Newton and the Spring 2007 His 3464. Did Newton discover gravity? What, then did he do? And what did...
-
Upload
winifred-mckinney -
Category
Documents
-
view
221 -
download
2
Transcript of Newton and the Spring 2007 His 3464. Did Newton discover gravity? What, then did he do? And what did...
![Page 1: Newton and the Spring 2007 His 3464. Did Newton discover gravity? What, then did he do? And what did the have do do with it?](https://reader036.fdocuments.in/reader036/viewer/2022062321/56649ed45503460f94be4569/html5/thumbnails/1.jpg)
Newton and the
Spring 2007
His 3464
![Page 2: Newton and the Spring 2007 His 3464. Did Newton discover gravity? What, then did he do? And what did the have do do with it?](https://reader036.fdocuments.in/reader036/viewer/2022062321/56649ed45503460f94be4569/html5/thumbnails/2.jpg)
Newton at 83
Portrait by
Enoch Seeman
![Page 3: Newton and the Spring 2007 His 3464. Did Newton discover gravity? What, then did he do? And what did the have do do with it?](https://reader036.fdocuments.in/reader036/viewer/2022062321/56649ed45503460f94be4569/html5/thumbnails/3.jpg)
Sir James Thronhill’s
portrait of Newton
at 67
![Page 4: Newton and the Spring 2007 His 3464. Did Newton discover gravity? What, then did he do? And what did the have do do with it?](https://reader036.fdocuments.in/reader036/viewer/2022062321/56649ed45503460f94be4569/html5/thumbnails/4.jpg)
Newton in 1701 (at 59)
![Page 5: Newton and the Spring 2007 His 3464. Did Newton discover gravity? What, then did he do? And what did the have do do with it?](https://reader036.fdocuments.in/reader036/viewer/2022062321/56649ed45503460f94be4569/html5/thumbnails/5.jpg)
Newton at 46
![Page 6: Newton and the Spring 2007 His 3464. Did Newton discover gravity? What, then did he do? And what did the have do do with it?](https://reader036.fdocuments.in/reader036/viewer/2022062321/56649ed45503460f94be4569/html5/thumbnails/6.jpg)
?
Why does the moon orbit the earth?
The Problem:
??
??
![Page 7: Newton and the Spring 2007 His 3464. Did Newton discover gravity? What, then did he do? And what did the have do do with it?](https://reader036.fdocuments.in/reader036/viewer/2022062321/56649ed45503460f94be4569/html5/thumbnails/7.jpg)
Complicating the Problem
Galileo’s explanation:
inertial motioncircular
![Page 8: Newton and the Spring 2007 His 3464. Did Newton discover gravity? What, then did he do? And what did the have do do with it?](https://reader036.fdocuments.in/reader036/viewer/2022062321/56649ed45503460f94be4569/html5/thumbnails/8.jpg)
![Page 9: Newton and the Spring 2007 His 3464. Did Newton discover gravity? What, then did he do? And what did the have do do with it?](https://reader036.fdocuments.in/reader036/viewer/2022062321/56649ed45503460f94be4569/html5/thumbnails/9.jpg)
cosm
ic str
ing
![Page 10: Newton and the Spring 2007 His 3464. Did Newton discover gravity? What, then did he do? And what did the have do do with it?](https://reader036.fdocuments.in/reader036/viewer/2022062321/56649ed45503460f94be4569/html5/thumbnails/10.jpg)
"After dinner, the weather being warm, we went into the garden and drank tea, under the shade of some apple trees, only he and myself. Amidst other discourse, he told me he was in the same situation as when formerly the notion of gravitation came into his mind. It was occasioned by the fall of an apple as he sat in a contemplative mood."
William Stuckley, 1726
The legend of the apple
![Page 11: Newton and the Spring 2007 His 3464. Did Newton discover gravity? What, then did he do? And what did the have do do with it?](https://reader036.fdocuments.in/reader036/viewer/2022062321/56649ed45503460f94be4569/html5/thumbnails/11.jpg)
The structure of Newton’s argument is
p = The same force that affects apples also affects the moon
q = The moon falls 16 feet in one minute
Given the following statements:
A. If p then q
B. q
C. Therefore p
So he must proveboth A and B
![Page 12: Newton and the Spring 2007 His 3464. Did Newton discover gravity? What, then did he do? And what did the have do do with it?](https://reader036.fdocuments.in/reader036/viewer/2022062321/56649ed45503460f94be4569/html5/thumbnails/12.jpg)
Gravity likely weakens, but by how much?
