Concentrated mass

[stipalgl]

Kind of a ridiculous question (I'd rather not go into detail why I'm asking it) but I figure if any collection of bright minds can give some reasonable answers, it would be here.

In a purely hypothetical sense, if you took something the size of a tennis ball and it weighed roughly 6x10^18kg vs the Earth's roughly 6x10^24kg and you placed it in the middle of a city (let's say New York), would it be capable of generating its own gravitational field to disrupt nearby objects and to what extent?

Sorry I'm not a physics major or anything (far from it) so I thought I'd try my luck here. Thanks and sorry once again for the unusual question.

 

[Mark R]

Any mass creates its own gravitational field (in Newtonian gravity).

The gravitational field strength (g) is given by teh following equation:

g = (G * M) / r^2
where
G is the gravitational constant (G = 6.7 * 10^-11 N m^2/kg^2)
M is the mass
r is the distance from the (center of) mass

For the earth:
g = 6.7 * 10^-11 * 6 * 10^24 / (6.4 * 10^6) ^2 = 9.8 N/kg

For your superdense tennis ball at a distance of 10 km:
g = 6.7 * 10^-11 * 6 * 10^18 / (1 * 10^4) ^ 2 = 4.0 N/kg

So, at 10 km, your tennis ball would be exerting a gravitational pull approximately 40% of the strength of the earth's gravity.

If you had a weight tied to a piece of string, it would hang at an angle of 22 degrees from vertical, pointing towards your "tennis ball".

From the equation, you should be able to see that as you get closer, the gravitational strength increases rapidly.

Note that the relevant distance is distance to the *center* of the object (not the surface), so the gravitational field of the earth, at the earth's surface is much, much, much less than the gravitational field at the surface of your "tennis ball".

 

[Biftheunderstudy]

Nevermind that its density would be ~10^22 kg/m^3 well over nuclear density.

 

[Sunny129]

that would be exotic matter for sure. we know that such an object can theoretically exist without imploding under its own gravity by deduction alone (the earth's Schwartzchild radius is approximately 9mm, and would therefore have to be compressed into a sphere of radius 9mm to induce gravitational collapse and become a black hole...thus the Schwartzchild radius of something with a mass some 6 orders of magnitude less than the earth's mass would have to be much smaller than that of a tennis ball). using the same equation Mark R used to calculate the gravitational attraction of (6 * 10^18)kg at 10km, the gravitational force at such a mass's surface, were it compressed to the size of a tennis ball, would be:

g = 6.7 * 10^-11 * 6 * 10^18 / (3.55 * 10^-2) ^ 2 = 3.19 * 10^11 m/s^2

...in summary, such an object would be well beyond white dwarf matter density, and would approach neutron star densities.

 

[stipalgl]

Interesting replies so far. So objects scattered around would actually be impacted by something so small. That's pretty cool. I was basing the material in question on this article I recently read:

http://news.nationalgeographic.com/...ter-created-lhc-alice-big-bang-space-science/

I'm assuming the pull on objects not tied down wouldn't be significant however from a fairly close distance?

 

[Biftheunderstudy]

Re-read MarkR's post, the gravitational effects would be quite significant, and much more pronounced as you get closer.

I don't have time to look at any GR effects, but I suspect that this is still well within the Newtonian gravity limit so they *should* be unimportant. But that would be weird...

 

[Sunny129]

Interesting replies so far. So objects scattered around would actually be impacted by something so small. That's pretty cool.

it is most interesting to contemplate such a small object having such a significant gravitational influence...but its misleading at the same time, b/c in actuality, it is the object's mass alone that determines its gravitational pull from any given distance. if we were to take a (6 * 10^18)kg mass the size of a tennis ball and decrease its density to approximate the earth's density, the spherical object would become considerably larger, and its surface gravity quite low (after all, according to Mark R's calculation above, such an object would cause an acceleration of only 4 m/s^2 on objects 10km distant...so that acceleration would be much less from the object's surface were its density made approximately equal to earth's density, b/c its radius would be much larger than that of a tennis ball at that point).

I'm assuming the pull on objects not tied down wouldn't be significant however from a fairly close distance?

i'm assuming you meant to say "would" instead of "wouldn't?" b/c the gravitational pull on other objects would increase substantially as they approach an object of such high density.

 

[SMOGZINN]

Another thing to consider is that this object would not long be on the surface of the Earth if put there. It's density would be so much greater then the ground around it that it would sink into the ground like a lead ball dropped into the ocean, and continue until it hit the center of the Earth.

