Gravitational Force Between Bodies

[Linkz]

Hey there!
I just made an experiment to see how the gravity on Universe Sandbox acts between different masses.
The experiment I made was designed like this:

The Earth and the Moon with 0 velocity and a big distance between them, then i would create a Sun (also v=0) far from them. Both the Earth and the Moon were at the same distance from the Sun, but I noticed that the Moon would accelerate more and crash into the Sun before Earth did.

The problem here is that gravitational force is calculated by 2 masses, so the Gravitational Force between the Earth and the Sun should have been greater than that between the Sun and the Moon, causing the Earth to accelerate more and crash into the Sun earlier than the Moon, but that's not what happened, seeing as the Moon was clearly under more influence from the Sun, which would have been impossible.

[Chaotic Cow]

Interesting. Was the Moon within the hillsphere on the Earth?

If not then the Sun has a much greater force on the moon than Earth.

Atleast I think.

[Dan Dixon]

I like experiments.

Have you heard about the experiment that Gallileo performed where he dropped two different weights from the leaning tower of Pisa?
http://www.jimloy.com/physics/galileo.htm
Both weights hit the ground at the same time.

Now think of the Earth & Moon as the weights and the Sun as the ground. If the Moon and Earth are the same distance from the Sun then the Sun will pull on them with the exact same force and so they will hit the Sun at almost exactly the same time.

You're right that the gravitational force between the Earth and the Sun should be greater (than the Moon and Sun). This is because both the Earth is also pulling the Sun toward it. Since the Earth has more mass than the moon it pulls on the Sun more (but it's a pretty small amount).

That's strange that the Moon is accelerating more in your tests. Maybe this is because the Moon is being notably accelerated by the Earth.

Does that help? Let me know if you don't understand or are still experiencing strange results.


Here's my comment from another thread that talks about this same concept:
http://universesandbox.com/forum/index.php/topic,63.msg374.html#msg374

[Linkz]

Yea the problem with Galileo's experiment is the second mass.
Gravitational force is the weakest of the 4 main natural forces, so the effect between the Earth and a Bowling Ball for example would be virtually one-sided.
But when talking about planets and stars, the gravitational force on both bodies are already noticeable.

So I redid the experiment, this time I put the Sun in the center and the Earth and Moon on opposite sides, at precisely 91.2 AU from the Sun each, all of them with v=0. After a while, the Moon's acceleration was again higher then the Earth's.

[Chaotic Cow]

I tried it and did them both at 1AU on opposite sides it seems that earth got a smaller boost of speed near the end than the moon hitting it first.

[avadod]

didn't they say that the leaning tower of piza fell from an earthquake

[FGFG]

not at all. It was built on a very unstable terrain (something similar to argil) so, after years it started to lean.

P.s. The tower was unstable even before his completion: If you look at it you can notice that some floors are more inclined of others (it is very visible with the last floor, the smallest one

Here there is attached a big image

[Dan Dixon]

So I redid the experiment, this time I put the Sun in the center and the Earth and Moon on opposite sides, at precisely 91.2 AU from the Sun each, all of them with v=0. After a while, the Moon's acceleration was again higher then the Earth's.

Could you set up this experiment and then save it. I find it odd that you're getting these results.

The earth and moon should hit the sun at the same time (assuming they're not too close to each other) and that they start the same distance from the sun.

[bessy]

mmm now i ran it thru in my mind if US takes into account mass distribution more of the moons mass will be closer than the earths giving it faster fall acceleration think of gravity been a bank that gets steeper the closer you get

because the moon is smaller more of its mass will be at a steeper point than the earths so it will slide down the bank faster always
so it would get there first in real life
also the earth will create a bigger bank of its own along the suns bank which will cause the earth to have a less steap bank than the moon which will make it slide down at a slower acceleration than the moon






hope this helps
if not i wasted a 15 sec "dream scape sim" in my mind

[atommo999]

so that explains why the moon has a bigger boost than the earth... the line is steeper for the moon 

[bessy]

yep

also if you had a bowling ball and a feather at the same height and let them go on the moon the feather would hit first its great how funny that is but true

im not good with math but if you give me somthing to think about i will

also if you look at a black hole for instance eg the milky way 1 it looks really small compared to the galaxy in whole but for eg if we tuck the 4th dimension out of the diagram of it, it would look like a black Saturn and its rings, Saturn being the black hole and the rings being the stars around it
but because the gravity is so strong it makes space bend to the extreme as it may look like the milky way is only 50k light years across near the black hole its way more because as you approach it you become smaller in a larger space which in turn makes time move slower
meaning that even tho objects closer to the black hole should appear to move faster they don't as the black hole slows time down the closer you get so objects further out appear to move faster than the object closer
see i removed dark matter how easy was that

funny old universe isn't it

[Alex_Ian_Hamilton]

Hi bessy, I don't think you idea works out.