Newton figures this out by combining his
own insights with those of his predecessors
![Page 13: Newton and the Spring 2007 His 3464. Did Newton discover gravity? What, then did he do? And what did the have do do with it?](https://reader036.fdocuments.in/reader036/viewer/2022062321/56649ed45503460f94be4569/html5/thumbnails/13.jpg)
What he already knew
a = 32 ft/sec2 (by measuring it)
d = 1/2 a t2 (from Galileo)
Inertial motion (his own “corrected” version)f a
f of tension in a string
The relation between a planet’s period and its distance from the sun
![Page 14: Newton and the Spring 2007 His 3464. Did Newton discover gravity? What, then did he do? And what did the have do do with it?](https://reader036.fdocuments.in/reader036/viewer/2022062321/56649ed45503460f94be4569/html5/thumbnails/14.jpg)
r1
r2 r
If r is the average distance of a planet from the sun
And T is the time it takes the planet to circle the sun
Then Kepler’s 3rd Law says: T2 r3
![Page 15: Newton and the Spring 2007 His 3464. Did Newton discover gravity? What, then did he do? And what did the have do do with it?](https://reader036.fdocuments.in/reader036/viewer/2022062321/56649ed45503460f94be4569/html5/thumbnails/15.jpg)
cosm
ic str
ing
To find the tension in the cosmic string Newtonexamined the case ofa rock on a string
![Page 16: Newton and the Spring 2007 His 3464. Did Newton discover gravity? What, then did he do? And what did the have do do with it?](https://reader036.fdocuments.in/reader036/viewer/2022062321/56649ed45503460f94be4569/html5/thumbnails/16.jpg)
![Page 17: Newton and the Spring 2007 His 3464. Did Newton discover gravity? What, then did he do? And what did the have do do with it?](https://reader036.fdocuments.in/reader036/viewer/2022062321/56649ed45503460f94be4569/html5/thumbnails/17.jpg)
f m v2/r
![Page 18: Newton and the Spring 2007 His 3464. Did Newton discover gravity? What, then did he do? And what did the have do do with it?](https://reader036.fdocuments.in/reader036/viewer/2022062321/56649ed45503460f94be4569/html5/thumbnails/18.jpg)
f mv2/r
v = d/t =
f m(2r/T)2 /r =
m42r2
T2x 1
rm42r
T2=
2r/T
m(42r2/T2) x 1/r
Now Newton applies this result to the moon case:
![Page 19: Newton and the Spring 2007 His 3464. Did Newton discover gravity? What, then did he do? And what did the have do do with it?](https://reader036.fdocuments.in/reader036/viewer/2022062321/56649ed45503460f94be4569/html5/thumbnails/19.jpg)
m42rT2
But, from Kepler’s Third LawT2 r3
m42rT2
= m42rr3
= m42
r2
So f
kThus f
2
r2
![Page 20: Newton and the Spring 2007 His 3464. Did Newton discover gravity? What, then did he do? And what did the have do do with it?](https://reader036.fdocuments.in/reader036/viewer/2022062321/56649ed45503460f94be4569/html5/thumbnails/20.jpg)
f is 1r2
At 1 earth radius: At 2 earth radii:
F F
1
(2r)2 r2
1= some amount F1 X F1
=
1
22F 1
r
2r
![Page 21: Newton and the Spring 2007 His 3464. Did Newton discover gravity? What, then did he do? And what did the have do do with it?](https://reader036.fdocuments.in/reader036/viewer/2022062321/56649ed45503460f94be4569/html5/thumbnails/21.jpg)
Newton’s next move: To show
that the moon (like apples)
falling body
can be considered a
![Page 22: Newton and the Spring 2007 His 3464. Did Newton discover gravity? What, then did he do? And what did the have do do with it?](https://reader036.fdocuments.in/reader036/viewer/2022062321/56649ed45503460f94be4569/html5/thumbnails/22.jpg)
From Newton’s Principia Mathematica
![Page 23: Newton and the Spring 2007 His 3464. Did Newton discover gravity? What, then did he do? And what did the have do do with it?](https://reader036.fdocuments.in/reader036/viewer/2022062321/56649ed45503460f94be4569/html5/thumbnails/23.jpg)
![Page 24: Newton and the Spring 2007 His 3464. Did Newton discover gravity? What, then did he do? And what did the have do do with it?](https://reader036.fdocuments.in/reader036/viewer/2022062321/56649ed45503460f94be4569/html5/thumbnails/24.jpg)
Two cases of projectile fall
Thrown slowlyThrown hard
![Page 25: Newton and the Spring 2007 His 3464. Did Newton discover gravity? What, then did he do? And what did the have do do with it?](https://reader036.fdocuments.in/reader036/viewer/2022062321/56649ed45503460f94be4569/html5/thumbnails/25.jpg)
![Page 26: Newton and the Spring 2007 His 3464. Did Newton discover gravity? What, then did he do? And what did the have do do with it?](https://reader036.fdocuments.in/reader036/viewer/2022062321/56649ed45503460f94be4569/html5/thumbnails/26.jpg)
d = 89.4 mi
1 mi
(400
1)
Throw at 4.92 mi/sec for 18.66 sec
(4001)2 + (89.4)2
= 4002
C
B
CB =
D
= CD
= 5280 ft
So CD = 4002 mi - 1 mi
= 4001 mi
(89.4)
CB - BD
BD = ½ x 32 ft/sec2 x (18.166)2
![Page 27: Newton and the Spring 2007 His 3464. Did Newton discover gravity? What, then did he do? And what did the have do do with it?](https://reader036.fdocuments.in/reader036/viewer/2022062321/56649ed45503460f94be4569/html5/thumbnails/27.jpg)
Since f a, a f
f is also 1r2
Therefore a is 1r2
At 1 earth radius: At 2 earth radii:
a= 32 ft/sec2 a= 1/22 x 32 = 8 ft/sec2
![Page 28: Newton and the Spring 2007 His 3464. Did Newton discover gravity? What, then did he do? And what did the have do do with it?](https://reader036.fdocuments.in/reader036/viewer/2022062321/56649ed45503460f94be4569/html5/thumbnails/28.jpg)
The moon is 60 earth radii away
Therefore at the distance of the moon
1602
x 32
or 32602
ft/sec2
a =
![Page 29: Newton and the Spring 2007 His 3464. Did Newton discover gravity? What, then did he do? And what did the have do do with it?](https://reader036.fdocuments.in/reader036/viewer/2022062321/56649ed45503460f94be4569/html5/thumbnails/29.jpg)
In one minute (60 sec) the moon will “fall”
d = 1/2 a t2 = 1/2 x 32602
x 602 =
16 feet
He has thus proven A (if p then q)
![Page 30: Newton and the Spring 2007 His 3464. Did Newton discover gravity? What, then did he do? And what did the have do do with it?](https://reader036.fdocuments.in/reader036/viewer/2022062321/56649ed45503460f94be4569/html5/thumbnails/30.jpg)
To prove B (q: the moon “falls” 16 in 1 min) Newton drew the following construction
A
F
C.
