>The Sun’s gravity (red arrow) pulls the Earth straight toward it the whole time — so why no collision? Because the Earth is also moving sideways (green arrow) at 29.8 km/s. Each moment it does fall toward the Sun, but its sideways speed carries it past — it keeps missing. The dashed line shows where inertia alone would send it; gravity bends that straight path into a closed loop. An orbit is simply falling, continuously, and always missing.
Reading stuff like this always makes me think "well that is fortunate." Of course there is survivorship bias so its not exactly surprising. But it also makes me wonder what could change the status quo.
I guess these are the things that could change it:
- suns becomes lighter (earth shoots into space)
- earth accelerates (earth shoots into space)
- sun becomes heavier (earth falls into sun)
- earth decelerates (earth falls into sun)
I guess in theory some large interstellar object could pass to close too earth and fling us off into space or into the sun.
I think that was one of the arguments of the Anthropic principle [1], that there doesn't appear to be any reason why there are 3 spatial dimensions and 1 time dimension, or why the fundamental constants are what they are - but if they weren't then there wouldn't be anyone to exist to say "well that is fortunate".
I really liked your animations, but isn't step 14 incorrect? Earth's axis processes, but on a very long timescale. In the span of a day, the axis should be effectively stationary. That's why its the rotation 'axis' - it's the fixed line it rotates about. That's why Polaris is the north star: the axis of rotation points effectively directly at it at all times no matter the season. During summer in the northern hemisphere, the tilt is towards the sun, giving us more direct heating, and in the winter it's away from the sun. This isn't due to the axis moving, but due to the axis' relative position changing throughout earth's orbit around the sun.
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.
For something more rigorous, I would like to take this opportunity to share rebound[1], something we use for n-body simulations in our field (planet formation). Perhaps few people here are already familiar with it. It has a Python interface but the C interface is very easy to use as well and has plethora of pre-set examples which can be visualized using GLFW. It's very very cool!
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!
i had the same thought. likewise the sun formed from particles circling around the galactic core. that matters later when it is explained how the sun is moving.
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
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.
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
>The Sun’s gravity (red arrow) pulls the Earth straight toward it the whole time — so why no collision? Because the Earth is also moving sideways (green arrow) at 29.8 km/s. Each moment it does fall toward the Sun, but its sideways speed carries it past — it keeps missing. The dashed line shows where inertia alone would send it; gravity bends that straight path into a closed loop. An orbit is simply falling, continuously, and always missing.
Reading stuff like this always makes me think "well that is fortunate." Of course there is survivorship bias so its not exactly surprising. But it also makes me wonder what could change the status quo.
I guess these are the things that could change it:
- suns becomes lighter (earth shoots into space)
- earth accelerates (earth shoots into space)
- sun becomes heavier (earth falls into sun)
- earth decelerates (earth falls into sun)
I guess in theory some large interstellar object could pass to close too earth and fling us off into space or into the sun.
> well that is fortunate
I think that was one of the arguments of the Anthropic principle [1], that there doesn't appear to be any reason why there are 3 spatial dimensions and 1 time dimension, or why the fundamental constants are what they are - but if they weren't then there wouldn't be anyone to exist to say "well that is fortunate".
[1] https://en.wikipedia.org/wiki/Anthropic_principle#Dimensions...
yes, exactly. It didn't have to be this way, but it had to be this way to observe it. Survivorship bias.
I really liked your animations, but isn't step 14 incorrect? Earth's axis processes, but on a very long timescale. In the span of a day, the axis should be effectively stationary. That's why its the rotation 'axis' - it's the fixed line it rotates about. That's why Polaris is the north star: the axis of rotation points effectively directly at it at all times no matter the season. During summer in the northern hemisphere, the tilt is towards the sun, giving us more direct heating, and in the winter it's away from the sun. This isn't due to the axis moving, but due to the axis' relative position changing throughout earth's orbit around the sun.
Thank you all for the comments and showing the weaknesses in the model and visualisation. I'll try to understand the issues and fix them soon.
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.
For something more rigorous, I would like to take this opportunity to share rebound[1], something we use for n-body simulations in our field (planet formation). Perhaps few people here are already familiar with it. It has a Python interface but the C interface is very easy to use as well and has plethora of pre-set examples which can be visualized using GLFW. It's very very cool!
[1]https://github.com/hannorein/rebound
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!
Ha ha, you're looking at the man behind the curtain.
(I thought the same: suspecting it's a kind of crossfade between accreting bodies and finished Earth.)
That doesn’t look right: in the 7th panel (too fast it escapes) the force and velocity of earth are constant? 0_o
Great job! 14 is misleading though - while the context is one day, the animation depicts axial precession which takes place over ~26,000 years
My physics bias would like to see earth forming while it's constituents were orbiting around the sun.
In any case, nice visualization.
i had the same thought. likewise the sun formed from particles circling around the galactic core. that matters later when it is explained how the sun is moving.
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
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
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
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