[MUSIC PLAYING]
Hey, I'm Ben Bowlin.
And today's question is, how
much does planet Earth actually
weigh?
Well, it'd be more
proper to ask what
is the mass of planet Earth?
And the quick answer to this
question is it's approximately,
are you ready, 6 times
10 to the 24th kilograms.
In layman's terms,
that's a lot of weight.
It's heavy.
Just in case you're wondering,
this is a reproduction.
It's not to scale.
I am not that strong.
So there's another
interesting sub-question here,
and that's how did
anybody figure this out?
It's not like the planet
Earth can just drop on a scale
each morning before
it takes a shower.
It turns out that you can
calculate the mass of something
if you know the magnitude
of its gravitational pull.
And that's because
any two masses
have a gravitational
attraction for one another.
So if you put two bowling
balls near each other,
they're going to attract
each other gravitationally.
This attraction is
extremely slight.
I mean, it's not going
to destroy the planet
to put your bowling
balls too close together.
But if your instruments
are sensitive enough,
you can measure that
gravitational attraction
that these two
bowling balls have.
And from that
measurement, you could
determine the mass
of the two objects.
The same is true for two
golf balls, for instance.
But in this case, the
attraction is even smaller
because the amount of
gravitational force
depends on the mass
of the objects.
Newton, a small
time physicist you
might have heard
of once or twice,
showed that spherical
objects make it possible
for us to create a simplifying
assumption that all
of the object's
mass is concentrated
at the center of the sphere.
He then came up with
an equation that
expresses the
gravitational attraction
that two spherical objects
have on one another.
Its force equals the
gravitational constant times
the mass of the first
object, wait for it,
times the mass of
the second object,
wait for it, over the
distance between the two
objects squared.
Assume that Earth is
one of these masses
and that a 1 kilogram
sphere is the other.
So the force between them
is 9.8 kilogram meters
per second squared.
We can calculate this force
by dropping the 1 kilogram
sphere, va-voom, and
measuring the acceleration
that the Earth's
gravitational field applies
to it, which is 9.8
meters per second squared.
The radius of the Earth
is 6,400,000 meters.
So if you plug all these
values in-- I'll wait.
Great job-- and
solve for n1, you
find that the mass of
the Earth is 6 times
10 to the 24th kilogram.
So that's how much the Earth
weighs, or more properly,
the mass.
Thank you so much for watching.
Do you have any other
questions, anecdote,
suggestions for
upcoming episodes?
I'd love to hear from you.
Please leave a comment down
here and our YouTube page,
and we will see you next time.
