You are truly a phenomenal teacher and explainer, with an extraordinary ability to distill beautiful understanding out of great complexity! Thank you for all your hard work in sharing your intellect and talent with us. I'm an instant subscriber for life, and will definitely share your Top-Notch content with others! Thanks again!😊
I'll admit that I made it all the way to about 13 minutes in until the realization that you were basically constructing a complex Fourier series struck me like, well, an orbiting satellite... just after I had some flashbacks to the brachistochrone. I'm curious about what would happen if we restricted the assumption regarding the planet's sphere of influence and turned it into something closer to a true three-body problem; I suppose that'd be an entirely different chapter! In any case, seriously cool (and very on-brand) way to tie a common thread between a whole bunch of concepts.
By the way, the true three-body problem should behave almost exactly as shown in this video, at least for the parameters shown. In other words, this nearly square orbit is a real solution and likely exists somewhere in the Universe. However, as more and more objects are added (as will be done in the follow-up video), the interactions will become more problematic.
Considering additional moons to solve this problem, sound a lot like using Fourier series to approximate the square shape. Great video, beautifully done !!!
@@AllThingsPhysicsTH-cam In this (th-cam.com/video/r6sGWTCMz2k/w-d-xo.html) video first few seconds show a close resemblence of the star-planet-moons system, and I think you can use it to achieve greater results, given the information in the video.
There is only one general way to make approximations using Harmonic Series, especially approximations of regular polygons inside of a Euclidean space. Fourier transforms and Z-transforms are the way and the answer :)
That's literally exactly what it is - if you wanted to look at the "North-South" distance of the moon from the sun and plot it on a horizontal axis, you'd be using sine and cosine functions to generate a square wave. With a complex enough system of sub-moons (and assuming each subsystem is independent from all the others) you could create an orbit of any shape you like. You could even encode a sound wave :)
Thanks. I've been surprised to see a few people comment that they find the music distracting. I thought the volume was low enough that nobody would be bothered by it.
I love how the kind of people who'd watch this video would all already know what 3b1b means. We're all part of the same slice of the universe, alternating between videos from Derek, Destin, Dianna, and the rest. Cool. This channel is today's discovery. I'm a subscriber now.
I tried something similar myself when I tried make an animation that makes a square with just rotations and got the same result and I was hoping I could make exactly a square, well that didn't work out, but I found the right radius for each rotation by using triangles and Pythagorases law. I tried to make an equation where the 'planet' radius minus the 'moon' radius would be the same length as half the diagonal of the square to reach the corner. I was actually really proud of this solution and the animation looked sick either, this is a great video and helped understanding the enormous dimensions that our solar system is, thank you
Heh. After 12 days this video had about 1200 views and the subscribers were at around 200. And then, bam, the algorithm showed me some love! I hope it continues!
I'm a big fan of veritasium, vsauce etc, you're the next big thing man, super interesting, fascinating, crystal clear, great voice, great music, super chill, i really hope you blow up soon you're the man
Definitely a relationship with Fourier series. You could construct a square with an infinite number of planets, where the amplitudes of the Fourier series for a square equate to the radii of the orbits. I'm not sure if you can ensure the masses or radii vanish fast enough to meet the orbit criterion, but so long as you had points with that separation it would form a square.
From my experiences from 3b1b, my first thought was "well you could always make a Fourier series," what I was particularly surprised was how we essentially constructed one through astronomical terms and equations, and how much it resembled a square with just two rotational objects. Rubinetti's music is always a good way to set the learning mood, and I didn't even notice for the first few minutes! Well made, very smooth.
I love finding videos like these by up and coming TH-camrs that explain things so amazingly well. Keep up the great work, and you’ve more than earned my subscription!
As a Kerbal Space Program player, there is another way to make celestial bodies. 1. Construct a spaceship with a part clipped into another. According to Pauli exclusion principle, this will generate an enormous repulsion force, launching the part to billions of times the speed of light. 2. As the physics engine crumbles to dust under the vast distances that the object travelled, planetary orbits will become square and shaky, the planets themselves spaghettify.
16:16 I was actually writing a comment about the Hill radius when I was watching by 4:20, but you explained this very well by the end of the video. Very well done, sir!
Thanks. I almost discussed the Hill radius earlier in the video, but it seemed a bit out of place and distracting, so I decided to hold off until the end.
Timing of speech, music, animations, all on point. Well done! I'm no physicist, i'm just a curious programmer, but man I loved your format. I wish I've had better physics teachers in my youth...
Glad you like it. Please feel free to spread the word! By the way, I have a collaborator (Jose A. Miranda) who teaches at Universidade Federal de Pernambuco.
@3:41 if you are watching on a phone or small screen that you can shake, if you shake the screen you might be able to see that the apparent circle is not actually a circle. Thank you again for the attention to detail. It deserves a follow!
Woah that’s so amazing!! My first idea when I just saw the question was to somehow change the relative masses of the objects in just a two object system, so you could vary the gravitational force and therefore vary the distance between them. I knew that idea wouldn’t really be possible irl so I was really blown away when I watched this. Thanks :)
I'm glad I clicked on this video. Very well done! I looked at your page expecting to see many videos, given how high quality this one is. The fact that this is only your 4th video on this channel is truly amazing!