First-off, you're using a simplification of general relativity (designed only to visualise a very complex theory full of maths) as a basis to solve a problem seen using Newtonian Physics (Universe sandbox can't do relativistic physics).

Also, then that means light things would experience more acceleration then heavy things; so does this mean that if I have a bowling ball it'll fall with an acceleration, while if I chop it into little bits then all the bits (and thus the whole of the bowling ball) would fall with a greater acceleration?

Furthermore, if you take this to the extreme, then super light things would experience near infinite acceleration (so how would that work with the atoms of an atmosphere, let alone the photos of light).

Considering Newtonian dynamics, the force applied to an object under the influence of gravity is:



Now considering we’re looking at acceleration (which will result in the speed of motion), we need to convert the force into acceleration using:



Now if we combine these, then we get:



We can use algebra to get:



If you look as what I did, I have cancelled out the smaller mass (m), and now have an acceleration simply based on:



I could have a planet (with huge mass) at that distance from the sun and it’d experience the same acceleration as if it were a lightweight feather... (as long as I keep the Suns mass and distances the same)

The equation is more commonly written:



I can also prove this with my handy assistant (I’ve always wanted to say that), who actually did drop a feather and a spanner on the moon:
http://www.youtube.com/watch?v=5C5_dOEyAfk
Within the accuracy of the video, they both impact at the same time.

P.S. If I’m made a mistake the anyone please say, I’m hoping to study Astrophysics at University next year, I need any help I can get. 

[bessy]

well i can't say i know much about the maths or have i even studied it i just had a little think about the problem above

quote for Alex

Furthermore, if you take this to the extreme, then super light things would experience near infinite acceleration (so how would that work with the atoms of an atmosphere, let alone the photos of light).



ok extreme if the gravity field was strong enough eg a extremely heavy object things like photons would have infinite acceleration towards it thats why they cannot escape say a black hole and for say your bowling ball the area closest to the black hole would be over the edge of the little lip it creates eg the lag range would be inside of it thus causing the side closest to the black hole to accelerate faster than the back
and for eg the atmosphere of a planet would bit ripped away as the lag range passes thru it

see a simple representation below

[bessy]

also objects like photons are traveling at c but still you can see them get altered eg when they get 2 close to say the atoms of a glass window there direction gets altered depending on how they hit the glass and in some cases they get so close they go right round the atoms and go back the way they came eg when its refracted even atmospheres alter there direction there is a point on a atom where you can get so close that even light cannot escape even in a single hydrogen atom

[Alex_Ian_Hamilton]

Hi Bessy,

The extreme I was referring to is relating to the concept that lighter objects fall faster (i.e. with greater acceleration), for instance on the moon (it’s best not to think about black holes, they’re unnecessarily complicated).
If you take this to a logical conclusion, then very very light (low mass) things will experience very very high acceleration; atoms are pretty light (low mass), and so they would experience greater acceleration towards the ground in this model. So atmospheres (made of atoms and/or very light molecules) would experience more gravitational acceleration. That’s fly in the face of escape velocity.
Photons (sorry typo in my last post) have an even smaller mass (a result of them having energy and travelling at the speed of light), they’d be attracted to the moon even faster.
The moon isn’t a black hole, so I don’t think that makes sense.

When you’re talking about being next to a black hole, yes you will experience a different amount of force if you have parts of the object closer to (or even in) the event horizon of the black hole; this leads to Spaghettification (where you’d be stretched if you fell into a black hole, check Wikipedia); but my bowling ball example was considered from the more mild gravitational field of the earth, in this case, the distance of the centres of mass would be important, not the distance of the leading edge. If you think about it, if one half of the bowling ball is closer to the earth, then the other half is equally further from the earth, it evens out to make a centre of mass.
For planets not touching each other, we can generally use the concept of a centre of mass, check here:
http://en.wikipedia.org/wiki/Newton's_law_of_universal_gravitation#Bodies_with_spatial_extent
Read the section titled “Bodies with spatial extent”.

