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Current time:0:00Total duration:8:13

Why gravity gets so strong near dense objects

Video transcript

in the video on black hole several people asked what is actually a pretty good question which is if if the mass of say a black hole is only two or three solar masses why is the gravity so strong obviously the Sun's gravity isn't so strong that it keeps light from escaping so why would something or even a star that's two or three solar masses it's gravity isn't so strong that it keeps light from escaping why would a black hole who has that has the same mass why would that keep light from escaping and to understand that let's just think a little bit about and well I'll just do a Newtonian Newtonian classical physics right here I won't get into the whole general relativity of things and this really will just give us the intuition of why a smaller denser thing of the same mass can exert a stronger gravitational pull so let's imagine so let's take two examples let's say I have some star here let's say I have some star here that has a mass let's just call that mass m1 and let's say that it's radius let's say that it's radius let's just call this R and let's say that I have some other mass some other mass right at the surface of this star it's somehow able to survive those surface temperatures and this smash over here has a mass of has a mass of m2 the universal law of gravitation the universal law of gravitation tells us that the force between these two masses the force between these two masses is going to be equal to the gravitational constant times the product of the masses so m1 times m2 times m2 all of that over the square of the distance over the square of the distance R squared now let me be very clear you might say wait this magenta mass right here is touching this larger mass isn't the distance zero and you have to be very careful this is the distance between their center of masses so the center of mass of this large mass over here is are away from this mass that's on the surface now with that said let's take another example let's say that this large massive star or whatever it might be eventually condenses into something a thousand times smaller so let me make it let me draw it like this and obviously I'm not drawing it to scale so let's say we have another case like this and I'm not drawing it to scale so this object maybe it's the same object or maybe it's a different object that has the exact same mass as this larger object but now it has a much smaller radius it now has a much smaller radius so that radius now the radius is one over let's just say it's one thousand let's say it's one thousand of this radius over here so it's 1 maybe I'll just call it R over a thousand so if this was if this had a million kilometer radius so that would make it roughly about twice the radius of the Sun if this was a million kilometer radius right over here this would be a thousand kilometer radius so maybe we're talking we're talking about something that's approaching a neutron star but we don't have to think about what it actually is let's just think about the thought experiment here so let's say I have this thing over here and let's say I have something on the surface of this so let's say I have that same mass it's on the surface of this thing so this is m2 right over here so what is going to be the force between these two masses how how strong are they going to want to how what's the force pulling them together so it's just that the universal law of gravitation again the force this is called this force 1 and let's call this force 2 once again it's going to be the gravitational constant times the product of their masses so the Big M one times the smaller mass M 2 all of that over this distance squared this radius squared remember it's the distance to the center of masses this centre of mass here we're considering M 2 to kind of be just a point mass right over there so what's the radius squared it's going to be R over 1000 r over 1,000 squared or if we simplify this what will this be this is the same thing is we'll get this is the same thing and I'll just I'll just write it in one color just because it takes less time gravitational constant m1 m2 over R squared over 1,000 squared or over 1 million over 1 million that's just a thousand squared or we can multiply the numerator and the denominator by a million and this is going to be equal to 1 million 1 million let me make I'm going to write out 1 million let me scroll to the right a little bit times the gravitational constant times M 1 M 2 all of that over R squared now what is this thing right over here what is this thing over here that's the same thing as this F 1 so this is going to be 1 million 1 million times F 1 so even though the masses involved are the same this yellow object right here is the same mass as this larger object over here it's able to exert a million times the gravitational force on this point mass and actually vice versa they're both being attracted they're both exerting this on each other and the reality is is because this thing is smaller because this M one on the right here this one I'm coloring in because this one is smaller and denser this particle is able to get closer to its center of mass now you might be saying okay well I can by that that you know this just comes straight from the universal law of gravitation but wouldn't something closer to this center of mass experience that same thing if this was a star if this is a star wouldn't photons that are one thought that are over here wouldn't this experience the same force if this distance right here if this distance right here is R over a thousand wouldn't some photon here or add them here or molecule or whatever it's over here wouldn't that experience the same force this million times the force is this thing and you got to remember all of a sudden when this thing is inside of this larger mass what's happening it no longer has the entire the entire mass is no longer pulling on it in that in that direction it's no longer pulling it in that inward direction you now have all of this mass over here you now have all of this mass over here let me think of the best way that's doing it so you could think of it all of this mass over here it's pulling it in an outward direction is pulling it in an outward direction it's not telling all that with that mass out there is doing since that mass itself is building is being pulled inward that mass itself is being pulled inward it is pushing down on this it is exerting pressure on that point but the actual gravitational force that that point is experience is actually going to be less it's actually going to be mitigated by the fact that there's so that there's so much mass over here that there's so much mass over here pulling in the other direction and so you can imagine if you're in the center of a really massive object if you are in the center of a really massive us so that's a really massive object if you're in the center there would be no net gravitational force being pulled on you because you're at its center of mass the rest of the mass is outward so at every point it will be it will be pulling you out word and so that's why is you if you were to enter the core of a star if you were to get a lot closer to its center of mass it's not going to be pulling on you with this type of force and the only way you can get these type of forces is if the entire mass if the entire mass is contained in a very dense region in a very small region and that's why a black hole is able to exert such strong gravity that not even light can escape hopefully that clarifies things a little bit