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We're now going to learn a
little bit about gravity.

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And just so you know, gravity is
something that, especially

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in introductory physics or
even reasonably advanced

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physics, we can learn how to
calculate it, we can learn how

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to realize what are the
important variables in it, but

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it's something that's really
not well understood.

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Even once you learn general
relativity, if you do get

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there, I have to say, you can
kind of say, oh, well, it's

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the warping of space time and
all of this, but it's hard to

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get an intuition of why two
objects, just because they

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have this thing called
mass, they are

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attracted to each other.

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It's really, at least to me,
a little bit mystical.

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But with that said, let's learn
to deal with gravity.

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And we'll do that learning
Newton's Law of Gravity, and

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this works for most purposes.

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So Newton's Law of Gravity says
that the force between

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two masses, and that's the
gravitational force, is equal

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to the gravitational constant G
times the mass of the first

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object times the mass of the
second object divided by the

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distance between the two
objects squared.

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So that's simple enough.

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So let's play around with this,
and see if we can get

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some results that look
reasonably familiar to us.

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So let's use this formula
to figure out what the

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acceleration, the gravitational
acceleration, is

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at the surface of the Earth.

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So let's draw the Earth,
just so we know what

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we're talking about.

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So that's my Earth.

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And let's say we want to figure
out the gravitational

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acceleration on Sal.

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That's me.

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And so how do we apply this
equation to figure out how

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much I'm accelerating down
towards the center of Earth or

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the Earth's center of mass?

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The force is equal to-- so
what's this big G thing?

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The G is the universal
gravitational constant.

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Although, as far as I know, and
I'm not an expert on this,

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I actually think its measurement
can change.

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It's not truly, truly a
constant, or I guess when on

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different scales, it can be
a little bit different.

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But for our purposes, it is a
constant, and the constant in

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most physics classes, is this:
6.67 times 10 to the negative

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11th meters cubed per kilogram
seconds squared.

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I know these units are crazy,
but all you have to realize is

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these are just the units needed,
that when you multiply

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it times a mass and a mass
divided by a distance squared,

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you get Newtons, or kilogram
meters per second squared.

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So we won't worry so much about
the units right now.

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Just realize that you're going
to have to work with meters in

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kilograms seconds.

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So let's just write
that number down.

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I'll change colors to
keep it interesting.

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6.67 times 10 to the negative
11th, and we want to know the

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acceleration on Sal, so
m1 is the mass of Sal.

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And I don't feel like revealing
my mass in this

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video, so I'll just leave
it as a variable.

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And then what's the mass 2?

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It's the mass of Earth.

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And I wrote that here.

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I looked it up on Wikipedia.

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This is the mass of Earth.

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So I multiply it times the
mass of Earth, times 5.97

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times 10 to the 24th kilograms--
weighs a little

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bit, not weighs, is a little
bit more massive than Sal--

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divided by the distance
squared.

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Now, you might say, well, what's
the distance between

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someone standing on the
Earth and the Earth?

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Well, it's zero because they're
touching the Earth.

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But it's important to realize
that the distance between the

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two objects, especially when
we're talking about the

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universal law of gravitation, is
the distance between their

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center of masses.

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For all general purposes, my
center of mass, maybe it's

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like three feet above
the ground, because

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I'm not that tall.

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It's probably a little bit lower
than that, actually.

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Anyway, my center of mass might
be three feet above the

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ground, and where's Earth's
center of mass?

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Well, it's at the center of
Earth, so we have to know the

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radius of Earth, right?

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So the radius of Earth is--
I also looked it up on

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Wikipedia-- 6,371 kilometers.

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How many meters is that?

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It's 6 million meters, right?

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And then, you know, the extra
meter to get to my center of

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mass, we can ignore for now,
because it would be .001, so

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we'll ignore that for now.

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So it's 6-- and soon.

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I'll write it in scientific
notation since everything else

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is in scientific notation--
6.371 times 10 to the sixth

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meters, right?

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6,000 kilometers is
6 million meters.

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So let's write that down.

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So the distance is going
to be 6.37 times 10

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to the sixth meters.

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We have to square that.

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Remember, it's distance
squared.

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So let's see if we can simplify
this a little bit.

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Let's just multiply those top
numbers first. Force is equal

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to-- let's bring the
variable out.

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Mass of Sal times-- let's
do this top part.

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So we have 6.67 times 5.97
is equal to 39.82.

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And I just multiplied this times
this, so now I have to

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multiply the 10's.

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So 10 to the negative 11th times
10 to the negative 24th.

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We can just add the exponents.

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They have the same base.

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So what's 24 minus 11?

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It's 10 to the 13th, right?

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And then what does the
denominator look like?

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It's going to be the 6.37
squared times 10

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to the sixth squared.

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So it's going to be-- whatever
this is is going to be like 37

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or something-- times-- what's
10 to the sixth squared?

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It's 10 to the 12th, right?

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10 to the 12th.

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So let's figure out what
6.37 squared is.

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This little calculator I have
doesn't have squared, so I

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have to-- so it's 40.58.

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And so simplifying it, the force
is equal to the mass of

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Sal times-- let's divide, 39.82
divided by 40.58 is

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equal to 9.81.

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That's just this divided
by this.

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And then 10 to the 13th divided
by 10 to the 12th.

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Actually no, this isn't 9.81.

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Sorry, it's 0.981.

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0.981, and then 10 to the 13th
divided by 10 to the 12th is

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just 10, right?

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10 to the first, times 10,
so what's 0.981 times 10?

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Well, the force is equal to 9.81
times the mass of Sal.

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And where does this get us?

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How can we figure out the
acceleration right now?

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Well, force is just mass times
acceleration, right?

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So that's also going to just be
equal to the acceleration

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of gravity-- that's supposed to
be a small g there-- times

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the mass of Sal, right?

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So we know the gravitational
force is 9.81 times the mass

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of Sal, and we also know that
that's the same thing as the

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acceleration of gravity
times the mass of Sal.

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We can divide both sides by the
mass of Sal, and we have

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the acceleration of gravity.

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And if we had used the units the
whole way, you would have

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seen that it is kilograms meters
per second squared.

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And we have just shown that, at
least based on the numbers

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that they've given in Wikipedia,
the acceleration of

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gravity on the surface of the
Earth is almost exactly what

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we've been using in all the
projectile motion problems.

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It's 9.8 meters per
second squared.

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That's exciting.

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So let's do another quick
problem with gravity, because

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I've got two minutes.

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Let's say there's another
planet called the

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planet Small Earth.

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And let's say the radius of
Small Earth is equal to 1/2

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the radius of Earth and the mass
of Small Earth is equal

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to 1/2 the mass of Earth.

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So what's the pull of gravity
on any object, say same

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object, on this?

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How much smaller would
it be on this planet?

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Well, actually let me save
that to the next video,

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because I hate being rushed.

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So I'll see you

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