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- Hacker News
- 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)
by ck2 - The equations required to calculate perturbations, and the effort required to do it by hand with just paper, really are brain melting.
https://descanso.jpl.nasa.gov/monograph/series2/Descanso2_S0...
Basically pages and pages of differential equations, either modelled analytically or approximated (as accurately as possible) with Chebyshev polynomials.
Aside from the basic Kepler orbits, everything influences everything else. This doesn't make much of a different in the short term, but space is biiiiig and it doesn't take much for tiny influences to have a measurable effect.
There's a slightly simpler introduction to detailed perturbative planetary orbit calculations in Feynman's Lectures on Physics.
FWIW the solar system isn't unconditionally stable. Even without wandering visitors, there's a small chance Mercury might drift outwards and collide with one of the other Inners in the next few billion years.
- It feels like touring space, and I like that it seems like a creative work. Regarding the part after the tour, my only regret is that I wish the camera had a bit more freedom. Also, when I select Mars or another planet, it seems to sometimes show the other planet instead.by twosky
- This is neat! I love that your Step 15 shows an accurate version of the 3d helix, rather than the highly-viral "vortex" animation from a few years back[0]
It'd be awesome to scale this up to the Milk Way, and beyond, watching everything move in relation to larger time scales.
[0]https://astrorhysy.blogspot.com/2015/03/and-yet-it-moves-qui...
by jumploops - 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!by kmaitreys
- Very nice! Nitpick: the Moon is tidally locked, so it should always face the Earth with the same side.by artemave
- 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.by qunabu
- I've just published the first batch of patches and new features. I've learnt a lot during the process and from the comments which was one of the main goals, so I'm really happy about this process. Thanks again!by qunabu
- Really cool project! I always struggled to understand the motion of the planets looking at 2D images in textbooks. So I really enjoyed the ability to click and drag to explore the motion of the planets in 3D. I think it helps me build a more accurate mental modal of our solar system.
I also loved the music and narration, I'm curious what you used to create the narration? I noticed the narrator seemed to struggle with numbers sometimes, for example on step 1: "The Sun is ~333 000× heavier" The ~333 000× portion does not seem to be read properly. Not sure if that's only a problem I am experiencing on my browser though.
by simon145 - I'm going to fix this soon. I've used elevenlabs for both narrator and musicby qunabu
- This was a lot of fun to explore. I find that naturally I want to click through the animations and observe them for a while before delving into the steps and reading the blurb. It's a bit like skimming around a textbook's headings & figures before reading the chapter, it builds motivation and interest.
One simply change to improve the experience is to keep the Next/Back at fixed locations. The animations and transitions are beautiful, and looking away to chase the moving buttons causes me to drop the visual context.
As a workaround I set the height of .tour-body to 900px and the the whole thing became so much more immersive, like the old planetariums.
by Syntonicles - 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!
by VikingCoder - 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.)
by JKCalhoun - >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.
by nonethewiser - It's not as lucky as you think. We formed from the same cloud that made the sun, so the material that made the earth was already in a fairly stable orbit.by Thiez
- The tutorial made it seem a little too much like there is only one speed that would keep us in orbit. Any slower and we'd crash, any faster and we'd leave.
In fact, though, if you've ever played any game with orbiting mechanics you'd see that it's extremely difficult to get out of orbit if you're in orbit. Going faster simply increases the size of your orbit, and going slower simply shrinks it.
Note that no space program has ever managed (or tried) to send an object into the sun. We're already starting off with such a high orbital velocity, 30km/s, that we'd need to send a rocket backwards at nearly that speed just to slow it down enough to make it crash into the sun. That would require massively more energy than anything we've ever done before.
by SamBam - > 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...
by matja - 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.by jrflo
- This is exactly right; the phenomenon is known as axial parallelism.by savoyard
- Everything you're saying is right, but I'm not seeing what's wrong with step 14. Did they edit it?
> Earth turns once every 23 h 56 min (one sidereal day) about an axis tilted 23.4° (the blue line). That spin gives us day and night; the tilt gives us the seasons.
Nothing in step 14 to me implies s procession of the axis.
by SamBam - 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.
by rfgplk