is also infinite range and follows a basic inverse square law, just like gravity. But it only has an effect when there is a net charge and the universe tends to be neutral on most macroscopic scales.
• May 4th, 2009, 01:46 PM
I'm gonna do the math and see what I can get.

Sun = mass=1.9891 x 10(30)kg

mercury = 46-70 million km from sun, mass = 3.3022x10(23)kg, orbit 88 days

venus = you get the picture,

It'll take a while for we to wiki and do the math and factor in variables but I'll post once it's eventually finished, I wish someone had a referencer of this being done before, I know we assume it will be verifiable with math, but has it been?
Not sure what the n solution is but I'll check into it first.

Thanks for the responses guys.
• May 4th, 2009, 02:57 PM
Dishmaster
I have done some plotting a while ago for a talk I gave. Is that what you had in mind? I just took the Keplerian laws and the Newtonian approach to the law of gravity to calculate the revolution times and orbital speeds, drawn as the solid red line. The red line is not a fit to the data. The values of the planets are taken from the literature.

• May 4th, 2009, 04:05 PM
KALSTER
Your second graph looks like an inverted galaxy orbitial_speed/distance_from_centre graph. Any relation?
• May 4th, 2009, 04:47 PM
Dishmaster
Indeed there is a relation. Galactic rotation curves are also based on the Keplerian laws. The only difference to the solar system is that the central mass cannot be considered to be constant, but changing with radius. In the solar system, more than 99% of the mass is in the sun. This is different in galaxies.

This makes things a bit more complicated. If the normal Keplerian law would be valid for galaxies, a galactic rotation curve would like this (the units are arbitrary):

But measurements showed all kind of rotation curves with different shapes.

This is why the "Dark Matter" hypothesis was invented. I made these plots for an introductory talk on MOND.
• May 4th, 2009, 08:55 PM
well my point would be if gravity was because of mass/relativity and all that. It would mean (and please correct my thinking if it's wrong) that based on the size of the sun each planet should be orbiting the sun and the length of it's yr would be dependant on it's total mass of the planet (and a similar connection between earth and the moon), something that doesn't match this would indicate there may be some chemical bond involved or electro magnetic +/- or something to that effect, at a galactic (super-macro) level. (or that I'm missing a piece of the puzzle)
• May 4th, 2009, 10:15 PM
Quote:

Originally Posted by Dishmaster
Indeed there is a relation. Galactic rotation curves are also based on the Keplerian laws. The only difference to the solar system is that the central mass cannot be considered to be constant, but changing with radius. In the solar system, more than 99% of the mass is in the sun. This is different in galaxies.

This makes things a bit more complicated. If the normal Keplerian law would be valid for galaxies, a galactic rotation curve would like this (the units are arbitrary):

But measurements showed all kind of rotation curves with different shapes.

This is why the "Dark Matter" hypothesis was invented. I made these plots for an introductory talk on MOND.

So basically the force from the center of the galaxy is making it to where the math would be changed? Do we know what the mass weight & distance of the center of the galaxy is from the sun, and time for 1 orbit?

Also it looks like there's A LOT more math involved then I thought, I'd still like to take a crack at it though. I'm sure it's been done, but I'd like to see what kind of answer I get, plus it'd be a fun challenge. I've been collecting all the information I'll need at work during free time at work.
• May 5th, 2009, 01:29 AM
Dishmaster
Quote:

well my point would be if gravity was because of mass/relativity and all that. It would mean (and please correct my thinking if it's wrong) that based on the size of the sun each planet should be orbiting the sun and the length of it's yr would be dependant on it's total mass of the planet (and a similar connection between earth and the moon), something that doesn't match this would indicate there may be some chemical bond involved or electro magnetic +/- or something to that effect, at a galactic (super-macro) level. (or that I'm missing a piece of the puzzle)

Ideally, the revolution of planets around the sun is independent of the size or mass of the planets and to first order independent to the size of the sun. The mass of the sun and the distance of a planet from the sun are basically the only factors that determine the orbital velocity. The graphs I show are based on this assumption, and they are in good agreement with the measured values. In reality, the gravitational field of the sun is slightly modified in its immediate vicinity because of its finite size, mainly affecting the orbit of Mercury, and is disturbed by the fields of all the other bodies in the solar system (planets, moons, asteroids, etc.), but since the sun contains more than 99% of the mass in the solar system, their contribution is almost negligible. These disturbances, however, prevent the exact prediction of the planetary orbits for the next centuries. The smaller the mass of an object, the more it is affected by the gravitation of others. This is the reason, why the trajectories of asteroids, comets and spacecraft have to be measured and re-calculated in order to keep up with reality. It is just impossible to know the contributions of each and every particle in the solar system.

Galaxies are much more complicated, because the majority of its mass is generally not concentrated in the galactic nucleus. The galactic disc contains a considerable amount of mass. This is the reason why galaxies cannot be treated by a centralised gravity approach like planetary systems. Not only the galactic centre, also the galactic disc has a gravitational influence. This makes it much more complicated to treat the reaction of stars within a galaxy. It cannot be solved with analytical equations, but has to approximated by numerical models. The distance of the sun to the galactic centre is about 8 kpc, but the exact distance is hard to establish. The sun moves with a speed of about 240 km/s on an orbit around the galaxy; one revolution takes about 200 million years. If you use these two numbers, you can roughly estimate the amount of mass contained within the solar orbit.
• May 5th, 2009, 05:35 PM
Quote:

Originally Posted by Dishmaster
Ideally, the revolution of planets around the sun is independent of the size or mass of the planets and to first order independent to the size of the sun. The mass of the sun and the distance of a planet from the sun are basically the only factors that determine the orbital velocity. The graphs I show are based on this assumption, and they are in good agreement with the measured values. In reality, the gravitational field of the sun is slightly modified in its immediate vicinity because of its finite size, mainly affecting the orbit of Mercury, and is disturbed by the fields of all the other bodies in the solar system (planets, moons, asteroids, etc.), but since the sun contains more than 99% of the mass in the solar system, their contribution is almost negligible. These disturbances, however, prevent the exact prediction of the planetary orbits for the next centuries. The smaller the mass of an object, the more it is affected by the gravitation of others. This is the reason, why the trajectories of asteroids, comets and spacecraft have to be measured and re-calculated in order to keep up with reality. It is just impossible to know the contributions of each and every particle in the solar system.

