Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: Vereava on 22/10/2010 22:42:52

Or does this only work as 'equal mass but not equal density'?
Or rather, if I had a ball of tin 25,000 miles wide, and a ball of manganese 50,000 miles wide (we're talking spherical with no surface imperfections, equivalent in every way except in diameter) would they have the same gravitational pull?
Bonus question, how important is density when relating to gravitational force?

I'm sure you know this, though the phrasing of your question might suggest otherwise, but as for your title question: D = M / V, M1 / V1 = M2 / V2, so yes.
I'm assuming what you're really interested in is the bonus question, and what you mean to ask is that for spheres of different sizes (volumes) and masses, if they have the same density, do they also have the same gravitational pull? I'd like to say yes, but that's just my intuition.

Or does this only work as 'equal mass but not equal density'?
Or rather, if I had a ball of tin 25,000 miles wide, and a ball of manganese 50,000 miles wide (we're talking spherical with no surface imperfections, equivalent in every way except in diameter) would they have the same gravitational pull?
Bonus question, how important is density when relating to gravitational force?
If you had that amount of tin and manganese, you'd be so rich that you probably wouldn't be asking these questions [;D]
You can have equal densities but unequal masses if the volumes are different, or equal masses and unequal densities if you have appropriate volumes.
Density is the measure of mass per unit volume of a substance. If you know the density of a substance, you will need to also know it's total volume to calculate it's total mass. Or, if you know it's total mass, and you also know it's volume, you can calculate the density of the substance.
I'm not sure what the densities of tin and manganese are (and I'm too lazy to look them up) but, I suspect the mass of the manganese ball will be much greater because it has a much greater volume, so it will have a greater gravitational effect.
I would think that, for solid regular objects like spheres, gravity will be a function of total mass only  density will have no effect. However, for fluids (gasses in particular) things might get a bit more tricky, but I'm really not sure about that.

Or does this only work as 'equal mass but not equal density'?
Or rather, if I had a ball of tin 25,000 miles wide, and a ball of manganese 50,000 miles wide (we're talking spherical with no surface imperfections, equivalent in every way except in diameter) would they have the same gravitational pull?
Bonus question, how important is density when relating to gravitational force?
Lets start in reverse order, mass and gravity of objects in weightlessness of space:
"Any object in weightless space larger than a couple of hundred miles in diameter has enough mass for its gravity to overcome largescale irregularities and force it into a spherical shape. This gravitational compression also generates significant amounts of heat at the center of the planet. This heat melts, or at least softens, any solid materials within the planet, facilitating the planet’s collapse into a spherical shape.
Objects in space smaller than about 100 miles in diameter, such as most asteroids, comet nuclei and small moons, lack the mass to create a gravitational field strong enough to compress themselves into spheres. These little worlds often take on what I call the “sick potato” look."
http://www.clarkplanetarium.org/blog/whyareplanetsspherical
Now we established that Mass and gravity is directly related: more mass more gravity
Lets use substances instead of objects for now.
Now we ask can,(density = mass / volume), the ratio be equivalent of different substances under these conditions...
where there is no other or very little external affecting forces
Since
Mass controls gravity...
Gravity controls volume...
Is it safe to say, with no outside influence?
Mass controls volume
If there is a single substance with a particular mass it will have a particular volume and therefore have a particular density
Since elements have different atomic numbers, their atomic weights are different, no matter what the gravity is being imposed, their mass per unit volume also will be different and visa versa.
In weightlessness of space, this will exibit a difference in gravitational effect on itself, affecting its volume.
Under the weightlessness of space Density = mass / volume of two different objects,
no matter the same or different substances, can not maintain a different ratio combination,
equivalent to produce the same density of each other,
when its own gravity can manipulate its volume.
More mass,> more gravity,> less volume,> more density...
I say a conditional No!

Wow. Thank you for your responses. I feel much better now, haha.
I will give you guys a much clearer picture of what I was thinking because I was really excited initially and couldn't get my thoughts straight.
I'm picturing the two spheres, planets, whatever you want to call them, floating in a normal vacuum. Weightless space is unrealistic for this problem since even in a vacuum there is mass and energy defined as "quantum jitters", and if mass creates gravity then there is gravity everywhere, and therefore, weightless space is.. well, it doesn't make sense to me since weight is the measure of an object's reaction to gravity, etc etc.
I'm wondering about density because, if you think about it, the more dense an object is, the closer the atoms are together. So if an object made of manganese with an atomic number of 25 is twice the volume* as an object of tin with an atomic number value of 50, wouldn't this mean that the two objects would have an equal gravitational pull?
*Edit: used to say 'size'

So if an object made of manganese with an atomic number of 25 is twice the size as an object of tin with an atomic number value of 50, wouldn't this mean that the two objects would have an equal gravitational pull?
Ah! You have to be a bit careful when you say "twice the size". For example, if both objects happened to be cubes, and the lengths of the sides varied by a ratio of 2:1, the volumes would vary by a ratio of 8:1 (2 x 2 x 2 = 8)

Twice the volume* ?

