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 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.
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.
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.
>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".
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.
Seems like somehow orbiting bodies finally come to an "equilibrium point"... where orbital speed cancels out gravitational pull towards the sun, so a balance is achieved ?
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.
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'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!
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.
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!
Just one note about the moon orbit around the Earth, it is far more subtle; almost just orbiting the Sun alongside Earth. I can't explain better than minute physics, highly recommend: youtube.com/watch?v=KBcxuM-qXec
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.
The "focus" on planets doesn't work quite correctly. I love that you included true size, but it would be great if the focus worked, and one could zoom between the planets (until the planet shows up).
I also think Saturn's rings don't wobble that fast.
Really cool and I love educational apps like this. One suggestion is to show the rotation of the earth as the particles come together to form it rather than a static image.
Step 5 shows the earth going as slow as 21.5 km/sec at aphelion and as fast as 39km/sec at the perihelion. I believe that should be closer to 29.3 and 30.3 km/sec, respectively.
Really cool project. I'm curious what was the most surprising thing you learned while building this that changed your own understanding of how gravity or orbits work?
What I did is a straight forward model, yet it's still complex. The way to figure it out how it works by observation from earth without tools we have now it's insane. How Copernicus, Kepler, Galilei, Newton, Hubble, Einstein figure it out it just amazing. Science deserves all the kudos!
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
Another interesting concept here is that the solar system is a second generation(minimum) system, too much iron+ for a first generation system. So the first generation star had explode to form all the heavy metals. Where is the original stellar remnant? Is there a Black hole or neutron star or whatever it is called if it can't even make it to neutron star levels in roughly the same galactic orbit as our sun?.
A good follow up question that nobody knows the answer to is "how much iron is in the sun?" The problem as I understand it is we can only directly see the very outer layer where there is no iron, so the standard answer is statistically none, only fractional percentages. But based on the distribution of elements in the solar system I sort of expect a sizable iron core.
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.
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
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.
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.
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.
This is exactly right; the phenomenon is known as axial parallelism.
Oh neat, didn't realize there was a term for it!
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.
>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.
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.
Seems like somehow orbiting bodies finally come to an "equilibrium point"... where orbital speed cancels out gravitational pull towards the sun, so a balance is achieved ?
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.
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.)
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.
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!
Very nice! Nitpick: the Moon is tidally locked, so it should always face the Earth with the same side.
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...
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 fun! It would be cool to get new updates that model ongoing/future satellite launches or Artemis missions.
Very cool!
Just one note about the moon orbit around the Earth, it is far more subtle; almost just orbiting the Sun alongside Earth. I can't explain better than minute physics, highly recommend: youtube.com/watch?v=KBcxuM-qXec
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
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.
Looks very cool!
The "focus" on planets doesn't work quite correctly. I love that you included true size, but it would be great if the focus worked, and one could zoom between the planets (until the planet shows up).
I also think Saturn's rings don't wobble that fast.
Really cool and I love educational apps like this. One suggestion is to show the rotation of the earth as the particles come together to form it rather than a static image.
Step 5 shows the earth going as slow as 21.5 km/sec at aphelion and as fast as 39km/sec at the perihelion. I believe that should be closer to 29.3 and 30.3 km/sec, respectively.
Really cool project. I'm curious what was the most surprising thing you learned while building this that changed your own understanding of how gravity or orbits work?
What I did is a straight forward model, yet it's still complex. The way to figure it out how it works by observation from earth without tools we have now it's insane. How Copernicus, Kepler, Galilei, Newton, Hubble, Einstein figure it out it just amazing. Science deserves all the kudos!
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.
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
Another interesting concept here is that the solar system is a second generation(minimum) system, too much iron+ for a first generation system. So the first generation star had explode to form all the heavy metals. Where is the original stellar remnant? Is there a Black hole or neutron star or whatever it is called if it can't even make it to neutron star levels in roughly the same galactic orbit as our sun?.
A good follow up question that nobody knows the answer to is "how much iron is in the sun?" The problem as I understand it is we can only directly see the very outer layer where there is no iron, so the standard answer is statistically none, only fractional percentages. But based on the distribution of elements in the solar system I sort of expect a sizable iron core.
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.
Neat. How about mentioning the massive black holes at the center of the galaxies?
I though about this, I'll come in some iteration i suppose
I like it a lot. I'll show to my daughter. Thank you!
That doesn’t look right: in the 7th panel (too fast it escapes) the force and velocity of earth are constant? 0_o
Very nice. My kid is going to love this. Thank you!
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
Oh wow I never knew Saturn was tilted so much
This is just awesome. Thank you.
wow, that's amazing—a very good way to learn this.