>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.
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jrflo
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.
qunabu
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.
rfgplk
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.
kmaitreys
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!
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ziofill
That doesn’t look right: in the 7th panel (too fast it escapes) the force and velocity of earth are constant? 0_o
BigTuna
Great job! 14 is misleading though - while the context is one day, the animation depicts axial precession which takes place over ~26,000 years
Iolaum
My physics bias would like to see earth forming while it's constituents were orbiting around the sun.
In any case, nice visualization.
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stevenalowe
Looks great but on mobile the popover covers a quarter of the screen, obscuring the sun
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Brendinooo
Super fun! I might show it to my kids later today. Thanks for making it!
genpfault
> Einstein
How are you handling relativistic effects in the N-body simulation?
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ck2
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)
>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 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!
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.
Looks great but on mobile the popover covers a quarter of the screen, obscuring the sun
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?
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