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Newton's Law of Universal Gravitation

this we are going to talk about Newton's

law of universal gravitation now as the

legend goes Isaac Newton saw an Apple

fall from a tree and it's thought that

he began thinking does that same force

that caused the Apple to fall towards or

be attracted to the earth cause the moon

to be attracted to the earth and stay in

orbit so this was what he was thinking

was and he investigated this and he

found two things first of all he found

that the force of gravity was

proportional to the distance between the

two objects and more specifically he

said that the force of gravity is

proportional to the inverse square of

the distance between the object this is

what R represents the distance between

the Centers of the two objects if you're

not familiar with this symbol that means

proportional to in other words they will

change at the same rate they're not

equal to each other this change at the

same rate the other thing that he found

is that the force of gravity is also

proportional to the size of the objects

and or in other words their mass so we

have the mass of the first object times

the mass of the second object now these

two things go together to form this

equation right here so we have our

masses on top over the distance squared

and we had to add this thing in here

it's called the universal gravitational

constant now Newton didn't discover this

number right here but this is what that

constant is equal to u so G this capital

G is just substitute in this number with

these units Newton didn't discover this

this was discovered much later in the

late 1700s by a scientist named Henry

Cavendish now we won't get into his

experiment but basically he was able to

determine pretty accurately the force of

gravity between two objects of known

mass and knew the distance between them

and he was able to solve for this value

and he determined it to be this right

here so we need that to solve any

question involving gravitation between

two objects so here's an example of a

question that's going to involve solving

for the gravitational force

we'll read this one and then we'll solve

this one together says determine the

force of gravitational attraction

between a 74 kilogram boy sitting 1.45

metres away from a sixty seven point

five kilogram girl basically all we have

to do here is just plug in the numbers

into the equation so here's the equation

we're going to use and now we can simply

plug in all the values so there's the

value for G and then we can plug in the

two different masses and then finally

the distance between the two masses and

now we can plug everything into our

calculator and we get a force of

gravitational attraction of one point

five eight times ten to the negative

seven Newtons so since it's a force it's

going to be a Newton and if you don't

believe me you can see where these units

come into play for our gravitational

constant here we have two kilograms here

which is going to cancel those two

kilograms there we have a meter that's

squared right here which is going to

cancel that meter per squared and we're

left with units of Newton's so that's

why the units look the way they do with

that constant there and so there's our

final answer and that is the law of

universal gravitation