Wow, thank you! At this point I'm sort of embarrassed by the first one, but I guess we all gotta start somewhere. Hopefully the quality will continue to go up.
Tidal forces would preclude an orbit like this which is why we dont see it in nature even though its entirely possible (or we'd only see it happen for a short time)
3:20 "in order to form a closed path the moon would need to complete an integer number of orbits around earth in one year a condition that's extremely unlikely to arise by random chance". We seem to see a lot of small integer ratios in the solar system. A lot more than you would expect by chance.
That's true. Perhaps given enough time our moon would end up with a closed trajectory. I think there are sometimes subtle interactions at play in many systems that are often ignored, and such interactions can lead to ratios that seem surprising.
thats because of orbital resonance, which pushes the orbits of satellites to become that way. Here's a neat video: th-cam.com/video/Qyn64b4LNJ0/w-d-xo.html
@@person8064 Interesting. However, this video seems to suggest that it is critical that one of the orbits be elliptical, so this may not apply if all orbits are circular.
Amazing video! With such good explanations, it's weird to see that you only have ~1600 subscribers. More people need to see this, and I hope they will. I think your channel will blow up eventually
When this video was posted there were only 155 subscribers (approximately). So in some sense the channel already has blown up, but I'm hoping it continues!
I don't know what impress me the most : the fact that almost-square orbits are really a thing somewhere in the universe, or the stunning quality of that video. Either way, I will definitely be orbiting around your channel now that I subscribed. Thank you for that content !
I'm puzzled by something. If gravitational attraction is proportional to mass and inversely proportional to the square of the distance, and the sun is 333,000 times more massive than the earth, then the gravitational attraction of the earth and sun would be equal when the distance from the sun is the square root of 333,000 (about 577) times the distance to the earth. In the square orbit diagram in this video, the distance of the moon from the earth is much greater than 1/577th its distance to the sun, which means the sun would have a much greater influence on its orbit than the earth. Wouldn't this change the shape of the orbit? What am I missing here?
What you're missing is some very subtle calculations. You are correct that the gravitational force on the moon from the star is larger than the gravitational force on the moon from the planet. But that doesn't necessarily mean that the star will influence the moon more so than the planet. That's what the Hill sphere discussion was all about. It's a bit subtle, but as long as the moon is "close enough" to the planet, then the planet and moon act as a subsystem as if the star were not there at all (in terms of the moon's orbit around the planet). What "close enough" means here is that the moon needs to be within the radius of the Hill sphere of the planet. I hope that makes some sense. By the way, your TH-cam channel looks quite interesting. I play guitar and mandolin and when I was young my goal was to be a rock musician.
The entire Planet-Moon system is falling towards the Star. The Star's pull on the Planet is very similar to the Star's pull on the Moon, and the difference between these is easily overcome by the Planet and Moon's pull on each other.
If the earth and moon suddenly stopped having gravity, both the earth and the moon would continue orbiting the sun at the exact same distance. If you turn on the earth's gravity again, the moon continues to orbit the sun along with the earth, but also slowly orbits the earth in addition to its normal solar orbit.
The key part you're missing is that the planet is also being pulled by the star. You need to think of this relative to the planet. In that case, the star isn't pulling on the moon much, because the star is pulling on the planet a bit less. What you actually need to calculate is if the difference between the stars pull on the moon and planet is greater than the planets pull on the moon. The Hill sphere that the video goes over is the place where this is the case, and so the moon's orbit is stable.
Perhaps unsurprisingly, square orbits occupy a similar space to squaring the circle. You're right, it's fascinating when two seemingly unrelated concepts share some deeper connection
This moons orbit has its most distant point from the sun at about sqrt(2) times the closest distance. Right? Would that imply that moon has seasons that are in fact driven by orbital distance as opposed to our home planet where they come from the axial tilt? If so it would experience four summers and winters each year! How would the swing in temperatures compare to the seasons we experience in medium latitudes?
Interesting thought, and one I had not thought about. Considering the distances involved, the moon would certainly experience "seasons" as a result of its orbit and so I believe you are correct; four summers and four winters per year! Cool!
Yes, I had the same thought. The difference between summer and winter would be quite severe, since the solar irradiance would vary by a factor of (sqrt(2))^2=2. Twice as much sunlight in summer than in winter!
Great video! One piece of feedback I would give is that at 9:42 you go from a dark background to a white one and that really hurt as a person watching your video at night in a dark room. I would suggest either keeping to a dark background throughout, or not switching so quickly between contrasting backgrounds.
Idk I think that’s being too critical. They kinda require opposite backgrounds and he did do a transition. I just keep my phone so dark that can’t even happen lol
The part that surprised me the most was how at the end this basically turned out to be the same as the engineering problem of turning rotational motion into linear motion. Mind is truly blown
I don't know what to add other than that I like this video a lot. Really reminding me why I went to university in the first place. I'm happy I stumbled upon this.
Oh hey, like Engare! That's this little indie simulator/puzzle game thing about drawing outlines with orbits like this. It comes at this all from an art direction instead of a physics one, so it had little in the way of explanations and equations- but it did give me a general feel for this sort of thing.
