I don't like the explicit split of Newtonian and relativistic gravity, this is often how it's presented in educational content, but it creates too much confusion; for instance it gives the illusion that they are somehow separate theories even though Newtonian gravity is a limiting case of Einsteinian gravity when v << c and gravitational fields are weak (see Poissons eq for Newtons gravitational potential.
Lastly, you should consider rendering spacetime similar to Alessandro Roussels spacetime visualization https://www.youtube.com/watch?v=wrwgIjBUYVc; probably the best and most innovative one I've seen.
I did laugh at how the Gravity built the Earth, with a tiny North America and all, and then as more mass was accumulated, North America got to get bigger and bigger and bigger!
that probably happened a few times as well we "stolen" planets or mass from other star systems in the same baby nursery as our sun
there is also likely a planet that passed through and yanked away a lot of debris, most of the simulations for tilt etc. don't work without the mystery missing planet
I could watch PBS Space Time all day for that kind of stuff, often do letting it play in the background on repeat, so much better than the news
Not in the sim right now — it's purely Newtonian (symplectic leapfrog, classical gravity). I show the concept on the last slide ("Einstein: gravity is curved spacetime") — a curve in space wrapping around a star/planet that pulls nearby objects into the well. The quantitative case, Mercury's ~43″/century perihelion precession, I'd add next as a 1PN correction — haven't gotten to it yet. Will try to figure it out how to show this
It works pretty well on iPhone, except the descriptive text fills most of the bottom half of the screen, overlapping the sim which is centered on the screen.
If the sim were instead centered on the free space (the top half of the screen) it’d be perfect.
Very nice, fairly efficient too.
I don't like the explicit split of Newtonian and relativistic gravity, this is often how it's presented in educational content, but it creates too much confusion; for instance it gives the illusion that they are somehow separate theories even though Newtonian gravity is a limiting case of Einsteinian gravity when v << c and gravitational fields are weak (see Poissons eq for Newtons gravitational potential.
Lastly, you should consider rendering spacetime similar to Alessandro Roussels spacetime visualization https://www.youtube.com/watch?v=wrwgIjBUYVc; probably the best and most innovative one I've seen.
That doesn’t look right: in the 7th panel (too fast it escapes) the force and velocity of earth are constant? 0_o
This is nice.
I did laugh at how the Gravity built the Earth, with a tiny North America and all, and then as more mass was accumulated, North America got to get bigger and bigger and bigger!
My physics bias would like to see earth forming while it's constituents were orbiting around the sun.
In any case, nice visualization.
that probably happened a few times as well we "stolen" planets or mass from other star systems in the same baby nursery as our sun
there is also likely a planet that passed through and yanked away a lot of debris, most of the simulations for tilt etc. don't work without the mystery missing planet
I could watch PBS Space Time all day for that kind of stuff, often do letting it play in the background on repeat, so much better than the news
* https://www.youtube.com/@pbsspacetime/search?query=planets
Dr. Becky is also awesome
* https://www.youtube.com/@DrBecky/videos
Great job! 14 is misleading though - while the context is one day, the animation depicts axial precession which takes place over ~26,000 years
Super fun! I might show it to my kids later today. Thanks for making it!
> Einstein
How are you handling relativistic effects in the N-body simulation?
Not in the sim right now — it's purely Newtonian (symplectic leapfrog, classical gravity). I show the concept on the last slide ("Einstein: gravity is curved spacetime") — a curve in space wrapping around a star/planet that pulls nearby objects into the well. The quantitative case, Mercury's ~43″/century perihelion precession, I'd add next as a 1PN correction — haven't gotten to it yet. Will try to figure it out how to show this
Looks great but on mobile the popover covers a quarter of the screen, obscuring the sun
I should have mentioned that its not mobile friendly so far. I will try to fix this.
It should be better now
It works pretty well on iPhone, except the descriptive text fills most of the bottom half of the screen, overlapping the sim which is centered on the screen.
If the sim were instead centered on the free space (the top half of the screen) it’d be perfect.
There a toggle button to show hide description if you missed it
the way the original mathematicians figured all this out absolutely melts my brain
no computers, no calculators, barely working telescopes looking at the moons orbiting Jupiter
(don't be limited by episode title, lots of amazing astrophysics in there)
* https://www.youtube.com/watch?v=8yhk1EZq9tY