Gravity. It keeps us on Earth, keeps the galaxy
together, and is found to be strongest at
a black hole.
Black holes are usually what is left at the
end of the life of a massive star, a star
that has a mass greater than about 2.7 solar
masses.
This happens because the star has run out
of elements that it can fuse together.
Stars carry on fusing hydrogen atoms to helium,
lithium, beryllium and on and on... until
it gets to iron.
When most of the fuel has been made into iron,
fusion stops and the radiation pressure disappears.
This pressure is what keeps the star stable
for most of it's main sequence.
For example, our suns gravity is trying to
attract all it's mass into it's centre, and
it also has radiation pressure from the fusion
that pushes outwards onto the star.
When these two forces are balanced, the star
does not change size and remains stable.
Once the radiation pressure goes, the gravity
of a massive star is so strong that it overcomes
all kinds of degeneracy pressures in order
to collapse into what we call a singularity.
A singularity is a point of infinite density
with a gravitational pull so strong that even
light cannot escape it's pull.
Does this only apply to large masses?
It is actually a misconception that only giant
stars can become black holes.
In fact, you can make a black hole out of
our sun, the Earth, or even a human...
You just need to concentrate that matter into
a small enough volume, and this is the bit
that a big star can easily do with it's gravity.
To demonstrate this, here's a question.
I'm standing on the Earth, at a distance of
about 6371 km away from the centre of the
Earth.
At the surface, I experience roughly 9.8 m/s
squared of acceleration due to gravity.
Now I'm 6371 km above the ground, in space.
So now I'm double the distance away from the
centre.
How much acceleration do I experience now?
I'll give you a moment to think.
The correct answer is 4 times less.
This is because Newton's law of gravitation
shows that the gravitational field strength
is inversely proportional to r^2, with r being
the separation between two objects.
Here is a graph demonstrating this principle.
As you can see, at 2 times the radius of the
earth the gravitational field strength has
dropped by 4 times as much.
And when the distance to the centre of the
Earth gets closer and closer to 0, the gravitational
field strength increases at a massive rate.
So does this mean that at the centre of the
earth, we will experience as much gravity
as a black hole and get instantly spaghettified?
The answer is no, because Newtons equation
assumes that the masses you are calculating
with are point masses, meaning that the mass
is at a very tiny singularity; a bit like
a black hole.
The equation works well when you're outside an object,
such as when we are outside the Earth.
However when you go deeper into the earth,
there is mass all around you.
When you finally reach the centre, the mass
will be tugging you from all directions equally,
so there is no net force and this means that
at the centre you can actually just float
around like you would in space.
In order to get a black hole, we need to make
the Earth more like a point mass so that we
can get close enough to feel very strong gravity.
As you can see from the graph we showed before,
the field strength has an asymptote at the
y axis, this shows that if you get infinitesimally
closer to the point mass, you get infinitely
larger values for the field strength, no matter
what your mass was.
So if you can make a mass get down to a special
size where even light cannot escape it's gravitational
pull, we get a black hole.
This size is a sphere, the radius of which
is known as the Schwarzschild radius
You can derive the equation for the schwarzchild
radius by using the speed of light as v in
the equation for escape velocity.
Once a mass is smaller than the Schwarzschild
radius, the black hole formed will have an
event horizon at that radius from the centre
of the black hole.
The event horizon is the distance at which
the escape velocity is the speed of light.
If you're closer to the black hole than this
distance, you can never escape it.
But if you're further away than that distance,
then there is still a glimmer of hope that
you can escape it's gravitational pull.
You just need to be going fast enough.
Heres a fun fact.
The Schwarzschild radius of the earth is 8.87
millimetres.
Yep, thats right. Less than a centimetre.
If you can manage to squeeze the earth into
that size, then you've succeeded in making
your very own black hole.
The last misconception that we are covering
today is that black holes suck up matter like
a vaccuum cleaner, and eventually will end
up swallowing the whole universe.
This is not true, as a black hole simply follows
newtons law of gravitation.
If you get far enough away from a black hole,
the force you feel towards it will be, for
all practical purposes, 0.
There's a supermassive black hole at the centre
of our galaxy, but because all the stars are
at great distances away from it, they can
orbit the centre without any danger of falling
in.
Instead of a vacuum cleaner sucking things
up, think of a black hole being a bit like
this cat.
If you're far away from it, it won't pose
a threat at all. But if a sock comes near
it, it pulls it in. Never to be seen again.
Today we learned about newtons law of gravitation
and what a black hole is. We cleared up some
misconceptions and discussed the Schwarzschild
radius.
But what are black holes truly like?
And will a black hole made from the earth
exist forever?
What does Einstein's theory of general relativity
have to do with it?
That's a tale for another time.