Wooooow this channel has less subscribers than me, that is a shame for the entire universe. When I clicked on this video I didn't know what to expect but when I started watching I was hooked immediately, what an amazing way to explain the shapes orbits draw out. I wish you the best of luck with your channel, and will post a shot-out to my community tab, in case it reaches somebody. Never subscribed with such determination before.
Thank you so much. I really appreciate the comment and the shout-out! And with all due respect, I hope to surpass the number of subscribers on your channel before too long! ;)
As a kid, when I first heard about the epicycles theory (that old disproven theory that Mercury and Venus do "epicycles" around the sun, back in the days of geocentrism) and learned that the orbit style could be simulated by a moon around a planet, and tracing the moon's path around the star, I pretty much instantly was like "oh yeah so a moon orbiting its planet four times would draw a square, no?" Glad to see one of my childhood dreams being genuinely possible
I figured that eventually you'd have to increase the number of bodies orbiting in increasing numbers in ideal circular orbits to create a square orbit because of the concept of additive synthesis in music, where you can add octave harmonics of sine waves infinitely when in a particular phase with each other to create a square wave.
I appreciate the last few minutes of this video about making a perfect square! When I clicked, knowing how the Foriere transform works, I knew it could be possible with enough individual orbits at the right radii and frequencies. That said, I was curious whether those radii and frequencies would actually result in stable orbits or if the system would be unstable and fail to actually draw the square orbit. Looking forward to the follow up! Fantastic video though, really amazing quality throughout, good pacing and great depth!
13:48 hmm, kinda new point emphasized super well to be engrained in memory that the opposite sense of rotation in fourier series can provide access to farther - more corner like areas
The same sense rotation leads to faster motion at a larger distance from the star and a slower motion when closer to the star, while the opposite sense rotation does the opposite: slower motion when farther from the star and faster motion when closer.
You're going to take off man. Your presentation abilities are mature, the audio is pretty good, the animations are better than any reasonable youtuber could hope for, the camera/ lighting/ staging has room for improvement. But hey, this is what you do when you start a youtube channel, you hang up some sheets and get going and I'm shying away at video editing and you obviously know what you're doing.
Thanks. You’ve absolutely nailed it, though I’m unhappy with the live narration audio as well as the camera/lighting/staging stuff. But as you said, you gotta start somewhere. If you wait until everything is perfect, you’ll never get started. So up went the sheets and on went the camera. I do hope you’re also correct that this channel will get big. Feel free to share with others you think might be interested.
From the video title, I thought this was gonna be about a Fourier series of many objects around eachother. I'm amazed it works this well with just one moon.
Can't wait for part 2 :D Also, I'm always looking for new content creators like this and, based on this video, I'm excited to see what your future holds
Welcome aboard! And I too am excited to see what the future holds. I've got a huge list of videos already planned out, and it looks like the TH-cam algorithm has taken a bit of a liking to this latest video. Hopefully that will continue to happen with future videos!
The moment you mentioned a moon orbiting a planet orbiting a star it clicked in my brain that a square orbit was possible. I thought of the traditional idea of a singular small object orbiting a larger object.
I assumed you were going use more than 3 objects. Adding the orbits in a similar way to how you can make a square wave by adding up a series of sin waves
A long time ago people weren't sure how to make the orbits of planets circular when they looked odd, really elliptical. So they added epicycles and sub-epicycles and sub-sub-epicycles, ad nauseam. Weirdly enough if there are an infinite number of epicycles a circle can turn into an ellipse.
I want to see the corrected orbit. There are even online gravity simulators, so it would have been easy to show us a more accurate orbit, rather than assuming that the moon's orbit is a circle around its planet.
True, but the point is not to calculate the most accurate orbit, the point is how amazingly square an orbit you can get with a single moon! But, I do address this briefly in the follow-up video.
@@AllThingsPhysicsTH-cam Thank you for replying! By showing a non-physical "orbit", that point is not made, however, as that approximation might be insufficient for such extreme orbits (particularly in terms of stability). I just watched the follow up, which is nice, but really isn't about orbits at all anymore. I did notice you mention these issues. However, I don't see the point of talking about orbits at that point. If the pretense of orbits had been dropped from the beginning (explaining that it really was a ruse to talk about Fourier series), I would have no issue with it.
@@alterego3734 I think I see what you're saying. I'm not quite sure I understand what you mean by a "non-physical orbit." Does Earth orbit the sun? Yes. Is Earth's orbit a perfect ellipse? No, it is tweaked by many other objects. Do we still say Earth orbits the Sun? Yes. Similarly, a moon can orbit a star; the orbit is just tweaked (massively) by the presence of the planet. There is nothing "non-physical" about it. It is true that I approach the (original) problem using approximations, but that is almost always the case in physics, and I am very careful to follow up at the end and demonstrate that those approximations are satisfied. That's what the whole Hill sphere calculation is about. I believe that justifies everything I've done as being completely "physical", even though still done using approximations. And the three-body calculation shown in the follow-up video is "proof" (in a sense) that everything works out as expected. In the follow-up video, we begin by assuming the same approximations. I mean, why not, it worked great the first time? This approach then leads to the idea of moons upon moons and Fourier series, and allows us to "solve" the problem. But, I am careful to point out that the approximations do NOT hold in this case so that the final result is "unphysical." So while it is true that *I* knew in advance that the final result would be unphysical, I think the story would be much less compelling to the viewer if approached it by saying, "here's something that doesn't work, but let's do it anyway so I can talk about Fourier series." I think it's pretty clear by the end that this was (more-or-less) a "ruse" to talk about Fourier series, but I did it in a way that an actual physicist might have approached such a problem without knowing the answer in advance. And I would argue there's real value in that!
