Episode 21: Kepler's Three Laws - The Mechanical Universe

Episode 21. Kepler's Three Laws: The discovery of elliptical orbits helps describe the motion of heavenly bodies with unprecedented accuracy.
“The Mechanical Universe,” is a critically-acclaimed series of 52 thirty-minute videos covering the basic topics of an introductory university physics course.
Each program in the series opens and closes with Caltech Professor David Goodstein providing philosophical, historical and often humorous insight into the subject at hand while lecturing to his freshman physics class. The series contains hundreds of computer animation segments, created by Dr. James F. Blinn, as the primary tool of instruction. Dynamic location footage and historical re-creations are also used to stress the fact that science is a human endeavor.
The series was originally produced as a broadcast telecourse in 1985 by Caltech and Intelecom, Inc. with program funding from the Annenberg/CPB Project.
The online version of the series is sponsored by the Information Science and Technology initiative at Caltech. ist.caltech.edu
©1985 California Institute of Technology, The Corporation for Community College Television, and The Annenberg/CPB Project

[@afonsodeportugal]

3:46 How to draw an ellipse from its two _foci_ (plural of focus, the Latin word for fireplace); how to calculate its area; definition of eccentricity _e_ and how its value changes the ellipse. 11:05 How Johannes Kepler determined the orbit of the Earth from past observations of Mars. 12:10 How Johannes Kepler traced the orbit of Mars and how he realized it wasn’t circular, but elliptical. 14:16 How the Greeks generated the conic sections (ellipse, parabola and hyperbola) by slicing a cone with a plane. 15:30 Pappus of Alexandria improved the understanding of the ellipse ( _e_ < 1) by introducing the directrix, a line outside the conic section, which can also be used to trace parabolas ( _e_ = 1), and hyperbolas ( _e_ > 1); all three conic sections can be described by a common algebraic equation: _r = e.d_ /(1+ _e.cosθ_ ). 19:14 “Kepler’s first law states that each planet moves in an ellipse with the sun at one focus; the second law states that “a line from the sun to a planet sweeps out equal areas at equal times”; the third law states that “the square of the period of a planet is proportional to the cube of the length of the semi-major axis”.

[@ayoubsbai6339]

You are everywhere on this series lol

[@bozo7545]

Thank you so much! :)

[@sivakumar-oh2if]

Ya, he commented almost every videos on this series but he left some series

[@Albeit_Jordan]

This is the kind of thing that makes you feel high even when you're not...

[@anthonymichel7745]

hey, who else needs to watch this for physics?

[@lucasmunoz8325]

me lol

[@huntersamis983]

Me!

[@sebastianlopezalejos]

Me

[@robinaguinaldo4507]

Best way to review on what I went through to get my degree in astronomy. Best tool that I used to understand the mechanics that controls the world that we live in.

[@ayoubsbai6339]

@@afonsodeportugal agreed

[@spiderjerusalem4009]

Man, i wish i'd seen this earlier. Everyone who watched/learned through this during teenagehood are luckiest ever

[@moe-iv7uq]

For my Patterson General Physics dudes: 1. When the professor says “the Tyconic system,” he is referring to the way Tycho Brahe viewed the structure of the solar system. Describe this structure that Brahe imagined. The Earth was stationary at the center of the universe, the sun went around the Earth, and all of the other planets went around the sun. 2. What length is always constant for an ellipse? The distance from the center to either focus is some fraction of a ea, the symbol e represents the amount of eccentricity 3. What does eccentricity mean in this context? As in the social context of the word, somewhat off-center. When e shrinks to 0, when there’s no eccentricity, the result is a perfectly rounded figure, an ellipse called a circle. 4. What is the Latin word for “fireplace?” Focus, first used for ellipse by a man who become known as The Wandering Mathematician. In the sun, he saw the greatest fireplace in the universe. 5. What scientist was known as the “Wandering Mathematician?” Johannes Kepler. 6. Whose observational astronomical data was essential to Kepler in his work? Tycho Brahe’s. 7. How many pages did Kepler’s calculations total? Kepler’s pages numbered at over 900 pages 8. Describe the position of Mars when it is at opposition. Seen from either the Earth or the Sun, the position of Mars is the same. 9. According to the speaker, what determines the value of a scientific idea? It is not whether it is valid or invalid with it’s claims, instead, it lies in whether the idea is fruitful, or leads to new ideas, or to progress. 10. Using the video and/or your own internet search, list Kepler’s 3 Laws of Planetary Motion. Law 1. Each planet moves in an ellipse with the Sun at one focus. r = ed / (1+e cos (theta)) Law 2. A line from the Sun to a planet sweeps out equal areas in equal times. dA/dt = constant Law 3. The square of the period of a planet is proportional to the cube of the length of the semi-major axis, and it reveals a connection between the motions of different planets. T^2 = ((4(pi)^2) / (GM)) • a^3

