A basic question on gravity from a novice

[flinky]

First let me apologise if this is a dumb question, or it has been asked before but i can't find an answer anywhere. I am a bit puzzled by some aspects of gravity. I'm also a novice so the question is in simple language and may not be clear, i hope it is. it's also a two-part question. Finally as I am a novice simple answers would be appreciated.

so here goes...

Newtons law of gravity, is regarding the force of a gravitational field on 2 objects. But the equation only asks for the mass of the two objects. so...

1. does size not matter? ie: an Earth sized object with Earth's mass and a grapefruit sized object with Earth's mass would give the same results? if yes why are black holes such a big problem?

2. there is no way to work out a gravitational force of just one object? ie: the equation asks for two masses divided by the distance. so you can't work out an objects gravitational force without having another mass act upon it? again if yes can anybody really say an object has a gravitational field if it takes two objects?

the second part of my query and what really is confusing me at the moment is this:

a star with the mass of 'X' has an effective gravitational field that extends 'N' light years (for example).

the star is in a cluster of 10 million stars each with a mass of 'X' and an effective gravitational field that extends 'N' light years.

is the clusters gravitational field based on 10 million individual gravitational fields or is it based on a cluster with the mass of 'X' times 10 million. And if the latter would the clusters effective gravitational field extend proportionally (ie: 10 million times 'N' light years).

given that a gravitational field is infinite but it's effective range is a range that can capture a slow moving object of 'P' mass. ie: don't turn that point into an argument. you'll either get what i mean or you won't.

anyway, any enlightenment here would be gratefully appreciated and I'll warn you now will probably lead to follow up questions.

 

[phinds]

First let me apologise if this is a dumb question, or it has been asked before but i can't find an answer anywhere. I am a bit puzzled by some aspects of gravity. I'm also a novice so the question is in simple language and may not be clear, i hope it is. it's also a two-part question. Finally as I am a novice simple answers would be appreciated.

so here goes...

Newtons law of gravity, is regarding the force of a gravitational field on 2 objects. But the equation only asks for the mass of the two objects. so...

1. does size not matter? ie: an Earth sized object with Earth's mass and a grapefruit sized object with Earth's mass would give the same results? if yes why are black holes such a big problem?

Size does not matter. Why do you think black holes are a problem?

2. there is no way to work out a gravitational force of just one object? ie: the equation asks for two masses divided by the distance. so you can't work out an objects gravitational force without having another mass act upon it? again if yes can anybody really say an object has a gravitational field if it takes two objects?

Yes, it takes two objects because gravity is something that works on objects based on OTHER objects. One object has a gravitational field but that doesn't really mean anything unless you want to see what effect is has on ANOTHER object.

the second part of my query and what really is confusing me at the moment is this:

a star with the mass of 'X' has an effective gravitational field that extends 'N' light years (for example).

the star is in a cluster of 10 million stars each with a mass of 'X' and an effective gravitational field that extends 'N' light years.

Gravitational fields theoretically extend to infinity. Why would they stop after some set amount of distance? Oh, I see below that you already know that.

is the clusters gravitational field based on 10 million individual gravitational fields or is it based on a cluster with the mass of 'X' times 10 million. And if the latter would the clusters effective gravitational field extend proportionally (ie: 10 million times 'N' light years).

If you are outside the cluster, then the gravitational effect is for the whole cluster as though its mass were all at its center. The rest of your question is vague.

 

[Bandersnatch]

1. does size not matter? ie: an Earth sized object with Earth's mass and a grapefruit sized object with Earth's mass would give the same results? if yes why are black holes such a big problem?

Your intuition is right. Size doesn't matter. It can be shown mathematically, that a spherical body produces the same gravitational field as a point at the centre of the body containing all its mass would.
And indeed, black holes are no different than equally massive stars, gravitation field-wise. A planet around a black hole will happily follow it's orbit, just as it would if it were orbiting a star.
The popular media tends to play on the scary all-gobbling doomsday hole in the universe, but it's got nothing to do with reality. Sure you'd get a bad case of spaghettification by falling into one, but falling onto a star is not healthy either.

2. there is no way to work out a gravitational force of just one object? ie: the equation asks for two masses divided by the distance. so you can't work out an objects gravitational force without having another mass act upon it? again if yes can anybody really say an object has a gravitational field if it takes two objects?

You can work our the gravitational field produced by any single body.
http://en.wikipedia.org/wiki/Gravitational_potential#Mathematical_form
When you talk about Earth's gravitational acceleration, you're talking about the gravitational field at a certain distance from Earth's centre. As you know, g=9,81 does not depend on how skinny/fat you are, so things tend to fall equally fast.
The force exerted on an object in a gravitatonal field is dependent on its mass, as well as the strength of the field, which in turn is dependent on the mass of the central body. So you can't really talk about forces here without considering both bodies.

is the clusters gravitational field based on 10 million individual gravitational fields or is it based on a cluster with the mass of 'X' times 10 million. And if the latter would the clusters effective gravitational field extend proportionally (ie: 10 million times 'N' light years).