With just the right mass and speed, definitely plausible. However improbable, the universe has infinite times to try to make it happen which means its almost certain such a orbit actually occurs somewhere.
It certainly wouldn't be stable. Things would soon get out of sync, due to the numbers not being perfect, and if not that, then due to the effects of other objects and if not that, then due to the relativistic effects which would ultimately ruin it by gravitational radiation if nothing else.
@@medexamtoolscom You're right, but I don't think a minimum orbital count was specified. Now that I think about it, calculating the orbital derivative with respect to each orbital distance would be an interesting problem, as well.
You are truly a phenomenal teacher and explainer, with an extraordinary ability to distill beautiful understanding out of great complexity! Thank you for all your hard work in sharing your intellect and talent with us. I'm an instant subscriber for life, and will definitely share your Top-Notch content with others!
Thanks again!😊
Wow. I am truly honored by this message; it's hard to put into words how much I appreciate it.
@@AllThingsPhysicsTH-cam hi love it
Yep.
I'll admit that I made it all the way to about 13 minutes in until the realization that you were basically constructing a complex Fourier series struck me like, well, an orbiting satellite... just after I had some flashbacks to the brachistochrone. I'm curious about what would happen if we restricted the assumption regarding the planet's sphere of influence and turned it into something closer to a true three-body problem; I suppose that'd be an entirely different chapter! In any case, seriously cool (and very on-brand) way to tie a common thread between a whole bunch of concepts.
You are absolutely correct that Fourier series is where I'm headed, and the results are pretty spectacular. Be sure to watch the sequel!
It took me until one of the last animations with the rotating arrows to realize why it looked so familiar
By the way, the true three-body problem should behave almost exactly as shown in this video, at least for the parameters shown. In other words, this nearly square orbit is a real solution and likely exists somewhere in the Universe. However, as more and more objects are added (as will be done in the follow-up video), the interactions will become more problematic.
@@AllThingsPhysicsTH-cam would a many-body simulation at the end be an appropriate conclusion to the series?
@@AllThingsPhysicsTH-cam I thought this was the case
Considering additional moons to solve this problem, sound a lot like using Fourier series to approximate the square shape. Great video, beautifully done !!!
You're correct that Fourier is where I'm headed. Be sure to come back for the sequel, it's really cool!
@@AllThingsPhysicsTH-cam In this (th-cam.com/video/r6sGWTCMz2k/w-d-xo.html) video first few seconds show a close resemblence of the star-planet-moons system, and I think you can use it to achieve greater results, given the information in the video.
There is only one general way to make approximations using Harmonic Series, especially approximations of regular polygons inside of a Euclidean space. Fourier transforms and Z-transforms are the way and the answer :)
That's literally exactly what it is - if you wanted to look at the "North-South" distance of the moon from the sun and plot it on a horizontal axis, you'd be using sine and cosine functions to generate a square wave. With a complex enough system of sub-moons (and assuming each subsystem is independent from all the others) you could create an orbit of any shape you like. You could even encode a sound wave :)
just what I was thinkink.
What a great video, I especially love the chill 3b1b-ish vibe the subtile music adds!
Thanks. I've been surprised to see a few people comment that they find the music distracting. I thought the volume was low enough that nobody would be bothered by it.
Imo it is not distracting, and adds to the ambiance for this type of video
Do you see the similarities to this video? th-cam.com/video/r6sGWTCMz2k/w-d-xo.html&ab_channel=3Blue1Brown
@@AllThingsPhysicsTH-cam I think it was great. Definitely 3b1b vibes
I love how the kind of people who'd watch this video would all already know what 3b1b means. We're all part of the same slice of the universe, alternating between videos from Derek, Destin, Dianna, and the rest. Cool. This channel is today's discovery. I'm a subscriber now.
I'm absolutely shocked at the quality of the video. Thanks for teaching me something new. You've got my subscription, and hopefully many more!
Wow, thanks!
agreed, you deserve way more subs!
this
Good job. This videos goes straight to my “show to classroom” playlist!
Awesome!
I tried something similar myself when I tried make an animation that makes a square with just rotations and got the same result and I was hoping I could make exactly a square, well that didn't work out, but I found the right radius for each rotation by using triangles and Pythagorases law. I tried to make an equation where the 'planet' radius minus the 'moon' radius would be the same length as half the diagonal of the square to reach the corner.
I was actually really proud of this solution and the animation looked sick either, this is a great video and helped understanding the enormous dimensions that our solar system is, thank you
Wow, sounds like you really worked out something cool. Good for you!