[@5Andysalive]

worth noting that while looking silly today, the Brahe model for many years fit the available data and observations better than not just Ptolomy but also Copernicus. Ironically his own observation became then too precise to fit either model. Brahe's biggest achievement was his focus on observations and prime data over just following some ancient texts. Making him one of the founders of modern science. Keppler was another one. Bit of a shame, Brahe is usually reduced to his golden (brass) nose.

[@peretzo]

i am utterly amazed by this content, this series, this channel, the people & organization behind it; the fact that such fascinating, SUPERB material is accessible to (much of) humanity, free of charge. To anyone who’s involved in (arranging / uploading / managing) this - i salute you: You are making a difference. You are spending your time in a way which is worthwhile.

[@brainstormingsharing1309]

Absolutely well done and definitely keep it up!!! 👍👍👍👍👍

[@roberttelarket4934]

Without analysis(the Calculus) it is extremely difficult and cumbersome to among other things to convert data into legitimate physical models. That's why it took decades for the genius Kepler to formulate his three laws. Kepler had to use brute algebra among other non-calculus math to arrive at the laws. It was a feat and miracle. Tycho Brahe was a nothing in comparison to Kepler. He was just a recorder of data and non-correlator. He only had one great attribute his supreme eyesight in the absence of great telescopes to gather the data which very luckily Kepler was able to get hold of after Brahe's death. For this reason it can be truly said that Kepler was the first real scientist. Before him no one who postulated something backed it up with data.

[@billthomas7644]

While Tycho was reputed to have very good eyesight. Most of Brahe's data was from observations by his employees. Brahe had the money to have made the most accurate sighting instruments of the day.

[@charlessmith263]

Law no. 1 - All heavenly bodies go around in elliptical paths, with the focus of these paths on the sun. Law no. 2 - A line from a sun to a planet sweeps out equal areas at equal times. Law no. 3 - The square of the time period of an Earth's orbit is proportional to its cubic length on its semimajor axis.

[@mattyyaaaa]

thanks bro

[@toegang734]

Man, I'm here for this quality content.

[@Brandi.Nicole]

Ah! My textbook didn’t explain “how” fully Kepler found this out about Mars - marking for notes (and I will source) 11:28 here! Thanks!

[@kevinlu8487]

Glad that I can still watch it on youtube because the school internet blocked this video from watching...

[@roberttelarket4934]

I don't understand. Why would the school internet block it?

[@universocalculado4639]

O modo como Kepler descobriu sua primeira lei através de triangulações foi muito engenhoso . Legal que esse episódio relembrou um pouco de geometria analítica , explicando a equação das secções cônicas ( r = ed / 1 + e cos θ ) . Na segunda lei ( dA / dt = constante ) , segundo o episódio 19 essa constante vale ( 1/2 r x v ) então ( dA / dt = 1/2 r x v ) , no entanto , o momento angular é ( L = mrv ) , assim também ( dA / dt = L / 2m ) . Há , outra coisa , a terceira de Kepler ( T^2 = ( 4π^2 / GM ) a^3 ) é muito interessante .

[@Pedritox0953]

Wonderful video !!

[@brycering5989]

The Irony, Kepler tried to discover/predict an means by which the planets were held in the eliptic paths by building a modle that hung (due to gravity) and the little giggle we probably had when the modle sliped and fell. 19:00

[@Brandi.Nicole]

Get out! Not at 19 minutes yet. Trying to soak in the 900 mathematical equation statement 😅😂 but how funny. Sometimes you need a little help from the universe (aka gravity in this case!) to lead you in the right direction.

[@EliteTeamKiller2.0]

Who the hell is downvoting these? Flat earthers, I suppose?

