3blue1brownProof: The Geometry of Elliptic Orbits
Audience:
Any Math or Physics enthusiast can watch and understand the video, including Undergraduates like myself. It focuses on solving the differential equations to produce different sorts of shapes(circular, elliptical, etc.) that an orbit can take in a two body system. It showcases Gravity simulations between planets, and discusses the relation between energy and shapes of the orbits taken by the heavenly bodies.
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Comments
Binet’s equation / trick u = 1/r, takes me back to undergraduate maths :D
Motivation I love the topic. Why space orbits are not perfect circles. What a great thing to think about!
Clarity Excellent
Novelty Animation was great, clear and creative
Memorability Some of it is over my head but I got some main concepts (not good with physics).
Visuals were great, I appreciated the way the mathematics was displayed.
Motivation: 2.5 / 3 Clarity : 2.5 / 3 Novelty : 2 / 3
The concept is good. But I think it would be beneficial to motivate the concepts a bit more for the viewers.
Not sure what’s with the audio but it may require some tweaks to your settings.
To get a parabola as the intersection of a plane and a conic, the plane has to be parallel to the side of the conic.
This was a nice video. The explanations given were clear and easy to understand, and I could always pause between the derivations to keep track. You explained clearly how the polar equation of an ellipse dropped out of the differential equation. Two points to note however: 1. When you predicted that the solution of the differential equation is a cosine wave, it would’ve been nice if you verified it by showing it satisfies the equation, otherwise it just seems as though you’re coming up with it out of thin air and not justifying why 2. There are a few parts in your voiceover where you seem to stutter a little. Otherwise it was a pretty good video, the animations were nice, and the sandbox was interesting as well. Glad to watch!
You have not at all explained why this equations describe the shape of a conic section (1:08 in the video). You haven’t explained what eccentricity and distance from the directrix are. You haven’t explained how exactly e and d determine the shape (so for which values you obtain which shapes) and why. You haven’t explained why we the acceleration vector can be written in polar coordinates the way you showed it. You haven’t explained why two sets of differential equations derive from this equation and I could go on with this but that would be really demotivating. I’m really sorry but since you haven’t really done anything more than showing a formal proof without any further explanations, I can’t give you more than 2 points. If you want to improve your videos you should put yourself in the shoes of somebody who has never heard of the topic or even better try showing it to someone who doesn’t now the topic and ask him/her what he/she did not understand. Something simple you could immediately improve: You know that (at 0:56 in the video) a Hyperbola pops up because you actually have to consider double cone to get the shapes described by your equation but for someone not familiar with the topic, this could already be a first hurdle. This is why I suggest simply drawing a double cone or at least mentioning it.
I wish you the best of luck with all your future videos,
Celestial mechanics is a wonderful subject that I remember learning the basics of in my multivariable calculus class, but years later when I was tasked with teaching it (at a similar institution in the same state system), we were told specifically to omit that section. It’s sad, because it feels like the motion of the planets was the gateway to the Enlightenment and scientific discovery today.
I appreciated the “making sure we’re on the same page”, explicitly getting the audience onboard in-video. The algebraic derivations were also nicely paced. Minor nitpick (I honestly I don’t know how I would explain it better), but the change of the variable to “u” is a bit unmotivated. Going through the details and getting a harmonic oscillator was definitely farther than my old multivariable calculus course got to, but you somehow succinctly got to it and explained a bunch in under 10 minutes.
One interesting possible forward direction for you: the relativistic perihelion precession of Mercury, because it so nicely shows up as a correction term (though that may be harder to explain in detail; to keep a short video you’d have to just say it’s taken as a given).
I think it’s a nice derivation of of orbits move.
I think it’d be cool to spend more time focusing on the consequences of the equation. Namely, that certain energies or certain properties produce certain orbits and why they do so, given that we’ve done all the algebra to derive the equation here.