Feynman's Lost Lecture (ft. 3Blue1Brown)

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Strong rec Zhengyuan Yue · 2021-02 · Physics Stack Exchange · on “Why does motion under inverse square law follows elliptical motion?”

Feynman once talked about this topic in his "lost lecture" without using too much calculus. MinutePhysics and 3Blue1Brown has made a wonderful video [this video] to explain Feynman's reasoning. I highly recommend this video.

Recommends J.G. · 2019-01 · Mathematics Stack Exchange · on “High School Mathematical Research Project Ideas”

What are the requirements of your research project? I'm guessing they can't expect a high schooler to discover something new; they probably just want you to work through a non-syllabus proof, possibly after you conjecture the result from special cases. If you want to do something with a Rubik cube you could discuss its group theory, or number of configurations using combinatorics. Physics is harder because you might not have enough calculus, but 3blue1brown's video on why orbits are ellipses [this video] might give you some ideas for a more geometry-based analysis of gravity. I live in the UK, so what you're trying to do is probably similar to our GCSE maths coursework. Based on my memories of th

Recommends Sean E. Lake · 2019-07 · Physics Stack Exchange · on “Show that angular momentum is independent of the angle”

The $1/r$ potential interaction is, fundamentally, the same as what's in gravitationally orbiting bodies. How do you prove that $L$ is constant for those? (a couple of videos on the topic that might be helpful: a 3Blue1Brown video presenting an argument by Feynman showing why orbits are elliptical [this video] , an AP Physics level lecture on angular momentum and elliptical orbits [LINK] . If nothing else, you can work out \begin{align} \vec{L} &= \vec{r}\times (m\vec{v}) \\ &= r v \sin\theta \hat{n}, \end{align} where $\theta$ is the angle between $\vec{r}$ and $\vec{v}$ , and $\hat{n}$ is unimportant (it's perpendicular to the ellipse). The crucial part is that the origin is at one focus of the

Recommends J.G. · 2020-12 · Physics Stack Exchange · on “Formula for centripetal acceleration: simple proof that does not use calculus?”

While this result is specific to circular orbits, this switch-to-velocity-space technique is also useful in understanding ellipses. For example, in this video [this video] 3blue1brown uses it to prove area is swept at a constant rate in the elliptical orbits resulting from an inverse-square force.

Cites Abhimanyu Pallavi Sudhir · 2013-09 · Physics Stack Exchange · on “What are the fundamental problems of being in a world with only 2 spatial dimensions?”

The Weyl Tensor vanishes in 3 dimensions, which means there is no vacuum gravity (since the Einstein field equations imply $R_{\mu\nu}=0$ in a vacuum). Most of the interesting gravitational effects we know are a result of vacuum gravity, including apples falling, and stuff having orbits. Note that even Newtonian gravity is sufficient to show that there are no stable orbits -- see this video summary [this video] by 3blue1brown of Feynman's argument as to the existence of stable elliptical orbits in 3 dimensions.

Cites Narasimham · 2020-11 · Mathematics Stack Exchange · on “Ellipse Locus Feynman approach”

The following seeks to identify which alternate accelerations act ( gravitational, tangential, centrifugal) in Feynman's dynamics scheme leading to the same position of planet once again at the Newton classical position. Request you to please help in drawing a new force diagram including the perpendicular bisector accelerations leading to this alternate dynamic derivation. Feynman's Lost nb (30 - 50 sec) [this video] [LINK] A geometrical verification is made below using elimination by p- discriminant method A variable point P (in above rough sketch) on a circle radius $2a$ centered at origin and focal point F $(2c,0)$ . Finding envelope of perpendicular bisectors of PF. $$ ( 2a\ \cos t, 2a \sin t

Cites xXx_69_SWAG_69_xXx · 2021-02 · Physics Stack Exchange · on “What determines the shape of this orbit?”

Let me address your second point first; all Newtonian/Kepler orbits are elliptical; that means that the earth is currently in an elliptical orbit and will remain in one if a comet hits it (if the comet is not so large or so fast to cause the earth to cease orbiting). But I assume in your class; you are working with the circular orbit approximation; so I will use that in answering your question. You state correctly that $v=\sqrt{\frac{GM}{R}}$ and so obviously $G$ and $M$ don't change, therefore $R$ must change to maintain the equality. Specifically. $\frac{v_1^2}{v_2^2}R_1=R_2$ . Again this is using spherical orbit approximations; in reality there are more involved differential equations tha

Cites jxhyc · 2021-06 · Physics Stack Exchange · on “Can soneome help me understand this part of the Feynman's Lost Lecture?”

Feynman's lost lecture [this video] So at 17:38 [this video] , 3Blue1Brown states: We know that once the planet has turned an angle $\theta$ off the horizontal with respect to the sun, that corresponds to walking $\theta$ degrees around our circle in our velocity diagram, since the acceleration vector rotates just as much as the radial vector. I'm not sure I quite follow the logic here. Yes, I can see that the acceleration vector rotate just as much as the radius vector since the sun exerts its force along the radius vector. But what I don't understand is how that translate into saying that the when the position of the planet has turned an angle of $\theta$ with respect to the sun, that means that the

Cites athos · 2021-09 · Mathematics Stack Exchange · on “the Tangent Principle”

Feynman gave a geometric proof that planet's orbit around the sun is an ellipse, there's an youtube episode [this video] for that, and for the tricky part there's some discussion on stackexchange physics forum [LINK] , a more formal explanation can be found from the paper Paths of the planets [LINK] by R.H. Hall and N. Higson. However, Hall etc's paper used a "Tangent Principle", which says : If two curves (in polar coordinates) $r_1(θ)$ and $r_2(θ)$ have the same tangent at every $θ$ , then they are the same, up to scaling. I believe this is also implicitly used by Feynman. It sounds correct, however, how could one prove it?

Cites Cognoscenti · 2024-03 · Mathematics Stack Exchange · on “Determining the curve to which variable line segments are tangent”

A variable line passing through a fixed point $P(x_0,y_0)$ intersects the circle $x^2+y^2=a^2$ at some point $Q$ . If all the perpendicular bisectors of the variable line segment $PQ$ are tangent to a curve $C$ , determine $C$ if (i) $P$ is inside the circle (ii) $P$ is outside the circle (Note: in both cases, only select one point of intersection with the circle, do not find the perpendicular bisector of the chord between both points of intersection); Motivation: I was watching this video on Feynmann's lost lecture on planetary orbits and came across an interesting geometry puzzle; [this video] _ which moreover resolves the first part of the question but then my dense self could not understand w