Looking at three great twitter posts on ellipses

Over the last month I’ve seen several great twitter threads on ellipses. Sort of a strange coincidence, I guess. Today I finally got around to sharing them with the boys.

We started with this tweet from Lucas Vieira. I’m having a fight with WordPress on the embedding of this one – the tweet we are looking at is the “ballistic ellipse” one at the bottom.

The highest point of ballistic trajectories at constant speed form what I call the "ballistic ellipse". I discovered this when I was in high school, but apparently this was only published about in 2004! https://t.co/eSmpw9bQu6 pic.twitter.com/TwlXsyPwvc

— Lucas Vieira (LucasVB/1ucasvb) (@LucasVB) April 2, 2020

Here’s what the boys thought of the ideas in the animation:

Next we moved on to a post from Greg Egan that was inspired by Lucas’s post:

A satellite has the least kinetic energy when farthest from the central mass.

If it releases mini-satellites moving tangentially to its orbit, but whose KE per kg is less than its own by that minimum, they will all pass through the 2nd focus of its orbit, all at the same speed. pic.twitter.com/j9HljOTXwM

— Greg Egan (@gregeganSF) April 8, 2020

The kids had a tough time explaining what they were seeing here, so we talked about this picture for a little bit longer than usual:

Now we moved on to Jacopo Bertolotti’s Physics Factlet #216 on 1/r^2 orbits. This animation helped me make sense of a point about General Relativity that I’d heard, but never really understood.

#PhysicsFactlet (216)
Central forces that decay as 1/r² are special, as they guarantee that all bound orbits are going to be closed (Bertrand's theorem).
Small changes in the power will lead to significantly different kind of orbits. pic.twitter.com/AllIFyTwZd

— Jacopo Bertolotti (@j_bertolotti) April 7, 2020

The boys thought the animation was fascinating:

Finally, since Jacopo share his Mathematica code, we took a look at the program. The boys were surprised by how short it was. After looking at the code for a bit we changed some of the parameters and got a fun surprise:

I love that so many people share their amazing work on Twitter. Looking at these animations was a fun way to share a bit of math and physics with the boys this morning!

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