I really don't see what's the difference between these two. You treat the cluster as you do any other spherical body, i.e. as if all it's mass were concentrated in the centre.
You can also add the forces exerted by each individual star, but you'll get the same result.
However, the second part doesn't make much sense, since the gravitational fields extend to infinity. You could say that at some distance N from the cluster, the field is 10 million times as strong as it would be from a single star.
If you're going to call some X magnitude of the field as being its effective limit(i.e.you don't care for anything lower than that, which I believe is what you meant), then you have to remember that while the field increases in proportion to the cluster's mass, it decreases as an inverse square of the distance. So it would not make the field have magnitude X 10 million times farther, but the sqare root of 10 million as far.

 

[flinky]

thanks for the quick replies and much appreciated.

the first part about size and mass was really just getting confirmation of what I thought. it is still bizarre to me that size is irrelevant in this context.

phinds: first, thanks for replying. the black holes being a problem thing, what I meant was if size wasn't an issue, then as it doesn't matter if it's a point a singularity or a really big star gravity should be gravity. but things I've read and documentaries I watch all say the laws of gravity break down at this point, but they never really explain what they mean?

bandersnatch: again, thanks for the reply and thanks for understanding my query about the clusters.

from what you have both said am I right in believing that gravity is relative. i.e.: our planet is in a gravitational orbit of our sun, but outside our solar system the gravitational field would be of the whole solar system. or the milkyway has a gravitational field of it's own as does the Andromeda galaxy. but move far enough away then (as these two galaxies are colliding) they become one object with it's own gravitational field. so another object would be affected by the gravitational field of both galaxies acting as one. would this be a correct way of thinking?

that might not be very clear, sorry. but I'm trying to work out in my own head how gravity accumulates.

 

[phinds]

the black holes being a problem thing, what I meant was if size wasn't an issue, then as it doesn't matter if it's a point a singularity or a really big star gravity should be gravity. but things I've read and documentaries I watch all say the laws of gravity break down at this point, but they never really explain what they mean?

Nothing breaks down OUTSIDE the event horizon of a black hole, but AT the event horizon and inside it, things get screwy.

Outside the event horizon, there is no gravitational difference at all between a point mass singularity X miles away and, say, a neutron star with its center X miles away. WAY outside the event horizon, then even a normal star with the same mass would be gravitationally indistinguishable from a black hole.

 

[Bandersnatch]

from what you have both said am I right in believing that gravity is relative. i.e.: our planet is in a gravitational orbit of our sun, but outside our solar system the gravitational field would be of the whole solar system. or the milkyway has a gravitational field of it's own as does the Andromeda galaxy. but move far enough away then (as these two galaxies are colliding) they become one object with it's own gravitational field. so another object would be affected by the gravitational field of both galaxies acting as one. would this be a correct way of thinking?

I think you're overgeneralising a bit.
You have to remember that treating any multi-body system as having all of its mass concentrated in a single point is just an approximation.

If you are really far away from the solar system, then it's useful to add up all of the mass distributed among the Sun, planets, and space junk, and treat them as one object, because at this scale it is a very good approximation. As you get closer, however, the approximation becomes less valid, as individual planets' influences become noticeable.

When you are in such a distance from two galaxies that you can see them separated by 90° in the sky, then you can't really treat them as one with all mass concentrated in-between, as some of the forces actually cancel each other thanks to the separation.
But if you are so far away from both that you can barely discern them as separate objects, then not treating them as one would be just too anal.

The sphericaly distributed mass is a bit of a special case here, as adding up all the forces from the component bits of mass does indeed produce exactly the same force as if all of the mass were concentrated in the central point.
But since there are no ideally spherical objects in the universe(I think?), whenever you decide to use this approach, you have to remember that it's still an approximation.
The Moon might be treated as a sphere for most purposes, but sending a probe really close requires course correction for uneven mass distribution in the crust, etc.

The bottom line is, in the ideal situation you'd always want to take each individual particle in the world that has a mass, and add their force vectors together to get the net gravity. But since that's hardly doable, we use these handy approximations instead.

 

[twofish-quant]

from what you have both said am I right in believing that gravity is relative. i.e.: our planet is in a gravitational orbit of our sun, but outside our solar system the gravitational field would be of the whole solar system. or the milkyway has a gravitational field of it's own as does the Andromeda galaxy. but move far enough away then (as these two galaxies are colliding) they become one object with it's own gravitational field. so another object would be affected by the gravitational field of both galaxies acting as one. would this be a correct way of thinking?

I don't think so. Gravitational fields add. So when you are looking at the solar system, you have to add up all of the things within the solar system.