Also, I think you’re confused about the reason for refraction of photons; refraction is a process which results from the interaction between the photon (which is an electro-magnetic -wave) and the electrons in “orbit” (OK, a simplification) around the atoms, which are charged particles (charged particles can affect electromagnetic radiation);  as the photon passes by the electron then it may be absorbed and re-emitted later, and this process will reduce the effective speed with-which the photon travels through the object and can (in some cases) allow the photon to be re-emitted back in the direction it came from.
This is a consequence of the electromagnetic force, as described by Quantum Mechanics, not relativity.

However, I think I see what you’re saying, that theoretically, if an atom was infinitely small, then if you get infinitely close you’d experience infinite gravity (if you plug in the maths); but remember that an atom is not infinitely small, it’s not a point in space, it is a collection of particles (protons, neutrons and electrons). Even the Protons and Neutrons are made up of smaller things (Quarks).
However, if you look at the basic building blocks (electrons and quarks) then these are point particles with no volume; these fundamental particles may (according to the maths of relativity) exibit near infinite gravity when you get near infinitely close; they may even have an extremely small event horizon (so be black holes, if you get close enough), but we believe this is more a sign that relativity breaks down as you get into subatomic scales. (Newtonian gravity shows this same weakness)
In order to actually understand what’s going on gravitationally at these scales, we need a theory of quantum gravity; which hopefully the LHC (the new particle accelerator) will help us develop.

Just to be honest and up-front, I’m a part-time student (not a graduate), so I’m still trying to learn all this stuff; hence I’m open to any mistakes or flaws that people find in my answers, I just think you’ve got things a little wrong here.
The problem is that you’re thinking of relativity from a non-mathematics stand-point; considering that most universities teach relativity in their maths department (not physics departments), that just shows how maths-heavy a subject general relativity is (and I’m nowhere near capable to answer that sort of maths).

If anyone wants to learn more about this stuff without the maths, then I highly recommend http://www.astronomycast.com/, they have episodes on almost anything to do with this.

[bessy]

with objects traveling at c like photons they have a lot of momentum so when they move past a object like our star there direction gets altered by a mere fraction but think of what would happen if they were not moving and were relative to a star because of how light they were it would take no energy what so ever to accelerate them


also things like our atmosphere do get pulled to the earth with extreme force thats how we have pressure for eg gas is a gas because the atoms that makes it get repelled away from 1 another gravity pulls on them but they fight against it to see this just blow a balloon up, but in cases of our planet gravity gets weaker the further out you go so the gases that make up our atmosphere get pulled towards it with less force which is why the atmosphere gets compressed less which in turn means less pressure the further away from the surface you go untill you get to the nullification point aka lag range also if you made the moon more dense so it was much smaller it to could hold a atmosphere as gravity would be strong enough at the surface



if at a point we actually did make a experiment in where we made 2 static objects relative to say a star where 1 of the objects were extremely light and the other extremely heavy in comparison and they were the same density we would see but until then it is just a theory
testing this would not turn much results back on a small scale eg our feather and bowling ball as the change would be so small it would be a fraction of a nano-second

[bessy]

can i just add you know this idea of dark matter well we know that light is photons and they have mass it may be very little but they do have some what if it is light its self that is dark matter it sounds abit stupid i know but you can only see the light that is absorbed by your eyes for eg if you are in a vacuum some 1 could collect all the light from a star and direct it so it passes just a few centimeters away from your head and you wouldn't really notice it happened

what im trying to say is theres so much light in the universe that it would appear to have loads of weight in comparison to all the matter in the universe
i mean our star has been giving off light for 5billion years that means its visible for a lot of cubic light years thats alot of light and that just our star

[boxhead]

I'm getting into this discussion quite late and have only skimmed through the previous posts so please bear with me.

Bessy: Your idea that if a photon and a star were not moving relative to eachother is physically impossible I'd imagine because to do this you would have to accelerate the star to a speed of c which, according to special relativity, is impossible.

Also I don't think Alex's point was to say that atmospheric particles aren't pulled to Earth, but rather to say that they're pulled with the same gravitational acceleration as all other particles. (And also the forces referred to aren't that extreme, infact they're absolutely miniscule (I found a rough value of 4.7E-25 N for the force that air encounters at ground level, that force is only going to get smaller as one travels further away from earth). Air pressure is only so large because of the sheer vastness of the amount of particles in our atmosphere).

