Astronomy

Here's an interesting question: is there an upper limit to gravity?

We know there is an upper limit to relative speed: c

Likewise we know 0 K is the lowest possible temperature in the universe.

What about gravity?

We know a black hole has a gravity so intense even the topmost speed in the universe, the speed of light (c), is insufficient to escape from its grip. Ok. all black holes are dimensionless points, or near enough, and we know next to nothing about what goes on in them, if anything does. But not all black holes have the same mass. Some are more massive than others. So, it makes sense to suppose a black hole with 500,000 solar masses compressed into a point should be less powerful, gravitationally, than one with 3,000,000 solar masses so compressed.

It makes sense to suppose so, but is it sensible?

Well, you would need to know if black holes have an upper mass limit, or if at some point they big-bang on you.

Also, I would say that the upper limit on gravity would be a function of the total mass of the universe.

Quote: Dalex64

Well, you would need to know if black holes have an upper mass limit, or if at some point they big-bang on you.

That's an interesting question, too.

Quote:

Also, I would say that the upper limit on gravity would be a function of the total mass of the universe.

It's not that simple.

The Sun has a given mass and exerts gravitational attraction on the planets. Now, suppose you were to compress the Sun to a dimensionless point, like a black hole but without the usual process of collapse and explosion associated with it. The gravity then exerted by the black hole Sun on the planets would be exactly the same as it is now.

At this point it would help if I understood General Relativity well. It's something about how space is distorted. At a distance, the distortion depends on mass more than density, at close range density is more important. Or something along those lines. I think this thought experiment works as well with the Earth-Moon system, if you were to make a black hole Earth.

It's enough to give you a nose bleed ;)

Well, the force of gravitational attraction deceases at a rate that is proportional to the square of the distance between them.

More simply stated, if you double the distance between two objects, the gravitational force between them will be one over double-squared, or 1/4th of what it was when they were closer to each other.

The mass of the sun vs. the mass of the sun in the space of a point -

the closer you get to the sun, the stronger the gravity feels, until you are at the edge of the sun. (assume it has one)

if you keep going closer to the center, drilling into the sun, the gravitational force starts to drop, because the stuff behind/above you is pulling away from the center, so the sum of all forces is going to be less than if you were being pulled all in one direction.

if you shrink the sun to a point, you can now get closer to the center with all of the mass still pulling in one direction, so you can now get closer to the sun without going inside it, and the force of gravity will continue to go up.


don't know how well I'm explaining that.

another thing to think about is if you hollowed out a little room in the middle of the sun, a very strong room so you didn't feel the pressure of the stuff pushing down on you, at the center of the sun the gravity would be zero since everything around you is pulling equally in all directions. if you were at the edge of that room, you'd feel some gravity towards the wall of the room, since you were now closer to some of the mass, and farther away from the rest of the mass.

If you then compress the sun to a point in the middle of the room, you'd get crushed due to gravity. fast. and it would be much much stronger than if you were standing on the surface of the sun.

Quote: Dalex64

another thing to think about is if you hollowed out a little room in the middle of the sun, a very strong room so you didn't feel the pressure of the stuff pushing down on you, at the center of the sun the gravity would be zero since everything around you is pulling equally in all directions.

Technically that would be at the Sun's center of mass, rather than at its geometric center <w>.

And then you'd be pulled by the planets, asteroids and comets in the system, I suppose. I also suppose they wouldn't be strong enough to budge you.

[q}If you then compress the sun to a point in the middle of the room, you'd get crushed due to gravity. fast. and it would be much much stronger than if you were standing on the surface of the sun.

I'm not aware of any limit to the space-time distortion.

From outside the event horizon, a 1,000,000 solr mass black hole would distort more space and exert more gravitational attraction than a 500,000 solar mass one.

The former would have a larger event horizon.

I can't describe gravity at the event horizon, though. I'd have to look that up. That might be considered the limit of space distortion.

Since the distance from the mass is directly proportional to the gravitational attraction, a "compressed" Sun would have less influence over the planets if they were all in their current positions. In this way, it seems to operate very much like a magnet. If you have a small, but very strong magnet, it will exert less influence over objects the same distance away, than a larger, but weaker magnet, only because of the distance between the magnet and the object.

Black holes aren't actually holes sucking things in. They are objects, like the Earth, that other objects "fall" toward. The smallest is probably the mass of three or four of our Sun's compressed into an object 15 miles in diameter. The most massive, probably the size of our sun, but containing the mass of millions or billions of them.

Quote: Ayecarumba

Since the distance from the mass is directly proportional to the gravitational attraction, a "compressed" Sun would have less influence over the planets if they were all in their current positions.

This is where all the various technicalities get you.

In fact, the Earth does not orbit the Sun per se, but rather the center of mass of the Solar System. Curiously even the Sun orbits this center of mass. As I recall, it's located a few million kilometers over the Sun's surface. So it's close enough to the center of the Sun that saying the Earth orbits the Sun is true, or might as well be.

In the Earth-Moon system, both bodies also orbit a system center of mass. In this case it's located well within the Earth.

I should stop. I do get a headache when trying to sort all this out. And I've yet to mention tides. I plain don't get tides.

Quote: Ayecarumba

Since the distance from the mass is directly proportional to the gravitational attraction, a "compressed" Sun would have less influence over the planets if they were all in their current positions. .

This is not correct. In a compressed sun, the mass has not changed, and the distance between the planets and the center of mass of the sun has not changed.

The density of the sun has changed. The gravitational attraction would remain the same.

Same thing when the sun goes red giant. Density goes down, mass remains the same, planets not swallowed by the new sun will remain in the same orbit.

The sun is losing a little mass all the time due to radiation (sunshine!) but we aren't talking about that yet.

Quote: Dalex64

The sun is losing a little mass all the time due to radiation (sunshine!) but we aren't talking about that yet.

That's actually very small. Photons have no mass. The Sun also loses some mass due to the Solar wind it emits, but that, too, is tiny as compared to the Sun's mass. It may gain mass as well from scattered dust and gasses which get to close. Now and then a comet or asteroid can strike the sun, too. All such changes take literally ages to make a difference.

We know how much hydrogen the Sun uses up every second. I don't have the numbers handy, but the amounts are staggering. Yet most of the mass of fused hydrogen stays inside the Sun as helium. Some gets converted into energy and radiated away as light and heat, some mass comes out as Solar wind, as noted above, but the vast majority stays within.

I'm less clear about the interplay of mass on earth. Some gasses, notably hydrogen and helium, can achieve escape velocity by floating up the atmosphere. But we've launched some mass out of the Earth as well. Some of it has returned and burned up on re-entry, some has come down nearly whole in controlled re-entry (like all the crewed space capsules ever), and the rest is in close orbit around the Earth. A little is on the Moon, Mars, Venus, Jupiter,Titan and one comet, orbiting Venus, Jupiter, Mars, the Moon or the Sun (really), and five probes are on their way out of the Solar System forever (Pioneers X and XI, Voyagers 1 and 2, and the New Horizons probe to Pluto).

Compared to the mass of the Earth, though, it would be hard to measure.