3blue1brown but physics, exactly what we need.
Glad you approve! Please help spread the word!
Very cool, my favorite thing about TH-cam is finding hidden gems like this. Looking forward to a continuation!
Awesome, thank you!
Man was blessed by the algorithm and I am so thankful
Heh. After 12 days this video had about 1200 views and the subscribers were at around 200. And then, bam, the algorithm showed me some love! I hope it continues!
I'm a big fan of veritasium, vsauce etc, you're the next big thing man, super interesting, fascinating, crystal clear, great voice, great music, super chill, i really hope you blow up soon you're the man
Thanks so much! I hope so too! Please feel free to share with others who might be interested!
I can't believe you got all the way through this video without saying Fourier Series, I was screaming it at the TV..
Heh…I didn’t want to scare anyone away, and there’s really no need to say those words in this video. But just you wait!!
That's quality content, I am curious to see the relationship between the truly square orbit and Fourier transforms
Thanks. And yes, stay tuned for the next video, the connection to Fourier analysis is really cool!
Definitely a relationship with Fourier series. You could construct a square with an infinite number of planets, where the amplitudes of the Fourier series for a square equate to the radii of the orbits. I'm not sure if you can ensure the masses or radii vanish fast enough to meet the orbit criterion, but so long as you had points with that separation it would form a square.
@@binaryblade2 Indeed you are correct, and this is precisely what I'm working on. It's very cool (as you probably already know)!
Yes, I was thinking you could simply add a moon to the moon and get even closer
3b1b did it.
From my experiences from 3b1b, my first thought was "well you could always make a Fourier series," what I was particularly surprised was how we essentially constructed one through astronomical terms and equations, and how much it resembled a square with just two rotational objects. Rubinetti's music is always a good way to set the learning mood, and I didn't even notice for the first few minutes! Well made, very smooth.
Thanks! Feel free to share with others who might be interested!
I love finding videos like these by up and coming TH-camrs that explain things so amazingly well. Keep up the great work, and you’ve more than earned my subscription!
Thanks so much!
As a Kerbal Space Program player, there is another way to make celestial bodies.
1. Construct a spaceship with a part clipped into another. According to Pauli exclusion principle, this will generate an enormous repulsion force, launching the part to billions of times the speed of light.
2. As the physics engine crumbles to dust under the vast distances that the object travelled, planetary orbits will become square and shaky, the planets themselves spaghettify.
Awesome video.. Very very cool.. And the animations were beautiful. The whole video is incredible..
Thank you. So glad you liked it!
Yeah, I liked the interaction with the animation, too! :-)
3blue1brown fans got recommended this channel at the same time :) with similar style and quality, hope this channel got bigger!
16:16 I was actually writing a comment about the Hill radius when I was watching by 4:20, but you explained this very well by the end of the video. Very well done, sir!
Thanks. I almost discussed the Hill radius earlier in the video, but it seemed a bit out of place and distracting, so I decided to hold off until the end.
The video says it was posted 2 weeks ago, but the vibes are like early 2000s educational tv show and I am LOVING IT
Glad you like it!
This reminds me of the Smarter Every Day video where Devin showed you can draw any shape by concatenating sine curves.
Timing of speech, music, animations, all on point. Well done!
I'm no physicist, i'm just a curious programmer, but man I loved your format.
I wish I've had better physics teachers in my youth...
Thanks. I appreciate your noticing the little things!
I'm from Brazil and I'm always looking for new good science channels to watch, I loved this video, do more if possible
Glad you like it. Please feel free to spread the word! By the way, I have a collaborator (Jose A. Miranda) who teaches at Universidade Federal de Pernambuco.
i'm from Brazil too
I feel so lucky finding excellent content from rising channels like this, not just the random nonsense the algorithm usually recommends.
Glad to hear it. Feel free to share with others who might be interested so the channel will grow!
I was so sure to hear the word ‘Fourier series’ at least once in the whole video 😅 guess there has to be a sequel now
And a sequel there will be!
I finally understand what a sidereal month is, thanks! Some things need to be seen to be easily understood.
Agreed…visualizations are super helpful!
I found a new Physics channel! Yay!!
You did indeed! I hope you enjoy it!
@3:41 if you are watching on a phone or small screen that you can shake, if you shake the screen you might be able to see that the apparent circle is not actually a circle.
Thank you again for the attention to detail.
It deserves a follow!
Thanks! Please consider sharing with others who might be interested!
Woah that’s so amazing!! My first idea when I just saw the question was to somehow change the relative masses of the objects in just a two object system, so you could vary the gravitational force and therefore vary the distance between them. I knew that idea wouldn’t really be possible irl so I was really blown away when I watched this. Thanks :)
My pleasure. Stay tuned for the sequel!
wow, i didn't expect after watching this that this channel has so few subscribers. deserves at least 100k
Wow, thanks! Feel free to share with anyone you think might be interested!
This is fantastic! Excellent work. Truly good stuff.
Thanks so much!
I love how this video was kind of in the style of 3blue1brown. Same quality as 3b1b as well, might I add. Thank you so much for this.
Thanks for watching. Feel free to share with others who might be interested!
Maybe consider the fourier series of square and check if all the mass relation still hold will do? Very interesting question.