[@TX_BoomSlang]

Geocentrists

[@awesomeperson2237]

students

[@5Andysalive]

The Brahe model for many years fit the available data and observations better than not just Ptolemy but also Copernicus. Ironically his own observation became then too precise to fit either model. Brahe's biggest achievement and legacy was his focus on observations and prime data over just following some ancient texts (which the academic competetion was quite comfortable with) Making him one of the founders of modern science. Keppler was another one. Bit of a shame, Brahe is usually reduced to his golden (brass) nose.

[@StormsandSaugeye]

I remember seeing the footage about kepler from Cosmos, a Personal Voyage. Is this where Sagan got the video?

[@tedg3250]

thanks, I love you

[@willizzzkidzz110]

Those are some pretty intense feelings you have for this video Ted

[@tedg3250]

@@willizzzkidzz110 😂 just intense love for Knowledge that's all..

[@rkreike]

Q: When a planet moves a around a star, with different velocities at it’s perihelion and it’s aphelion, does that mean that time on that planet goes slower or faster, because time goes slower when an object moves faster?

[@christopherellis2663]

CENTURIES begin in the first year,not the last.

[@MineOfTheLegends]

To all you physics 20 bros, are we expected to watch this entire video??

[@caiatabalipa]

Carl Sagan is the best...

[@Green-cr2jj]

I have to watch this for my Algebra 2 teacher, anyone wanna send the answers?

[@RamasamyArumugam1927]

Even in the year 1985, the commentator talks about discovering the mathematical secret of "God's creation".

[@Rico-Suave_]

Watched all of it 27:25

[@michaelgonzalez9058]

That means all planets contain electronity

[@razaali4616]

"There are at least 9 planets, and maybe even more..."

[@tovahkaplan9222]

tuesday june 19 2018 9:00 am allison ryan

[@andreranulfo-dev8607]

Who also is in love with the Red Hair?

[@davidwilkie9551]

A POV that Time Duration Timing is pure elemental function infinitesimal Singularity-point constant composition of Perfect Gas Relativity allows for the default condensation characteristics of log-antilog Conformal Fields of musical mathematical reciprocation-recirculation potential positioning measures of shell-horizons in holography-quantization, and point-line-circle conic-cyclonic manifestations of 0-1-2-3-4-etc exponentiation-ness sequences such as the arrangements discovered by Kepler's Observation fit the QM-TIME Completeness cause-effect Actuality, here-now-forever Math-Physics in/of this Totality, the Eternity-now Interval. Attribution to Actuality.

[@sebastianlopezalejos]

Who got sent by Aníbal

[@onuresen8031]

İyi

[@christopherellis2663]

Equal areas of arc in equal periods of time. I learnt that 25 years ago, and you can't even read it straight

[@michaelgonzalez9058]

Decahidren

[@oker59]

August 19, 1610 “You are the first and almost the only person who, even after but a cursory investigation, has, such is your openness of mind and lofty genius, given entire credit to my statements…. We will not trouble ourselves about the abuse of the multitude, for against Jupiter even giants, to say nothing of pigmies, fight in vain. Let Jupiter stand in the heavens, and let eh sycophants bark at him as they will….In Pisa, Florence, Bologna, Venice, and Padua many have seen the planets; but all are silent on the subject and undecided, for the greater number recognize neither Jupiter nor Mars and scarcely the moon as planet. At Venice one man spoke against me, boasting that he knew for certain that my satellites of Jupiter, which he had several times observed, were not planets because they were always to be seen with Jupiter, and either all of some them, now followed and now preceded him. What is to be done? Shall we side with Democritus or Heraclitus? I think, my Kepler, we will laugh at the extraordinary stupidity of the multitude. What do you say to the leading philosophers of the faculty here, to whom I have offered a thousand times of my own accord to show my studies, but who with the lazy obstinacy of a serpent who has eaten his fill have never consented to look at planets, nor moon, nor telescope? Verily, just as serpents close their ears, so do these men close their eyes to the light of truth. These are great matters; yet they do not occasion any surprise. People of this sort thin that philosophy is a kind of book like the AEneid or the Odyssey, and that the truth is to be sought, not in the universe, not in nature, but (I use their own words) by comparing texts! How you would laugh if you heard what things the first philosopher of the faculty at Pisa brought against me in the presence of the Grand Duke, for he tried, now with logical arguments, now with magical adjurations, to tear down and argue the new planets our of heaven.”