I'm not going to do any math to back this up, so this is just some guesswork, but I think it would also start to gain mass as it's massive surface gravity started to rip atoms apart and collapse them into it's surface. I think you would get something similar to the supernova effect as it gathered mass until it had enough to overcome the crushing gravity and kick off fusion reactions and expand.

Any way you look at it, you would not want to be anywhere near such a thing. And by near I mean in the same solar system.

 

[Sunny129]

Another thing to consider is that this object would not long be on the surface of the Earth if put there. It's density would be so much greater then the ground around it that it would sink into the ground like a lead ball dropped into the ocean, and continue until it hit the center of the Earth.

I'm not going to do any math to back this up, so this is just some guesswork, but I think it would also start to gain mass as it's massive surface gravity started to rip atoms apart and collapse them into it's surface. I think you would get something similar to the supernova effect as it gathered mass until it had enough to overcome the crushing gravity and kick off fusion reactions and expand.

Any way you look at it, you would not want to be anywhere near such a thing. And by near I mean in the same solar system.

interesting theory...i would have to agree that, given its enormous surface gravity of 3.19 * 10^11 m/s^2 (as i calculated above), it would definitely accrete earth matter if it started its existence on the earth's surface. though i suspect the consequences would be less like a supernova and more like the average nova...actually i'm not sure how to classify it, b/c a nova is defined as the nuclear chain reaction caused by the accretion of mass on the surface of a white dwarf...and what we're dealing with here is an object that would physically behave much more like a neutron star than a white dwarf. i know neutron stars can accrete mass from a companion star just as a white dwarf can - i just don't know if the resulting nuclear chain reaction is still called a nova as it is with a white dwarf.

anyways, i suspect this would be the case simply b/c the object is more like a neutron star (a supernova remnant) than a white dwarf (a main sequence star remnant, and the possible progenitor star of a future supernova if it has a main sequence or giant companion star). i.e. we're starting with an object that is already well beyond the densities and gravitational attraction required to set into action a supernova. the next step in the evolution of such an object would be a black hole...and even if the object were able to eventually accrete the entire earth's mass, the entire earth wouldn't be nearly enough mass to put this object over the tipping point of gravitational collapse. that is to say, its mass is still only 1/1,000,000 of the earth's mass. neutron stars typically weigh in at around 1.5 to 3 solar masses, while the combined masses of the earth and this object would still only be marginally more massive than the earth itself. since once earth mass is arbitrary in comparison to a solar mass, this object would need to accrete much more than one earth mass (~3 solar masses to be precise) in order to collapse into a black hole.

and while there are plenty of locations within our solar system that would be safe from this object's immense gravitational field (after all, Mark R showed us that its gravity at a distance of only 10km is less than half of earth's surface gravity), it might certainly be advisable to get out of the solar system (as you suggested) to keep from getting fried by the insane nuclear chain reaction caused by accretion on this object, whether its only accreting one earth masses or 3 solar masses.

 

[Mr. Pedantic]

I don't think it would have enough mass to cause it to remain as a neutron star or even a white dwarf. From an astronomical point of view 10^18kg isn't really that much, and it would probably just explode outwards and destroy everything that way.

 

[Sunny129]

i hadn't thought about it that way. i suppose such an object can't really exist in the sense that, were it suddenly to appear on the earth's surface (or anywhere but on or in another object large enough to maintain equally high densities), it would expand explosively due to a lack of sufficient pressure (or shear mass for that matter) bearing down on it from all directions. so in reality, such an object cannot exist to begin with.

but suppose such an object could exist to begin with. suppose we had the ability to more or less instantaneously bring into existence a (6 * 10^18)kg mass the size of a tennis ball somewhere on the surface of the earth. would the object expand violently due to the lack of mass and pressure around it? or would its extreme surface gravity cause it to start accreting earth material and grow in size? i suspect explosion/expansion would happen since the object is essentially a giant nucleus of neutrons (and the occasional proton here and there), which is held together by the strong force...whereas the accretion process depends on the force of gravity, a force 10^38 times weaker than the strong force.

 

[Brian Stirling]

To have that much matter in so small a volume would require enormous force to overcome the electron degeneracy pressure. The gravitational force though enormous at those distances, would not be anywhere near strong enough to hold it together. So, assuming the force holding it together were to go away the mass would explode with more than enough force and energy to rid Earth of its infestation!


