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### Course: Cosmology and astronomy > Unit 2

Lesson 4: Cepheid variables# Why gravity gets so strong near dense objects

Why Gravity Gets So Strong Near Dense Objects. Created by Sal Khan.

## Want to join the conversation?

- If you were in the middle of the earth (theoretically), would you be pulled apart by the gravity in every direction? (serious answers please)(69 votes)
- Nope. If you were in the center of the earth, you would have only a part of the earth's mass in any given direction, so the pull of gravity in any direction would be less than what we experience on the surface, since here
*all*of earth's mass is laying in just one direction from us. And since the stronger gravity we experience here isn't anough to cause us any damage, neither would the gravity in the center.

In fact, I'd figure (I'm no expert though) that the roughly equal amount of gravity coming from every direction in the center would kinda cancel each other out, and if there was a cavity in the very middle of the earth you could just sort of float around in it. Just guessing about this though.(99 votes)

- so then if it was possible to put a tube through the exact center of the earth and you jump in it, would you be pulled back and fourth and eventually stop in the center, and while in the very center of the earth, still in the tube would you float, because the earth is pulling evenly in all directions?(39 votes)
- Theoretically yes.(38 votes)

- If you were just inside the event horizon of a black hole would the gravity pulling you in be the same as you being twice as close to the black hole?(13 votes)
- The closer you get, the stronger the gravitational pull is because you are getting closer to the big massive object. That means the bigger the black hole, the stronger the pull is.(2 votes)

- what is the oldest star that has been found?(6 votes)
- Hey, how can HD 140283 can be 14.5 billion years if the age of the Universe is 13.7 billion years? That's what I never understood.(5 votes)

- The earth revolves round the sun because the sun attracts the earth. The sun also attracts the moon and this force is about twice as large as the attraction of the earth on the moon. Why does the moon not revolve round the sun ?(6 votes)
- Because it doesn't want Earth to be lonely.(5 votes)

- If the net gravitational force gets smaller as you get nearer to the center of the mass, does that work with a smaller star too? And would it work with the Earth, like the closer you get to the center of the Earth, the less gravitational force, so you wouldn't be crushed? Or do you get crushed because of the pressure? Thanks!(3 votes)
- Gravity operates in the same manner for all objects, including the Earth and stars. If you could somehow travel to the center of the Earth, you'd get crushed by the pressure, not gravity.(8 votes)

- What does Relativistic mass mean?(4 votes)
- When an object accelerated to near the speed of light, its mass changes, increasing as the object gets closer and closer to the speed of light. Taking this effect into account gives you the relativistic mass, which at high speeds becomes very, very different from the rest mass.(5 votes)

- Most of the videos on cosmology and Astronomy, are very much informative and descriptive about the science behind the infinite universe.... but how can I understand exactly 'Gravity' where does it come from.. and how is created? what mechanism make it be what it is from an atomic level if in fact that is how is originates?(4 votes)
- In fact, one of the bigger questions in science right now is what powers gravity. Gravity just seems to happen, while the 3 other fundamental forces have justifications with it.(4 votes)

- Well if the black hole is just a point in three-dimensional space then as per the video, shouldn't "r" be equal to zero, making the gravitational force equal to infinity?

This seems paradoxical to me. Another result would be that all light and matter in the universe would be sucked into the black hole "instantaneously"and would therefore violate the universal speed limit. Please help.

Also, how exactly is the gravity proposed by general relativity different from Newtonian gravity.(4 votes)- That is why we refer to the black hole as a singularity. Our current physical models break down as some value approaches infinity. We really can't say what happens to matter in the black hole beyond the event horizon.(3 votes)

- Am I a dense object that exerts strong gravitational force on things like gas molecules or other not very dense molecules? Does one rock in my yard attract small dense objects to it more than others? Do all objects have gravitational forces, or only planet cores are dense enough to create G force?(2 votes)
- Everything exerts a gravitational force, the question is how strong it is. So yes, you would exert a gravitational force on everything, but it's extremely weak.

To understand why, we can use Newton's law of universal gravitation. It states that. G is the gravitational constant, 6.67 * 10^-11, M1 and M2 are the masses of both objects, and r is the distance between the objects.`F = (G * M1 * M2) / r ^ 2`

The gravitational force between two people weighing 70 kg each and standing a meter away can then be calculated asThis comes out to be about 3.26957e-7 newtons, which is not a lot.`F = (6.67 * 10^-11 * 70 * 70) / 1`

.

The force strength is related to distance from the object, and mass (high distance or low mass makes the force weaker.) Density affects gravitational force when you consider surface gravity. Imagine two planets, both have the same mass. One planet is much more dense than the other one though (so the radius is also different.) The denser planet will have higher surface gravity because you are closer to the center, and vice versa for the lower density planet.

Lets say you were 10,000 km from the center of each planet though. Here, the gravitational force would be the same, because the mass and distance are equivalent.(5 votes)

## 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.