Indeed. Excellent thinking. And yes, this is precisely where the next video is headed!
This is my train of thought exactly before clicking on the video. :3 great ideas
I'm glad I clicked on this video. Very well done! I looked at your page expecting to see many videos, given how high quality this one is. The fact that this is only your 4th video on this channel is truly amazing!
Wow, thank you! At this point I'm sort of embarrassed by the first one, but I guess we all gotta start somewhere. Hopefully the quality will continue to go up.
This reminded me of FFT drawings. I suppose you could use the FFT to arrange the bodies in a way that their orbits draw whatever you like.
You're right, and that's where I'm going in the next video. Be sure to check it out!
Tidal forces would preclude an orbit like this which is why we dont see it in nature even though its entirely possible (or we'd only see it happen for a short time)
3:20 "in order to form a closed path the moon would need to complete an integer number of orbits around earth in one year a condition that's extremely unlikely to arise by random chance". We seem to see a lot of small integer ratios in the solar system. A lot more than you would expect by chance.
That's true. Perhaps given enough time our moon would end up with a closed trajectory. I think there are sometimes subtle interactions at play in many systems that are often ignored, and such interactions can lead to ratios that seem surprising.
thats because of orbital resonance, which pushes the orbits of satellites to become that way. Here's a neat video:
th-cam.com/video/Qyn64b4LNJ0/w-d-xo.html
@@person8064 Interesting. However, this video seems to suggest that it is critical that one of the orbits be elliptical, so this may not apply if all orbits are circular.
@@person8064 Isn't it true that because of orbital resonance, they will *always* converge on a "small" integer ratio?
I keep coming back to this video. I've seen all the pieces before, but the way you put it all together just blows my mind.@@AllThingsPhysicsTH-cam
I am fully confident that someone will attempt to pull this off at some future point in humanity’s existence.
Amazing video! With such good explanations, it's weird to see that you only have ~1600 subscribers. More people need to see this, and I hope they will. I think your channel will blow up eventually
When this video was posted there were only 155 subscribers (approximately). So in some sense the channel already has blown up, but I'm hoping it continues!
I don't know what impress me the most : the fact that almost-square orbits are really a thing somewhere in the universe, or the stunning quality of that video. Either way, I will definitely be orbiting around your channel now that I subscribed. Thank you for that content !
Thanks so much for the comment. New content is on the way!
Maybe we get to "Homer Simpson" Orbits next time? :-))
I'm puzzled by something. If gravitational attraction is proportional to mass and inversely proportional to the square of the distance, and the sun is 333,000 times more massive than the earth, then the gravitational attraction of the earth and sun would be equal when the distance from the sun is the square root of 333,000 (about 577) times the distance to the earth. In the square orbit diagram in this video, the distance of the moon from the earth is much greater than 1/577th its distance to the sun, which means the sun would have a much greater influence on its orbit than the earth. Wouldn't this change the shape of the orbit? What am I missing here?
What you're missing is some very subtle calculations. You are correct that the gravitational force on the moon from the star is larger than the gravitational force on the moon from the planet. But that doesn't necessarily mean that the star will influence the moon more so than the planet. That's what the Hill sphere discussion was all about. It's a bit subtle, but as long as the moon is "close enough" to the planet, then the planet and moon act as a subsystem as if the star were not there at all (in terms of the moon's orbit around the planet). What "close enough" means here is that the moon needs to be within the radius of the Hill sphere of the planet. I hope that makes some sense.
By the way, your TH-cam channel looks quite interesting. I play guitar and mandolin and when I was young my goal was to be a rock musician.
The entire Planet-Moon system is falling towards the Star. The Star's pull on the Planet is very similar to the Star's pull on the Moon, and the difference between these is easily overcome by the Planet and Moon's pull on each other.
@@tachrayonic2982 Very well said...much better than my explanation!
If the earth and moon suddenly stopped having gravity, both the earth and the moon would continue orbiting the sun at the exact same distance. If you turn on the earth's gravity again, the moon continues to orbit the sun along with the earth, but also slowly orbits the earth in addition to its normal solar orbit.
The key part you're missing is that the planet is also being pulled by the star. You need to think of this relative to the planet. In that case, the star isn't pulling on the moon much, because the star is pulling on the planet a bit less. What you actually need to calculate is if the difference between the stars pull on the moon and planet is greater than the planets pull on the moon. The Hill sphere that the video goes over is the place where this is the case, and so the moon's orbit is stable.
Perhaps unsurprisingly, square orbits occupy a similar space to squaring the circle. You're right, it's fascinating when two seemingly unrelated concepts share some deeper connection
This moons orbit has its most distant point from the sun at about sqrt(2) times the closest distance. Right?
Would that imply that moon has seasons that are in fact driven by orbital distance as opposed to our home planet where they come from the axial tilt? If so it would experience four summers and winters each year!
How would the swing in temperatures compare to the seasons we experience in medium latitudes?
Interesting thought, and one I had not thought about. Considering the distances involved, the moon would certainly experience "seasons" as a result of its orbit and so I believe you are correct; four summers and four winters per year! Cool!