What does matter is whether the details matter. One thing that you find when you do the math is that the "non-spherical" parts of a gravitational field become quickly less important. One way of thinking of it is that if you are in orbit around the earth, the fact that the moon is a separate body is important, and if you assume they are the same object, your calculations are going to be very, very wrong. If you look at the Earth and the moon from Alpha Centauri, and do the calculations as if they were one object, your answers are going to be close enough that the differences don't matter.

Also whatever the details matter depends on how detailed and accurate you want to be.

 

[twofish-quant]

Also if you know some basic algebra, you can do this equation...

gravitational field = object 1+ object2 + object3 + object4 + ...

Now you can use algebra to rearrange that equation into

gravitational field = spherical average + slightly non-spherical part + more non-spherical part + even more non-spherical part ...

It's a lot of messy algebra but it's just algebra.

If you want to see the messy algebra

http://en.wikipedia.org/wiki/Multipole_expansion

You can then show that at you move away from the system, the non-spherical parts become less and less important.

 

[someGorilla]

from what you have both said am I right in believing that gravity is relative. i.e.: our planet is in a gravitational orbit of our sun, but outside our solar system the gravitational field would be of the whole solar system. or the milkyway has a gravitational field of it's own as does the Andromeda galaxy. but move far enough away then (as these two galaxies are colliding) they become one object with it's own gravitational field. so another object would be affected by the gravitational field of both galaxies acting as one. would this be a correct way of thinking?

Actually, your intuition is correct (the fact that if you are far from the two galaxies you can express their field as if they were one massive point).
But what hampers your understanding is, I think, that you seem to think each object has "its" own gravitational field. Actually, each object contributes to the global gravitational field. I see you don't understand how "two" fields merge to become "one". Counting gravitational fields makes no sense. There's one field, permeating all space, influenced by the objects. Think of the illumination in a large hall. You might have lamps, each one projecting a patch of light onto the ceiling. You might have streaks of light coming in from a window. Add a swimming pool reflecting moving waves of light onto the ceiling. Each point of the ceiling is more or less bright depending on how much light it gets from how many sources. The ceiling here represents the field of course, and light its intensity. It is additive: where a patch of intensity 5 intersects another patch of 5, you get a zone of intensity 10.
The problem with this picture is that this is a "scalar" field, while gravity is a vector field: it has not only an intensity but also a direction – or you couldn't fall "down"! If you don't know what vectors are, that's the place to start.

 

[marty1]

I think size does matter when you are close. A grapefruit with Earth's mass might squish you if you are standing on it because you are closer to the atoms on the far side of the grapefruit than you would be to the far side of the earth. The math is easier using center of mass, but in reality you are being pulled by each atom individually.

 

[Drakkith]

I think size does matter when you are close. A grapefruit with Earth's mass might squish you if you are standing on it because you are closer to the atoms on the far side of the grapefruit than you would be to the far side of the earth. The math is easier using center of mass, but in reality you are being pulled by each atom individually.

Of course. If you compress an object far enough it will become a black hole. Density matters.

 

[flinky]

thanks for the replies. things are a bit clearer now, although a lot of other questions have popped up. but I'm going to re-read a couple of things first to see if i understand them better first.

I did think that everything was very precise in physics, so realising that things are more approximations makes a lot more sense.

the way gravity accumulates is still puzzling me a bit (not the actual maths part but more the mechanism behind it - eg: why doesn't magnetism accumulate in the same way?).

thanks again they have all been helpful and no doubt i'll be back with more questions.

 

[someGorilla]

I did think that everything was very precise in physics, so realising that things are more approximations makes a lot more sense.

Oh well, precise to a certain degree.

why doesn't magnetism accumulate in the same way?).

It does.

 

[HomogenousCow]

The equation given to high school students is just for point masses, for a non spherically symmetric distribution of mass you need a different equation.
Well..in classical mechanics sources of gravity add linearly, but it is nonlinear in general relativity, which is the modern theory of gravitation)
Electromagnetic sources do add linearly, because the equations that govern them (Maxwells equations) are linear.
To demonstrate what I mean by this, you need to understand what it means for something to be linear.
multiplication is linear, as in 3*(2+3)=3*2+3*3, while exponentiation is not linear (a+b)^2=/=a^2+b^2

The equation that gives us gravitational potentials in classical mechanics is:

(A linear operator acting upon the potential)=(the source term)

Now since the left hand side is linear, two potentials caused by two sources will add linearly

Linear operator(Potential one + Potential two)=(Source one+Source two)

A similar thing goes for magnetic fields.

 

[marty1]

technically we should sum over all combinations of distances and unit (point) masses in each object (particle by particle as they move), but after a several years of calculations we would discover that our floating point processors do not have enough bits of accuracy anyway and you do not need to know if you need 2 more atoms of rocket fuel or not.

 

[Drakkith]

technically we should sum over all combinations of distances and unit (point) masses in each object (particle by particle as they move), but after a several years of calculations we would discover that our floating point processors do not have enough bits of accuracy anyway and you do not need to know if you need 2 more atoms of rocket fuel or not.

I object! Those 2 atoms are vitally important!