Galaxies are much more complicated, because the majority of its mass is generally not concentrated in the galactic nucleus. The galactic disc contains a considerable amount of mass. This is the reason why galaxies cannot be treated by a centralised gravity approach like planetary systems. Not only the galactic centre, also the galactic disc has a gravitational influence. This makes it much more complicated to treat the reaction of stars within a galaxy. It cannot be solved with analytical equations, but has to approximated by numerical models. The distance of the sun to the galactic centre is about 8 kpc, but the exact distance is hard to establish. The sun moves with a speed of about 240 km/s on an orbit around the galaxy; one revolution takes about 200 million years. If you use these two numbers, you can roughly estimate the amount of mass contained within the solar orbit.

wow, it's crazy we have that all figured out already, we already can replicate the view of the cosmic web, it would take so long for humans to figure out everything about space, but given enough time I wouldn't put it past us.
• May 19th, 2009, 04:08 PM
Stuart Thomson
Quote:

Originally Posted by MagiMaster
From what I understood, all forces are theoretically infinite range, but only gravity can be felt at a distance since all the others tend to cancel themselves out fairly quickly.

Gravity and the electromagnetic force have infinite range.

Strong and weak nuclear forces do not, as their bosons have mass, and a short lifespan.

The range can be approximated using the energy-time uncertainty priciple (m is the mass of the exchange particle):

With

• May 20th, 2009, 11:44 AM
kojax
Re: Gravity Mathmatics
Quote:

I was wondering if it has ever been done, I'm more than positive somebody would have done this already but theoretically if gravity is correct then it should be provable by math if you take the mass of each planet/sun/moon, the year for that planet (1 rotation around the sun/planet (incase of moon) and the distance between each object, then theoretically the numbers should match up, and a formula can be made using the variables, Gravity, Mass, and Distance. Anyone know if any test have been done that they can guide me too(web link)?

Trouble is, we used the theory of gravity to determine all the masses. If we're wrong about gravity, then all those numbers are also wrong.
• May 20th, 2009, 10:34 PM
DrRocket
Re: Gravity Mathmatics
Quote:

Originally Posted by kojax
Quote:

I was wondering if it has ever been done, I'm more than positive somebody would have done this already but theoretically if gravity is correct then it should be provable by math if you take the mass of each planet/sun/moon, the year for that planet (1 rotation around the sun/planet (incase of moon) and the distance between each object, then theoretically the numbers should match up, and a formula can be made using the variables, Gravity, Mass, and Distance. Anyone know if any test have been done that they can guide me too(web link)?

Trouble is, we used the theory of gravity to determine all the masses. If we're wrong about gravity, then all those numbers are also wrong.

We also use the theory of gravity to calculate the orbits of all of the satellites that we have put in orbit and all of the trajectories ot all of the spacecraft that we have sent to other planets. If it were very far wrong that fact would be evident.
• May 21st, 2009, 03:40 AM
Dishmaster
These suggested differences are tiny and only appear at very low forces. This is why the rotation curves of galaxies normally stay unchanged close to the centre, but deviate at the outskirts. Some people also attribute (a part of) the infamous Pioneer anomaly to a modified gravitational law. And those probes showing that effect (Pioneer 10+11) are far out at the distant edges of the solar system, where the sun's gravity is very small. As long as the satellites stay close to the earth (and the sun), we wouldn't be able to notice any difference. However, there is another phenomenon called the flyby anomaly that changes the trajectories of spacecraft in a way that is still not understood.
• May 21st, 2009, 10:40 AM
DrRocket
Quote:

Originally Posted by Dishmaster
These suggested differences are tiny and only appear at very low forces. This is why the rotation curves of galaxies normally stay unchanged close to the centre, but deviate at the outskirts. Some people also attribute (a part of) the infamous Pioneer anomaly to a modified gravitational law. And those probes showing that effect (Pioneer 10+11) are far out at the distant edges of the solar system, where the sun's gravity is very small. As long as the satellites stay close to the earth (and the sun), we wouldn't be able to notice any difference. However, there is another phenomenon called the flyby anomaly that changes the trajectories of spacecraft in a way that is still not understood.

Precisely the point. The current theory of gravity seems to be working rather well, and "anomalies" are of such a small magnitude that they may or may not have anything to do with fundamental understanding of gravity.

While not claiming to understand the anomalies and not being able to explain them, there are non-gravitational effects and subtleties in general relativity that may be significant with respect to such small perturbations -- radiation pressure, frame dragging, ... who knows ? It is certainly worthwhile to understand the anomalies, but they do not provide justification at this point to think that general relativity is wrong. The anomalies, as noted at the sites to which you provided links, are on the order of a few millimeters per second.

I don't understand the differences well enough to know if this is viable, but I wonder if these anomalies might be sufficient to differentiate between general relativity and Einstein-Cartan theory. Does anyone know ?
• May 21st, 2009, 12:27 PM