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In the video on black holes

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several people asked what is actually a pretty good question, which is: If the mass of

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say a black hole is only 2 or 3 solar masses,

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why is the gravity so strong? Obviously the sun's gravity isn't so strong

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that it keeps light from escaping. So, why would something or even a star that is 2 or 3 solar masses,

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it's gravity isn't so strong that it keeps light from escaping

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why would a black hole that has the same mass keep light from escaping?

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And to understand that, let's just think a little bit about it.

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I'll just do a Newtonian

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classical physics right here.

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I wont get into the whole general relativity and things.

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This will really just give us the intuition of why a smaller, denser thing with the same mass

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can exert a stronger gravitational pull.

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So let's imagine-- so let's take two examples

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Let's say I have some star here

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that has a mass-- let's just call that mass m1

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and let's say that its radius,

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lets just call this "r"

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and lets say that I have

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some other mass right at the surface

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of this star. Somehow able to survive those surface temperatures

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and this mass over here

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has a mass of m2.

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The Universal Law of Gravitation tells us that the force between these two

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masses is going to be equal to the gravitational constant

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times the product of the masses.

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So m1 times m2

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all of that over the square of the distance

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"r" squared.

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Now, let me be very clear.You might say: Wait, this magenta mass

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right here is touching this larger mass.

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Isn't the distance 0?

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You need to be very careful!

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This is the distance between their center of masses.

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So the center of mass of this large mass over here is "r" away from this mass on the surface

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Now, with that said, let's take another example.

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Let's say this large massive star or whatever it might be, eventually condenses

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into something a thousand times smaller.

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So let me draw it like this.Obviosly I'm not drawing it to scale.

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So let's say we have another case like this (I'm not drawing it to scale)

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So this object, maybe it's the same object or maybe it's a different object,

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but it has the exactly same mass as larger object, but now has a much smaller radius.

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So that radius now is 1/1000.Let's say it's 1/1000 of this radius over here.

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So it's r/1000.If this had a million kilometer radius,

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so that will make it roughly about twice the radius of the sun.

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And this was a million kilometer radius right over here.

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This would be a thousand kilometer radius,

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so maybe we are talking about something that is approaching a neutron star.

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But we don't have to think about what it actually is,just think about the thought experiment here.

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So,let's say I have this thing over here and let's say I have something

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on the surface of this.So let's say I have the same mass that's on the surface of this thing.

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So, this is m2 right over here.

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So, what's going to be the force between these 2 masses?

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What's the force pulling them together?So that's the Universal Law of Gravitation again.

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The force, let's just call this F1(force 1) and let's just call this F2(force 2).

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Once again, it's going to be the gravitation constant, times the product of the masses

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So, the big m1, times the smaller mass m2, all of that over this distance squared.

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This radius squared.

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Remember, it's the distance to the center of masses.

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This center of mass here we are considering m2 to the kind of view

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just to point match right over there.

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So what's the radius squared?

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It's going to be "r" over 1 thousand squared ( r/(1000^2)).

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Or, if we simplify this,what would this be?

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This is the same thing as the gravitational constant times m1 times m2

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over "r" squared over 1 thousand squared or over 1 million.That's just a thousand squared.

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Or, we can multiply the numerator and denominator by 1 million

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and this is going to be equal to 1 million times the gravitational constant

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times m1 times m2, all of that over "r" squared.

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Now, what's this things right over here?

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That's the same thing as the F1.So this is going to be 1 million times F1.

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So, even though the masses involved are the same, this yellow object right here

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is the same mass as this larger object over here.

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It's able to exert a million times the gravitational force on this point of mass

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So they are both being attracted.They are both exerting this on each other.

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And the reality is that because this thing is smaller,because this m1 on the right here,

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this one I'm coloring in,because this one is smaller and denser, this particle is able to

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get closer to its center of mass.

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Now you might be saying: Ok,well..I can buy that.That you know, this just come straight

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from the universal law of gravitation.But what if something closer to this center of mass

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experience the same thing?

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If this is a star, wouldn't photons that are over here wouldn't this experience the same force

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If this distance right here is "r" over a thousand(r/1000), wouldn't some photon here or

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atom here or molecul or whatever it's over here, wouldn't that experience the same force?

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This milllion times the force of this thing and you got to remember,

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all of the sudden when this thing is inside of this larger mass, what's happening?

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The entire mass is no longer pulling on it in that direction.It's no longer pulling it in that inward direction.

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You now have all of this mass over here is pulling it in outward direction.

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All that mass is doing is that mass itself is being pulled inword.

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It is pushing down on this.It is exerting pressure on that point.

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But, the actual gravitational force that that point is experiencing is actually going to be less, it's actually going to me mitigated

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by the fact that there are so much mass over here pulling in the other direction.

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So, you can imagine that if you are in the center of a really massive object,

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there will be no gravitational force being pulled on you,because you are at the center of the mass

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The rest of the mass is outward,so at every point it will be pulling you outward.

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So, that's why you as you enter the core of the star,

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you will get a lot closer to the center of the mass.

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It's not goint to be pulling on you with this type of force and the only way you can get this

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type of forces is if the entire mass is contained in a very dense region,

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in a very small region.

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And that's why a black hole is able to exert such strong gravity that

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not even light can escape.

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Hopefully that clarifies things a little bit.