Brian

 

[Sunny129]

a (6 * 10^18)kg mass compressed down to the size of a tennis ball would indeed consist of degenerate matter...however i think the pressure to be overcome in order to maintain the object's size & shape would be more accurately described as neutron degeneracy pressure than electron degeneracy pressure, just b/c this object is well beyond white dwarf star densities (a white dwarf depends on electron degeneracy pressure to prevent gravitational collapse). granted both pressures are analogous to one another, but neutron degeneracy pressure can prevent the gravitational collapse of significantly more mass than electron degeneracy pressure...nevertheless, regardless of whether its a mass of electrons or a mass of neutrons, i agree with you that the outcome wouldn't be good for earth lol...

 

[Brian Stirling]

Yeah, definitely a neutron degenerate mass and not an electron degenerate mass...

The energy released from the explosion of this mass would more than end life on Earth -- it would surely reduce the Earth to cosmic dust....


Brian

 

[Biftheunderstudy]

Actually, it's passed neutron degeneracy and onto quark degeneracy, and yes I'm pretty sure it would explode...violently.

 

[stipalgl]

Thanks for all the cool replies. Very informative. And from my very limited understanding on the matter, I think something of that nature would be quark degeneracy and not neutron degeneracy, no?

 

[Sunny129]

i'm not so sure that we're at the quark degeneracy level yet...given your hypothetical object's size and mass, we determined earlier on that its surface gravity would be:

g = 6.7 * 10^-11 * 6 * 10^18 / (3.55 * 10^-2) ^ 2 = 3.19 * 10^11 m/s^2

while this is only a calculation of surface gravity (and not a direct calculation of density, would would be easy enough), it does give us a figure that can be compared to the surface gravity of the typical neutron star (which is, according to wikipedia's article on degenerate matter, approx. 2 * 10^11 times stronger than Earth's surface gravity)...so neutron star's surface gravity would be approx. [2 * 10^11] m/s^2 * [9.8 * 10^0] m/s^2 = [1.96 * 10^12] m/s^2. another wiki article, this one on neutron stars, claims that surface gravity can reach as high as [7 * 10^12] m/s^2. either way, that is a full order of magnitude stronger than our hypothetical object's surface gravity, so i can only assume that its density is also slightly less than that of a neutron star's, putting it just at the threshold of neurtron degenerate matter (and not at the threshold of quark degenerate matter, which requires much higher densities).

now perhaps Biff was taking into account that a neutron star in reality does not maintain a constant density throughout (just like any other mass held together by gravity) - it is least dense at the surface, and increases in density as you as you proceed toward the core. now some theoretical physicists theorize that the core of a neutron star is a quark-gluon plasma...so given the possibility that quark degenerate matter may exist in a neutron star, i can see who one might think that our hypothetical object might also consist of quark degenerate matter...but given that its surface gravity barely reaches neutron star surface gravity, i'm inclined to think that it is probably more like the neutron degenerate matter found in the upper layers and near the surface of a neutron star.

 

[Brian Stirling]

The thing is, the total mass is pretty small so getting that kind of density is hard to imagine. Getting below neutron density but stopping before full black hole collapse is the trick, I guess.

There are some really odd theoretical objects like quark stars and preon stars but I have to imagine that when a star larger than a few solar masses collapses the inertia of the collapse would compress the core beyond what gravity alone would so even if the mass is just more than a typical neutron star and small enough to create a quark star the inertia of the collapse would push it to densities that ultimately go all the way to a black hole.


Brian

 

[Biftheunderstudy]

Well, what I meant is that you can work out what the Chandrasekhar mass is (the mass where electron degeneracy can no longer balance gravity) for a white dwarf and do the exact same calculation for neutron degeneracy and find the mass for that. (By mass here, I really mean the pressures needed to push 2 neutrons together -- that was a gross oversimplification ::waves hands about Pauli exclusion principle:

Problem is, we really have no idea what the equation of state for something like a neutron star is, but the maximum degeneracy pressure seems like a known quantity.

My reasoning is that if you assume constant density for this tennis ball you come up with a density that is higher than nuclear density, but too large a radius for a black hole. Ergo, exotic matter.

The surface gravity argument is really for something that is balanced pressure-wise, this thing really does not want to be in this configuration (the neutron or quark or some other exotic particle degeneracy greatly exceeds the gravitational pressure).

I think what Brian Stirling says is mostly correct, Quark stars seem really...tweaky, in that you need just the right initial conditions to end up at quarks and not a black hole. Neutron stars themselves may have a superconducting quark core...whacky.