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PH 121 13.1-13.3

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Richard Datwyler

on 16 July 2018

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Transcript of PH 121 13.1-13.3

Newton's theory of gravity
This chapter starts with a bit of history.
I see no harm in this, we can learn some
of the steps of mankind through the ages.
Man has always looked to the heavens in
wonder.
This is most likely because of religion.
We know that God is above us, in the heavens
so thus we must look up.
Just think of Abraham in the Pearl of Great Price.
There is much to be said about celestial physics
and religion.
We won't go into that here, but rather take a
secular study.
Your text sites the Babylonians, as well as the
builders of Stonehenge.
Then the Greeks and Egyptians.
Each having models of planets and stars motion
Copernicus 1543 published a work setting
the sun as the center of the solar system.

(interesting to note that the Nephites had it down
1500 years before this)

Helaman12:15 And thus, according to his word the earth goeth back, and it appeareth unto man that the sun standeth still; yea, and behold, this is so; for surely it is the earth that moveth and not the sun.
It was about 100 more years before Copernicus'
idea was fully accepted.
It took the work of Kepler, and Galileo's telescope.
Kepler (whom Newton sited for his work)
developed 3 laws.
1. Planets move in elliptical orbits with the sun as one of the foci.
2. Equal areas in equal time
3. Relation between Period and radius
Newton
Poor farmer, went to school, plague broke out
went home after graduation.
Here he developed much.
One notion was that the earth attracted objects
(like apples) and that if this is true, why not big
objects, like the moon. And in addition, why not
the same type of force attracting the earth to the
sun.
Hence a universal force in the heavens.
He said the moon must be in free-fall around the earth, (I've drawn this picture before.
but it comes out to this equation.




Using circumference and period:




Combining gives the value of g at the moon
And we say 'that's neat' but what.
The next step was measuring
g at the surface of earth
Not to hard 9.8
And then comparing them.
Again we say 'that's neat'
but what.

The truly remarkable thing was to note
this with the ratio of the distances to these
locations.
namely distance to moon, and radius of earth.
Now we note that 3600 is about 60.2 squared.
as did Newton. He makes 3 steps of reasoning
1. If g on earth surface is 9.8
2. If force of gravity and g decrease inversely with square of distance from center of earth
3. Then g will have exact value needed to cause moon to orbit in 27.3 days.

And it does. 'pretty nearly'
Newton's law of gravity
This gave way to a law of gravity.
(or at least that is what he called it)
1. Inversely proportional to square of distance between objects
2. Proportional to product of masses




With G as a universal constant.
He said, "I deduced that the forces which keep the planets in their orbs must be reciprocally as the squares of their distances from the centers about which they revolve; and thereby compared the force requisite to keep the Moon in her orb with the force of gravity at the surface of the Earth; and found them answer pretty nearly.'
Once this Gravitational constant is known
one can calculate the force of gravity
between any two masses at any distance.

Interesting, this force of gravity is always there
it doesn't go away, it just gets super small.

This law of gravity works for Cavendish balance
as well as solar systems, and galaxies in motion.
Equivalence
Having just finished the chapter on
moment of inertia
we note that F=ma we call mass
a description of the inertia of an object
or how an object resists motion from an
imposed force.

This M in (F=ma) is an inertial mass.
The mass in Newton's law of gravity
is not inertia.
You'll note that F=ma has no gravity in it.
And that force of gravity equation has no
acceleration.
Manipulating the equation solves for this
gravitational mass.
The principle of equivalence says that inertial mass is equivalent to gravitational mass.
After much trial there has been nothing to prove otherwise.
But why, how does motion have anything to do with attraction?
Well, you'll have to get into General relativity to get that answered
which I don't think is taught here.
Sum up to Theory of Gravity
1 A force law for gravity is given
2 Principle of equivalence
3 And Newton's 3 laws work in celestial bodies too.
"How come orbits are always elliptical?"
"How did Copernicus discover that the Sun didn't revolve around the Earth?"
"Can we go over stop and think 13.1 and 13.2?"
"Didn't fully understand Kepler's laws"
"why, if the satellite is moving at a constant speed is it's acceleration not zero?"
Estimate the force of attraction between a 50 kg woman and a 70 kg man sitting 1.0 m apart.
2.3 x 10^-7 N
Calculate the force of the sun on the moon, and the force of the earth on the moon.

re = 3.84 x 10^8 m
rs= 1.5 x 10^11 m
mm=7.36 x 10^22 kg
me =5.98 x 10^24 kg
ms = 1.99 x 10^30 kg
19.9 x 10^19 N
43.4 x 10^19 N
The space shuttle orbits 300 km above the surface of the earth. What is the gravitational force on a 1.0 kg sphere inside the space shuttle?
(re=6.37 x 10^6 m)
8.97 N
Full transcript