Twice the volume* ?
For cubes, it will be eight times. The volume of a cube is, strangely enough, the cube of the length of a side.
The volume of a sphere is proporttional to the cube of it's radius, so, if you double the radius, the volume will also be eight times greater.

Twice the volume* ?
For cubes, it will be eight times. The volume of a cube is, strangely enough, the cube of the length of a side.
The volume of a sphere is proporttional to the cube of it's radius, so, if you double the radius, the volume will also be eight times greater.
so for theory's sake, Maybe it would be better if I used Beryllium and Germanium?
New set up: a sphere of Beryllium that has a volume of 160,000 m^3 and a sphere of Germanium that has a volume of 20,000 m^3... Am I there yet?

Twice the volume* ?
For cubes, it will be eight times. The volume of a cube is, strangely enough, the cube of the length of a side.
The volume of a sphere is proportional to the cube of it's radius, so, if you double the radius, the volume will also be eight times greater.
so for theory's sake, Maybe it would be better if I used Beryllium and Germanium?
New set up: a sphere of Beryllium that has a volume of 160,000 m^3 and a sphere of Germanium that has a volume of 20,000 m^3... Am I there yet?
I think so, but I've kinda forgotten what the question was [;D]
Assuming you picked volumes that will result in spheres of equal mass, then I believe they will have equal gravitational effects (if that was the question of course).

Twice the volume* ?
For cubes, it will be eight times. The volume of a cube is, strangely enough, the cube of the length of a side.
The volume of a sphere is proportional to the cube of it's radius, so, if you double the radius, the volume will also be eight times greater.
so for theory's sake, Maybe it would be better if I used Beryllium and Germanium?
New set up: a sphere of Beryllium that has a volume of 160,000 m^3 and a sphere of Germanium that has a volume of 20,000 m^3... Am I there yet?
I think so, but I've kinda forgotten what the question was [;D]
Assuming you picked volumes that will result in spheres of equal mass, then I believe they will have equal gravitational effects (if that was the question of course).
I was wondering if it was more about density rather than mass, because if two objects (made up of one substance each) are the same density, then they would have the same amount of mass, the only thing that would be different would be that one's diameter (in the case of beryllium and germanium) would be 8 times the size of the other...
Same density.. same amount of matter.. different size objects.. same gravitational pull? Right?
Even though one would be 1000 miles wide and the other is proportionally 8 times the size?

I was wondering if it was more about density rather than mass, because if two objects (made up of one substance each) are the same density, then they would have the same amount of mass, the only thing that would be different would be that one's diameter (in the case of beryllium and germanium) would be 8 times the size of the other...
Same density.. same amount of matter.. different size objects.. same gravitational pull? Right?
Even though one would be 1000 miles wide and the other is proportionally 8 times the size?
Ah, OK. For solid objects of uniform density, I think it's simply a question of the mass. The density has no effect.
I say that because, in Newtonian Mechanics at least, you can assume all the mass of a solid object acts at it's center of gravity, which, in the case of your spheres, would be right at the center of each sphere. So, the actual volume of the object does not matter. It's only the quantity of mass that has an effect.

I was wondering if it was more about density rather than mass, because if two objects (made up of one substance each) are the same density, then they would have the same amount of mass, the only thing that would be different would be that one's diameter (in the case of beryllium and germanium) would be 8 times the size of the other...
Same density.. same amount of matter.. different size objects.. same gravitational pull? Right?
Even though one would be 1000 miles wide and the other is proportionally 8 times the size?
Ah, OK. For solid objects of uniform density, I think it's simply a question of the mass. The density has no effect.
I say that because, in Newtonian Mechanics at least, you can assume all the mass of a solid object acts at it's center of gravity, which, in the case of your spheres, would be right at the center of each sphere. So, the actual volume of the object does not matter. It's only the quantity of mass that has an effect.
Well, if the objects are more dense because their atoms are more heavily attracted to each other, wouldn't objects that are more dense in turn create a stronger gravitational pull? I mean, more dense means more mass in the area, but why are these objects more dense?
Is gravity making the atoms behave differently? Therefore, if an object is more dense, wouldn't that mean it has more gravity?
I mean, obviously yes, this is the case, sense more density = more mass which in turn = more gravity, but what makes objects more dense? (I guess this is finally the question I was trying to ask!)
Think of the objects having an equal number of mols

Think of the objects having an equal number of mols
Bummer! I always had a big problem getting my head around mols.
Let me try this. Assuming the masses of the two spheres are identical but they have different densities, I believe that if you do a heck of a lot of integration, you'll find that they will accelerate towards each other equally, and that the effect will be no different than if you had assumed each was a point mass of zero volume.
Just don't ask me to show you the math!

So technically, you could have something the size of the sun pulling equally on something the size of a basketball?
I won't ask for any math as long as you don't :P

So technically, you could have something the size of the sun pulling equally on something the size of a basketball?
It's not really a technicality. The Sun and a Basketball actually do exert an equal attractive force on each other.
The Moon and the Earth exert an equal attractive force on each other and they both orbit around a common point which is not at the center of gravity of the Earth. So, it's really correct to say they both orbit around each other.

Very interesting, thank you!!