David Goodstein in these lectures is a gift to the world !

The algebra graphics are done so quickly that it actually helps to pause the video, write down the equations, and do the math yourself. 😬👍🏼

Kepler's achievements are even more remarkable when one considers the great tragedy that was his personal life... what an extraordinary man!

Entendi , depois que Kepler formulou suas três leis , ele criou um grande problema . Por exemplo , por que os planetas se movem em elipses com o raio vetor varrendo áreas iguais em tempos iguais ? e a resposta de Newton foi que , os planetas se movem dessa maneira , porque seu movimento é determinado pelo momento angular constante ( já que ele percebeu que a gravidade não gera torção , mas que a gravidade é apenas uma força de atração ) e pela lei de gravitação universal , gerando assim uma nova expressão para a primeira lei de Kepler ( r = L² / DM / 1 + cosθ ) . Há , mais uma coisa , que interessante essa comparação das ciências com as artes , a poesia e a música , achei legal .

3:39 “The crowning glory of the Renaissance”: using Newton’s inverse square law of gravity (law of universal gravitation) and Newton’s second law of motion to obtain a second order differential equation for the orbit of a planet; the solution to that equation is an algebraic equation that can be used to describe any conic section. 7:50 “Twist or torque cannot be applied by gravity”; substituting F by M.a in r x F = 0 and using the product derivative rule to obtain the differential equation d/dt(M.r + v) = 0, which can be integrated to obtain a constant quantity L, the angular momentum. 8:49 “A planet orbiting with constant angular momentum L stays in a single plane; its orbital speed varies in a precisely determined way; the area A swept by its radius vector r changes at a constant rate”, i.e. dA/dr =1/2r x v (Kepler’s second law). 11:02 “Newton’s discovery that the orbits of all objects in the heavens obey the equation of the conic sections started out as a question: why are the planetary orbits ellipses sweeping out equal areas in equal times? The answer is most easily found in polar coordinates where the rate of change of area dA /dt is equal to ½.r².dθ/dt. In terms of angular momentum, the result is a differential equation obeyed by all objects moving under any central force L = M.r².dθ/dt.” 17:58 Using Newton’s universal law of gravitation, the second law of motion and the conservation of angular momentum to obtain a x L = D.dȓ/dt, which is then integrated to obtain v x L = D.(ȓ + e) and finally r = (L²/DM)/(1+e.cosθ), the algebraic equation that can be used to describe any conic section.

Episode 21 established the pivotal foci, string-like nature of conic-cyclonic modulo-geometrical cross-sectional compositions,to use in building on point-line-circle Geometric Drawing techniques, for triangulation and charting in navigation systems and basic Observation of a beautiful Mathemagical Revolution, but still had not chipped away the dross to reveal the kind of knowledge in Michaelangelo's art and craft. Pure-math Fluxion-Integral Temporal Calculus structural-coordination holography-quantization is ready for 2023 Students to work on.

Thank you !

Now it seems logical that the trajectory of projectile is parabola. This is like the apple fall as well as the moon

All I want in this world is to see how these students look like today!

music at 4:00 really gets the blood going

there is a bit too much guesswork and assumptions on Kepplers mental and emotional life given the thin sources. Also Galileo was put on trial for a astrological prediction that went to far for the church. The heliocentricism became mixed in with it over time. That's actually quite complicated and confused everybody involved. Worth looking into. Which was btw highly controversial even within "the church" which was hardly a monolitic block with one opinion and no politics or arguments.

Sure, yes it is a part of history and western culture as it was the theory the scholars choose answered most of the problems of the previous Kepler chosen theory. -> I love how we title Newtown for solving the Kepler problem yet doing so resulted in the Newton Problem of having to solve the problem of gravity. And we're still waiting...

Where can i find a reference to the SOUNDTRACK?

22!

Anyone else notice the large number of left handed students in the audience?

Kepler's law are only assumption The difference between the Apogee and the perigee of the earth orbit is 5000000km. As per the Newtonian law gravitational force is inversely proportional to the squad distance. When the earth comes close to the sun gravitational force is more, when the earth goes 5000000km away from the sun the gravitational force is less. When an object want to escape from an orbit it wants to change its orbital velocity into escape velocity. For this change need extra force. There is no such non force present.

Beethoven in the thumbnail

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Thank you!