[@oker59]

[Galileo to Kepler, 1597] ....Like you, I accepted the Copernicun position several years ago and discovered from thence the causes of many natural effects which are doubtless inexplicable by the current theories. I have written up many of my reasons and refutations on the subject, but I have not dared until now to bring them into the open, being warned by the fortunes of Copernicus himself, our master, who procured immortal fame among a few but stepped down among the great crowd (for the foolish are numerous), only to be derided and dishonored. I would dare publish my thoughts if there were many like you; but, since there are not, I shall forebear.... [Kepler to Galileo, 1597] ....I could only have wished that you, who have so profound an insight, would choose another way. You advise us, by your personal example, and in discreetly veiled fashion, to retreat before the general ignorance and not to expose ourselves or heedlessly to oppose the violent attacks of the mob of scholars (and in this you follow Plato and Pythagoras, our true perceptors). But after a tremendous task has been begun in our time, first by Copernicus and then by many very learned mathematicians, and when the assertion that the Earth moves can no longer be considered something new, would it not be much better to pull the wagon to its goal by our joint efforts, now that we have got it under way, and gradually, with powerful voices, to shout down the common herd, which really does not weigh the arguments very carefully? Thus perhaps by cleverness we may bring it to a knowledge of the truth. With your arguments you would at the same time help your comrades who endure so many unjust judgments, for they would obtain either comfort from your agreement or protection from your influential position. It is not only your Italians who cannot believe that they move if they do not feel it, but we in Germany also do not by any means endear ourselves with this idea. Yet there are ways by which we protect ourselves against these difficulties.... Be of good cheer, Galileo, and come out publicly. If I judge correctly, there are only a few of the distinguished mathematicians of Europe who would part company with us, so great is the power of truth. If Italy seems a less favorable place for your publication, and if you look for difficulties there, perhaps Germany will allow us this freedom.

[@afonsodeportugal]

Why do some students always wear the same clothes and always seem to have the same facial expressions?

[@Dakers11]

Some are actors & others are students shot at different times.Then spliced together in editing. Dr. Goodstein stated this in an interview by Shelley Erwin in late 2002.

[@afonsodeportugal]

@@Dakers11 Thanks, man! But... why did they get actors? The students were not good looking enough to appear on television?

[@willizzzkidzz110]

@Afonso de Portugal FBI open up

[@costco8711]

eggo gang rise up

[@livingthedream5112]

So what

[@christopherellis2663]

Americans can do neither English nor Latin. Focus,foci, it's not faux sigh.but.keep the c hard

[@abcdef2069]

they should have renamed it and called it TYCHO (upper case) - kepler (lower case) 's three laws. tycho should have hired some mathematians to analyse his data early on. data analysis is easy.... well kind of.... well if you know what you are doing... well this was your data to begin with....well tycho was a dummy. didnt tycho know how to plot his data's and say this fast? "hmmmm, this looks like an ellipse". too bad no one knows his name. this is why high school education is so important, and it is free too.

[@eliashudsonofficial]

I wouldn't say he's dumb as much as he just wasn't progressed enough to know what he was doing. Like said in the video, his idea isn't bad because it was wrong, because his idea led Kepler to discover something much bigger and more elaborate that he couldn't have come up with on his own. Additionally, that difference of a 0.09 factor is super small and the only reason Kepler figured it out is because he poured so much time into that planet (Mars). Tycho was a renowned scientist, and he came pretty dang close for his time.

[@roberttelarket4934]

Absolutely not! Tycho was a nothing, just a data gather. He had only one thing going for him super-eyesight.

[@billthomas7644]

Kepler was exactly one of the mathematicians Tycho hired for this purpose. He also hired other astronomers and mathematicians such as Christen Longomontanus who was no slouch. Kepler was no doubt most capable in this regard but Tycho was extremely jealous of the data he had paid vast sums of his family fortune to obtain, especially after Nicolaus Ursus stole his ideas. Kepler only gained full access to the data after Tycho's death when Kepler eventually came to an agreement with Tycho's son in law, Frans Tengnagel. Tengnagel realised that Kepler had the skill to make good use of the data and committed to publish the Rudolphine tables in honour of Tycho and the Emperor.

[@billthomas7644]

@@roberttelarket4934 Not really he was a great designer of instruments.

[@fiveforbiting]

Soundtrack to awful, didn't finish

[@brainstormingsharing1309]

Absolutely well done and definitely keep it up!!! 👍👍👍👍👍