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PROF.
WALTER LEWIN: And I first want to discuss with you the three famous laws
by Kepler from the early 17th century.
These were brilliant statements that he made.
The interesting thing is that before he made these brilliant statements, he
published more nonsense than anyone else.
But finally he arrived at three golden eggs.
And the first golden egg then is that the orbits are ellipses--
he talked always about planets--
and the sun is at one focus.
That's Kepler's law number one.
These are from around 1618 or so.
The second--
Kepler's second law is quite bizarre how he found it out.
An amazing accomplishment.
If you take an ellipse and you put the sun here at a focus-- this is highly
exaggerated because I told you that most orbits look sort of circular--
and the planet goes from here to here in a certain amount of time, and you
compare that with the planet going from here to here in a certain amount
of time, then Kepler found out that if this area here is the same as that
area here, that the time to go from here to here is the same as to go from
there to there.
An amazing accomplishment to come up with that idea.
And this is called equal areas, equal times.
Somehow it has the smell of some conservation of angular momentum.
And then his third law was that if you take the orbital period of an ellipse,
that is proportional to the third power of the mean distance to the sun.
And he was so pleased with that result that he wrote jubilantly about it.
I'll show you here the data that Kepler had available in 1618, largely
from the work done by, of course, astronomers, observers like Tycho
Brahe, and others.
You see here the six planets that we're known at the time and the mean
distance to the sun.
For the Earth, it is 1 because we work in astronomical units.
Everything is referenced to the distance of the Earth.
This is 150 million kilometers.
And it take the Earth 365 days to go around the sun, Jupiter about 12
years, and Saturn about 30 years.
And then when he takes this number to the power three and this number
squared, and he divide the two, then he gets numbers which
are amazingly constant.
And that is his third law.
The third law leads immediately to the inverse square dependence of gravity,
which he was not aware of.
Newton later put that all together.
But he very jubilantly writes, "I first believed I was dreaming.
But it is absolutely certain and exact that the ratio which exists between
the periodic times of any two planets is precisely the ratio of the 3/2
power of the mean distance." And he wrote that in 1619.