As far as your point about light being dark matter, this is just a hypothetical stab in the dark but, I believe that rest mass is used in gravitational calculations, not relativistic mass (as relativistic mass depends on your frame of reference so can change). Photons have zero rest mass and so I do not think could be the missing "dark matter".

EDIT: Think what I just typed is wrong after further research. Don't know, ask an Astrophysicist, I'm a Materials Physicist :p (and only a student one at that)

Alex: I see no problems in your explanations, well thought out (though I didn't actually run the numbers, laziness is a bitch).

[bessy]

i said it to be a theoretical what if
also photons don't have to travel at c to prove this look at a black hole

to explain a star falls into it and lets out light some of that light would travel vertical to the black hole right if light cannot move slower than c then how does it get pulled back into the black hole if it cannot slow down
it would have to slow down before it gets pulled back right

think about that 1

[cadair]

OK, the concept of having a photon not moving relative to a star is physically impossible to even think about, there is no physics to use in that discussion because there are two possible ways to think about that (though they boil down to the same problem as either way around you have to things in the same reference frame and therefore stationary with respect to each other). 1) the star is co-moving with the photon, and therefore travelling at c. This is impossible under the theories of physics we use to describe the universe. 2) the photon is not moving and neither is the star, thinking about it this way round the photon would be massless and therefore not exist.

Photons do have to travel at the speed of light, this is a consequence of both Maxwells equations(classical view) and special relativity. If a star were to be on the event horizon of a black hole, (effectively into it but at the point where physics still works), then the light travelling perpendicular to the event horizon would (in its reference frame) be travelling at the speed of light however it would not be moving in the reference frame of the black hole due to the gravitational field, this is because the time dilation effect at the event horizon of the black hole is enough to slow time to a stop if you are viewing it from the reference frame not of the object being pulled into it. (also in the reference frame of the photon time has stopped anyway, for a photon its life consists of wee-----splat, as it created and destroyed instantaneously in its reference frame because it does not experience time.)

To extend boxheads comments about photons as dark matter(being an undergrad Astrophysicist :p) the reason is light is not enough to explain the dark matter phenomenon. The gravitation field of a photon is very very small and the maths has been done and it doesn't add up!

[Alex_Ian_Hamilton]

Hi, sorry for the delay, I’ve been busy studying my astrobiology (and obviously missed quite a bit).
Yup, as far as I’m aware, photons can never travel slower then c according to their frame of reference (wee-----spat, is that an astronomy cast quote there cadiar?); tho they can effectively move slower if travelling through an object (but this is because of the constant absorption and re-emission slowing it down).
The way I think of it is that anything without mass automatically has to travel as fast as it physically can, in the case of our Universe that’s c.

One other key to this black hole and light situation is that as light never gets slowed down, then as the photon travels away from a gravitational source (the photon is fighting gravity) it will lose energy (from an external observers reference frame), this would result in a red-shift (i.e. the photons wavelength would stretch) and if it shifted far enough then the energy from the photon would effectively be gone. This is for a photon moving directly away from the black hole, if the photon was moving at an angle, then its motion can bend and (potentially) it can get trapped in an orbit around the black hole.

The photon for dark matter concept is a cool idea, but it also wouldn’t work because of the form/tempurature of dark matter; have various observations of the effects of dark matter (motions of stars in galaxies, patterns in the CMB (cosmic microwave background), gradational micro lensing); all this shows us that (roughly speaking) the dark matter is concentrated in a cloud or halo, about spherical, around our galaxy; if you do the math (and I haven’t/can’t) then you work out that the velocity of the “particles” of dark matter must be below a set speed, or the dark matter would just fly off. This has proven that neutrinos (almost massless particles travelling at almost c) are not the dark matter, and (although I’ve never heard this interesting photon model) the model of photon dark matter goes the same way.
But on an interesting note, as I recall, most photons in the Universe are actually from the big bang; these photons are spread pretty much evenly (homogenously) throughout the universe and now form the CMB... :-)
http://en.wikipedia.org/wiki/CMB