Yes, I had the same thought. The difference between summer and winter would be quite severe, since the solar irradiance would vary by a factor of (sqrt(2))^2=2. Twice as much sunlight in summer than in winter!
i love this style of video with the dark background and calming music
Glad you like it!
Great video! One piece of feedback I would give is that at 9:42 you go from a dark background to a white one and that really hurt as a person watching your video at night in a dark room. I would suggest either keeping to a dark background throughout, or not switching so quickly between contrasting backgrounds.
Good point. I never really thought about that. Thanks for the feedback!
Idk I think that’s being too critical. They kinda require opposite backgrounds and he did do a transition. I just keep my phone so dark that can’t even happen lol
The part that surprised me the most was how at the end this basically turned out to be the same as the engineering problem of turning rotational motion into linear motion. Mind is truly blown
Cool. Just wait until the follow-up video!
Impressed indeed!!
Please continue to baffle my mind!
I strongly appreciate your work!
Thank you! Will do!
Adding more and more objects makes me think of a Fourier series.
Yes! And that's precisely where I'm going in the next video. It's super cool!
I don't know what to add other than that I like this video a lot. Really reminding me why I went to university in the first place. I'm happy I stumbled upon this.
Glad you enjoyed it!
Oh hey, like Engare! That's this little indie simulator/puzzle game thing about drawing outlines with orbits like this.
It comes at this all from an art direction instead of a physics one, so it had little in the way of explanations and equations- but it did give me a general feel for this sort of thing.
When I saw the title and thumbnail, I thought "That sounds easy, you just do a Fourier Series.". I feel happy now.
Hopefully you'll feel even happier after the sequel. Stay tuned!
You're my new favorite channel. Keep them coming!
That's great to hear! And believe me there is no shortage of ideas for videos!
I can only second this comment section. You ask an interesting question and give a great explanation of how it can be answered.
Thanks so much!
I am watching this video twice! just so i can analyse the properties a little better. Heck! Maybe i'll watch it a third time!
I absolutely enjoyed this video. I never considered this possibility. Great job!!
Wooooow this channel has less subscribers than me, that is a shame for the entire universe. When I clicked on this video I didn't know what to expect but when I started watching I was hooked immediately, what an amazing way to explain the shapes orbits draw out. I wish you the best of luck with your channel, and will post a shot-out to my community tab, in case it reaches somebody. Never subscribed with such determination before.
Thank you so much. I really appreciate the comment and the shout-out! And with all due respect, I hope to surpass the number of subscribers on your channel before too long! ;)
Praise the algorithm for showing me your channel.
Love the video!
Awesome! Thank you!
As a kid, when I first heard about the epicycles theory (that old disproven theory that Mercury and Venus do "epicycles" around the sun, back in the days of geocentrism) and learned that the orbit style could be simulated by a moon around a planet, and tracing the moon's path around the star, I pretty much instantly was like "oh yeah so a moon orbiting its planet four times would draw a square, no?"
Glad to see one of my childhood dreams being genuinely possible
Glad to have helped!
Amazing what a way to spend summer break
There's more to come!
When you showed the animation, I immediately thought Fourier.
Wait until you see the follow-up video. It's really cool!
Thank you for appropriate scaling. It is SO INFORMATIVE!
Outstanding science communicator! You just made my mood swing parallel to Earth for once!
Cool!
This is the best video I've ever seen on FM synthesis
Wow. Thanks!
Criminally underrated channel! you just earned a new subscriber :)
Welcome aboard! Please feel free to share with others who might be interested!
I figured that eventually you'd have to increase the number of bodies orbiting in increasing numbers in ideal circular orbits to create a square orbit because of the concept of additive synthesis in music, where you can add octave harmonics of sine waves infinitely when in a particular phase with each other to create a square wave.
You've hit the nail on the head. Stay tuned for part 2!
Satisfying, nice and clear illustration/animation
Thank you! Cheers!
Amazing video, David! A huge Thank You!
My pleasure!
I appreciate the last few minutes of this video about making a perfect square! When I clicked, knowing how the Foriere transform works, I knew it could be possible with enough individual orbits at the right radii and frequencies. That said, I was curious whether those radii and frequencies would actually result in stable orbits or if the system would be unstable and fail to actually draw the square orbit. Looking forward to the follow up!
Fantastic video though, really amazing quality throughout, good pacing and great depth!
Thanks so much!
Dude! This is indirectly connected to the way geneva gears work
Cool! I hadn’t made this connection.
13:48 hmm, kinda new point emphasized super well to be engrained in memory that the opposite sense of rotation in fourier series can provide access to farther - more corner like areas
The same sense rotation leads to faster motion at a larger distance from the star and a slower motion when closer to the star, while the opposite sense rotation does the opposite: slower motion when farther from the star and faster motion when closer.
My guy you be lookin like Robert downy jr and Jim carry at the same time
These are the kind if videos I would have love to have watched in Science lessons back at school.
My thoughts exactly...so I decided, why not make them?
@@AllThingsPhysicsTH-cam You're doing great work sir.
The thumbnail is sooo good! And not click-bait AT ALL!
That's nice to hear...there have been a few people claiming it IS clickbait, which I don't really understand.
