3 ms·
> 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
by nyc111 4y ago
> 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.
In Newtonian doctrine, a spherical object, like earth, attracts -as if- all its mass is concentrated at its center. So, if her reasoning is correct, the earth must already be a black hole, because all its mass is supposed to be concentrated at its center.
- al2o3cr 4y agoattracts -as if- all its mass is concentrated at its center That's only 100% true for a radius _outside_ of the object. At a radius _inside_ the object, only the mass closer to the origin counts so the "effective" mass of the object drops smoothly to zero.
- sliken 4y agoActually it's something like 2 radius, unlike the earth there's no stable orbits under 1.5 or 2 radii (I forget which). Outside of 2 radii there's no differences.
- jfengel 4y agoNo, because that approximation only works when you're outside the object. Once you're inside the object, any shell of mass outside your distance from the center cancels itself out (produces zero net force). So the escape velocity from earth at its surface is well below the speed of light. And below the surface, gravity is even less. Only a black hole packs enough mass into a small enough place to get the escape velocity above the speed of light.
- _Microft 4y agoIf GP wants to read about this, the name is actually "shell theorem": https://en.wikipedia.org/wiki/Shell_theorem https://en.wikipedia.org/wiki/Shell_theorem
- marcosdumay 4y agoThat's an approximation that works at some (very small) distance from the surface. It does really not work at the center of the object.
- sliken 4y agoYes, you can compress any object small enough and you end up with a black hole. And yes as far as anything else in the solar system is concerned, if the earth was compressed into a blackhole no orbits would change. Well relativistic effects mean there's no stable orbits below 2 radii (maybe it's 1.5), so various sats would get sucked in. However just because that's true, doesn't imply the earth is a blackhole, just that the orbits in the solar system wouldn't change. Similarly if the sun collapsed into a blackhole the earth's orbit wouldn't change, but it would get much colder.