Bessy, You’re wrong about the atmosphere, all the individual particles are pulled to the Earth with the same velocity assuming they’re at the same altitude (radial distance from the centre of the Earth); the pressure is entirely due to the increased number of collisions with your skin, not gravity; otherwise you’d feel more pressure from above then the side, this is not the case as I understand it.
As you travel to higher altitudes, the atmosphere gets thinner and therefore the number of collisions between gas and your skin drops, thus the pressure drops.
Also, the atoms of the gas don’t repel each other, they are in constant motion and there’s generally so much space between them that they don’t even collide that often, that is why gases compress so easily, because they have so much space, it’s liquids where inter-particle (molecule) collisions start becoming the dominant factor.
Once again, Wikipedia explains in detail (it’s mentioned in the first 2 chapters):
http://en.wikipedia.org/wiki/Gas
But you are right, if your made the moons smaller (but kept the same mass) then it could hold an atmosphere; this is because you’d be decreasing the distance from the centre of mass (r) and so the acceleration due to gravity (and hence the escape velocity) would go up, eventually leading to the ability of the moon to retain gases (when the escape velocity of the moon is high enough that the random motions of the gas molecules won’t go above this velocity).
Also, please be careful with the word theory, it’s not a loose term we should take lightly; theory is the term reserved for experimentally tested and (to-date) not dis-proven with logical and mathematical rigour; General Relativity is a very well tested and mathematically rigorous Theory, Quantum Mechanics is likewise a theory; many other things are simply hypotheses. Sorry to be anal, but I’ve had to deal with the “but it’s only a theory” argument one too many times... :-(

As always, if anyone spots a mistake then please say, I’m finding this an interesting conversation and Bessy, I hope you don’t think that I’m trying to be a pain...

[bessy]

thx for your replies i have taken them in thx for your time in adding a extra few things to explain it

i add these things to see what ppl think as this community is good in that sense as you go on proper sites and they are hell bent on believe that a theory is a fact

and as wise men say

imagination is where intelligence is born and dies where believe/hope begins

and yes im sure i probably quoted someone but never bothered to look it up maybe another time perhaps

[Chaotic Cow]

I like bessy explanation. Makes sense to me.

[Alex_Ian_Hamilton]

It’s always cool to talk about stuff like this; personally I find it a great way to get people thinking about things that otherwise might just be assumed are right.

I think the quote is:
The true sign of intelligence is not knowledge but imagination.
By Albert Einstein (how fitting)

Well I find that the word theory is very badly used in general language; people will say “I have a theory that it’s going to rain today”, when the meaning of the word theory (in physics) is along the lines of “a well-substantiated explanation of some aspect of the natural world, based on logical thought and with mathematical rigour”.
I get frustrated when people use the phrase that “it’s only a theory” when they want to completely discount what science is telling us (generally talking about evolution); tho I would hasten to say that no theory is beyond re-evaluation (that’s what sets science apart from faith), and we must keep an open mind if we do find something’s wrong.

Chaotic Cow (cool name BTW), I agree, it’s a nice hypothesis (note I don’t use the word theory :-), it sounds good and logical while being easy to visualise; but it’s wrong in this case.
I found it interesting to hear a podcast interview with a physics teacher who commented that the biggest problem they have with teaching Newtonian Mechanics is the “bad science” that people have picked up as youngsters, both from the simplifications that schools teach and from “common sense” that works in everyday life.
The thing is, our view of the world is always going to be effected by our day-to-day experiences (which is what makes “common sense”); but it’s a bit of a stretch to expect that things in outer-space will follow these rather limited experiences, from pressure to temperature, distance to time, our world is rather tame and small compared to what’s out there.

[Chaotic Cow]

Thanks for the compliment, Alex.

If it is wrong you should explain to us why it is.

I would love to know the real reason.

Unless you believe it just to be something with the Universe Sandbox and nothing to do with the real world.

[deoxy99]

You guys are too smart...

[Chaotic Cow]

You guys are too smart...

Smart isn't the word. I believe the word best to describe this is "Passionate"!

[rogeracox]

Okay---I'm still unclear on what I learned back in school.  If 2 bowling balls are 8 ft. apart, and each ball weighs 8 pounds, that formula says that {f}, the force = 64/64, which is 1 lb/square foot, right?  My question is, is 1 a BIG force number?  What number constitutes a very LARRRRRGE gravitational force?

[deoxy99]

You guys are too smart...

A lot smarter than me...but I am 10. You might be adults.

[monmarfori]

nearly 10 as should.