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# 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 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-- its gravity isn't so strong that
it keeps light from escaping. Why would a black hole that has
the same mass, why would that keep light from escaping? And to understand
that, I'll just do 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 take two examples. Let's say I have some star
here that has a mass m1. And let's say that its radius,
let's just call this r. And let's say that I have
some other mass right at the surface of
the star, somehow able to survive those
surface temperatures. And this mass over
here has a mass of m2. The universal law of
gravitation tells us that 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, all of that 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 0? 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 r 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
1,000 times smaller. So 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. Now the radius is 1/1,000
of this radius over here. So maybe I'll just
call it r/1,000. So 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
1,000 kilometer radius. So maybe 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 that'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 strong are
they going to want to-- What's the force
pulling them together? So let's just do the universal
law of gravitation again. Let's just call this force one,
and let's call this force two. Once again, it's going to be
the gravitational constant times the product of their masses. So the big m1 times
the smaller mass, m2, all of that over this distance
squared, this radius squared. Remember, it's the distance
to the center of masses. This center of mass here,
we're considering m2 to kind of be just a point
mass right over there. So what's the radius squared? It's going to be
r/1,000 squared. Or if we simplify this
what will this be? This is the same thing. And 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. That's just 1,000 squared. Or we can multiply the
numerator and the denominator by 1 million, and this is going
to be equal to 1 million-- I'm going to write
it out, 1 million. Let me scroll to the
right a little bit-- times the gravitational
constant, times m1 m2, all of that over r squared. Now, what is this
thing right over here? That's the same
thing as this F1. So this is going to
be 1 million times F1. 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, because
this thing is smaller, because this m1 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,
OK, well, I can buy that. 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, wouldn't
photons that are over here, wouldn't this experience
the same force? If this distance right here is
r/1,000 wouldn't some photon here, or atom here, or molecule,
or whatever it's over here, wouldn't that experience
the same force, this million times the
force as this thing? And you've got to
remember, all of a sudden when this thing is inside
of this larger mass, what's happening? The entire mass is no
longer pulling on it in that direction. It's no longer pulling it
in that inward direction. You now have all of
this mass over here. Let me think of the best
way that's doing it. So you can think of it
all of this mass over here is pulling it in an
outward direction. It's not telling. What that mass out
there is doing, since 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 experiencing
is actually going to be less. It's actually going to
be mitigated by the fact that there's so
much mass over here pulling in the other direction. And so you could
imagine if you were in the center of a
really massive object-- so that's a really
massive object. If you were 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 pulling you outward. And so that's why 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 types of forces is 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.