E
D
B
AEDADF
![Page 31: Newton and the Spring 2007 His 3464. Did Newton discover gravity? What, then did he do? And what did the have do do with it?](https://reader036.fdocuments.in/reader036/viewer/2022062321/56649ed45503460f94be4569/html5/thumbnails/31.jpg)
A
F
C.
E
D
B
His task is to find BD, the distance the moon “falls” in a given amount of time.
![Page 32: Newton and the Spring 2007 His 3464. Did Newton discover gravity? What, then did he do? And what did the have do do with it?](https://reader036.fdocuments.in/reader036/viewer/2022062321/56649ed45503460f94be4569/html5/thumbnails/32.jpg)
A
F
C.
E
D
B
To find BD Newton thinks like an engineer
![Page 33: Newton and the Spring 2007 His 3464. Did Newton discover gravity? What, then did he do? And what did the have do do with it?](https://reader036.fdocuments.in/reader036/viewer/2022062321/56649ed45503460f94be4569/html5/thumbnails/33.jpg)
A
F
C.
E
D
B
AED ADF
AEAD =
ADAF
SO AD2 = AE X AF
THUS AF = AD2
AE
![Page 34: Newton and the Spring 2007 His 3464. Did Newton discover gravity? What, then did he do? And what did the have do do with it?](https://reader036.fdocuments.in/reader036/viewer/2022062321/56649ed45503460f94be4569/html5/thumbnails/34.jpg)
A
D
represents 1 minute.
Therefore arc length AD is 1 min minutes in a month
x moon’s orbit
We now know AD
Arc AD
Earth
The whole circle is 1 month
![Page 35: Newton and the Spring 2007 His 3464. Did Newton discover gravity? What, then did he do? And what did the have do do with it?](https://reader036.fdocuments.in/reader036/viewer/2022062321/56649ed45503460f94be4569/html5/thumbnails/35.jpg)
A
F
C.
E
D
B
AF = AD2
AESince and since AE is known
Newton calculated AF to be ?
![Page 36: Newton and the Spring 2007 His 3464. Did Newton discover gravity? What, then did he do? And what did the have do do with it?](https://reader036.fdocuments.in/reader036/viewer/2022062321/56649ed45503460f94be4569/html5/thumbnails/36.jpg)
Recall the structure of Newton’s argument :
If p then q,
q:
therefore p
If the “apple force” is affecting the moon,then the moon “falls” 16 feet in 1 minute.
The moon does fall 16 feet in one minute.
Therefore the apple force affects the moon.
![Page 37: Newton and the Spring 2007 His 3464. Did Newton discover gravity? What, then did he do? And what did the have do do with it?](https://reader036.fdocuments.in/reader036/viewer/2022062321/56649ed45503460f94be4569/html5/thumbnails/37.jpg)
But, look at the following argument:
p: If you have enough money, you go to the movies
q: You go to the movies.
Therefore you have enough money.
![Page 38: Newton and the Spring 2007 His 3464. Did Newton discover gravity? What, then did he do? And what did the have do do with it?](https://reader036.fdocuments.in/reader036/viewer/2022062321/56649ed45503460f94be4569/html5/thumbnails/38.jpg)
Nature was more complicated than Newton ever dreamed.
![Page 39: Newton and the Spring 2007 His 3464. Did Newton discover gravity? What, then did he do? And what did the have do do with it?](https://reader036.fdocuments.in/reader036/viewer/2022062321/56649ed45503460f94be4569/html5/thumbnails/39.jpg)
"The most beautiful experience we can have is the mysterious. It is the fundamental emotion that stands at the cradle of true art and true science. Whoever does not know it and can no longer wonder, no longer marvel, is as good as dead.”