The Cosmic Classroom - Inverse Square Laws

Hi there. Welcome back to the Cosmic Classroom.
We'll now talk about the Inverse Square Law in
Physics, which is important under many circumstances.
For example, if you look at this, this sprinkler here. I
have a picture of a sprinkler. If the sprinkler is giving off certain
amount of water at each second. If you are close to the sprinkler
you'll get really wet. Many drops will reach you. As it gets farther
and farther away from the sprinkler, the water gets spread around and fewer
and fewer drops will reach you. You get less wet as you get further.
The Inverse Square Law tells you how much less wet do you get.
Is it a little bit less wet? Is it very much less wet?
So, the Inverse Square Law is important for luminousity.
If there is a star right there in the center of this picture
emitting a certain amount of energy. A certain amount of light every second.
If a person observes very close to that star it will see it
as something very bright. A lot of photons will
be reaching that person that's close to that star.
As a person moves further and further from the star,
the same amount of light gets distributed over a larger area.
The light gets diluted. It's less bright.
So, in the outer most shell there's less photons, less
light arriving in each one of those squares, than in this shell
and in this shell. You can try to see it yourself
by getting a balloon. Get a balloon. Draw a bunch of little things in there
and if you draw it when they are small you will see they are very close to
one and other. Because they have a small area to fit into it.
Now if you expand the balloon. If you blow it, you give more space
for those, for whatever drawing you made here and they get more diluted.
Just like luminousity does. Just like the water in the sprinkler does.
There's less of it further away. So, the Inverse Square Law, for luminousity
says that the brightness "b" depends on the luminousity, the amount of
light that the object is really emitting, per...
so the luminousity is the energy per unit of time,
divided by the area of this sphere. If the sphere is small,
the object will be really bright. If the sphere is larger
the brightness will decrease according to the square of
the size of the object. So the apparent brightness
decreases as 1 over R square. That's why it is called
the Inverse Square Law. OK? So if the distance doubles,
the brightness is decreased by one forth, because it's one
over two squared. If the distance halves
the brightness increases four times, because, because point five square...
one over that will give you four. Now the Inverse Square Law happens
in many other laws in Physics. So I told, I just showed you
brightness and luminousity, the relationship between brightness
and luminousity and how far away we are from the object that's emitting the
luminousity, but look, this is similar to what we see for gravity also.
Gravity is also Inverse Square Law. The force of attraction gets smaller
with the inverse of the square of the distance.
The electro-static force is also an Inverse Square Law.
These are all Inverse Square Laws, so the Inverse Square Law
is really powerful in Astronomy in many different ways.
So, it's just a way of quantifying how much dimmer an object becomes
as it moves further and further away from the source that's illuminating it.
I hope that helps. See you next time.