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Comment by xg15 | Hacker News Reader

> So, if you hold the mass fixed and compress an object into a smaller and smaller radius, then the gravitational pull gets stronger.

I find this bit interesting because I'm pretty sure I've read the exact opposite before. My previous understanding was that the gravitational pull is only determined mass - but a black hole can put an almost arbitrary amount of matter into the same space, therefore the gravitational pull is factually much stronger than for any "ordinary" object of the same radius.

However she is saying the compression itself is already increasing the pull.

So as an example, suppose our sun got replaced by a black hole of identical mass (but much smaller radius). Would this cause orbits of the planets to shrink (increased gravitational pull) or stay the same (identical gravitational pull)?

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She's cheating a bit, to make a valid point. The gravitational force exerted by an object is due, as you say, to the object's mass-energy. So, a solar mass black hole centered on the center of mass of the sun would have the same gravitational effect on earth as the sun does. But the force a test particle experiences due to the gravity of either object depends on the the square of distance of the test particle from the center of mass of the the object. The physical expanse of the object doesn't really matter, if you're outside of the object. But, with the sun, the closest you can get to the center of mass is roughly 700,000 km. Any closer than that and you're inside the sun. Once you're inside the mass radius of an object, the force you experience is due only to the proportion of the object's mass that is closer than you to the object's center of mass. So the gravitational force you experience (if you could survive being inside the sun) declines as you get closer to the center of mass, until it's zero at the center (the pressure you experience is a different matter - it steadily increases as you journey down the mass). The black hole's radius, though is only about 3km, and so you can approach to within that distance of its center of mass. At that distance from a solar mass, the gravitational force is enormous - sufficient to overcome the momentum of a photon, "drag" it back into the black hole. So, the gravitational force you can experience from an object does depend on it's size, even though the total force at astronomical and mere macro scale distances does not.

Gravitationally, nothing would change if the sun was replaced by a black hole of the same mass, at least for objects above the surface of the current sun. But being 1 kilometer above the event horizon of that black hole would be very different to being 1 km above the surface of the sun.

As the radius of a object shrinks (but with mass held constant), the _surface_ gravity increases. Remember that the pull of gravity decreases with the square of the distance away from the object. With a smaller object, you can get a lot 'closer' to all that mass, so gravity is stronger at its surface.

> If you remember Newton’s gravitational law, then, sure, a higher mass means a higher gravitational pull. But a smaller radius also means a higher gravitational pull. So, if you hold the mass fixed and compress an object into a smaller and smaller radius, then the gravitational pull gets stronger. Eventually, it becomes so strong that not even light can escape. You’ve made a black hole.

I think this is discussing the gravity on itself — or the peak gravitational pull, for nearby objects.

Compressing the Earth wouldn’t make far away objects experience it differently, but compressing Earth would increase the peak pull nearby — to the point of creating a black hole. Much more gravitational pull than anywhere on Earth experiences now. But that radius would be far, far inside of where the surface currently is.

Density increases nearby gravity by focusing mass.

Mass and energy are same thing. They effect gravitational pull the same. If you compressed the Earth the energy it takes to compress the Earth would increase the mass-energy of the Earth, and this would change the orbits of planets.

If you make an object smaller, you can get closer to it's center of mass, increasing your experience of it's gravitational force.

your experience of its gravitional force is dependant on distance.

the description of force experienced being spoken about is from the frame of a variable distance observer, not the gravitating body.

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