You're going to take off man. Your presentation abilities are mature, the audio is pretty good, the animations are better than any reasonable youtuber could hope for, the camera/ lighting/ staging has room for improvement. But hey, this is what you do when you start a youtube channel, you hang up some sheets and get going and I'm shying away at video editing and you obviously know what you're doing.
Thanks. You’ve absolutely nailed it, though I’m unhappy with the live narration audio as well as the camera/lighting/staging stuff. But as you said, you gotta start somewhere. If you wait until everything is perfect, you’ll never get started. So up went the sheets and on went the camera. I do hope you’re also correct that this channel will get big. Feel free to share with others you think might be interested.
a very sneaky and intuitive way to introduce fourier series using physics!
Heh...you noticed that, eh? I thought it was pretty slick!
From the video title, I thought this was gonna be about a Fourier series of many objects around eachother. I'm amazed it works this well with just one moon.
So way I! And don't worry, Fourier is what's coming in the sequel. Stay tuned!
Can't wait for part 2 :D Also, I'm always looking for new content creators like this and, based on this video, I'm excited to see what your future holds
Welcome aboard! And I too am excited to see what the future holds. I've got a huge list of videos already planned out, and it looks like the TH-cam algorithm has taken a bit of a liking to this latest video. Hopefully that will continue to happen with future videos!
Absolutely delightful, looking forward to the sequel!
Glad you liked it!
Great animations dude. I love to see such animations while listening to an explanation. Looking forward to see the next video
Thanks. And yes, be sure to stay tuned for the sequel!
Man this is so cool. The moment you raised the question I wanted an answer. Great video. Textbook "maybe math's actually cool" video.
Glad you liked it!
I predict huge things for this channel
Me hopes you are correct!
man hit us with a "beyond the scope of this course" in a youtube video he has full creative control over 😭😭
I was ready for the narrator voice to turn into 3b1b and starting to talk about Fourier Transforms at any point, lol
Heh. Just wait until the sequel!
I'm fascinated to see what kind of seasons would exist on that kind of orbit.
Yes, it's an interesting question because the "seasons" would be governed by the distance from the star instead of the planet's (or moon's) tilt.
This is a very well thought out video. I can’t believe I’ve never heard of this channel before!
Glad you liked it! (And you've never heard of this channel before because it hasn't been around very long.)
Really Impressive analysis. Very much impressive. Waiting for the part 2..
Part 2 will be even better (in my opinion)!
Truly the Bob Ross of physics!
This immediately struck me as a fourier series. All you need is more orbits.
That's where I'm headed in part 2. Stay tuned!
I love how conjecture is piled on conjecture piled on conjecture.
Great vid, looking forward to the next part.
Coming soon!
I did understand intuitively the solution before I started to watch, but I stayed for the mathematics. Good video ✌️
Excellent!
i liked / thumbed the video directly because i like your set up, you speak well and you use animation on screen.
Awesome! Thanks!
The moment you mentioned a moon orbiting a planet orbiting a star it clicked in my brain that a square orbit was possible. I thought of the traditional idea of a singular small object orbiting a larger object.
I assumed you were going use more than 3 objects. Adding the orbits in a similar way to how you can make a square wave by adding up a series of sin waves
Go watch part 2!
@@AllThingsPhysicsTH-cam thank you. I did, and part 3. I only recently came across your channel. I'm really enjoying it.
A long time ago people weren't sure how to make the orbits of planets circular when they looked odd, really elliptical.
So they added epicycles and sub-epicycles and sub-sub-epicycles, ad nauseam.
Weirdly enough if there are an infinite number of epicycles a circle can turn into an ellipse.
That's right. And I will discuss this in detail in the next video!
Can't wait for the next video about Fourier's Series! ;D
You and me both!
I want to see the corrected orbit. There are even online gravity simulators, so it would have been easy to show us a more accurate orbit, rather than assuming that the moon's orbit is a circle around its planet.
True, but the point is not to calculate the most accurate orbit, the point is how amazingly square an orbit you can get with a single moon! But, I do address this briefly in the follow-up video.
@@AllThingsPhysicsTH-cam Thank you for replying!
By showing a non-physical "orbit", that point is not made, however, as that approximation might be insufficient for such extreme orbits (particularly in terms of stability).
I just watched the follow up, which is nice, but really isn't about orbits at all anymore.
I did notice you mention these issues. However, I don't see the point of talking about orbits at that point.
If the pretense of orbits had been dropped from the beginning (explaining that it really was a ruse to talk about Fourier series), I would have no issue with it.
@@alterego3734 I think I see what you're saying. I'm not quite sure I understand what you mean by a "non-physical orbit." Does Earth orbit the sun? Yes. Is Earth's orbit a perfect ellipse? No, it is tweaked by many other objects. Do we still say Earth orbits the Sun? Yes. Similarly, a moon can orbit a star; the orbit is just tweaked (massively) by the presence of the planet. There is nothing "non-physical" about it.
It is true that I approach the (original) problem using approximations, but that is almost always the case in physics, and I am very careful to follow up at the end and demonstrate that those approximations are satisfied. That's what the whole Hill sphere calculation is about. I believe that justifies everything I've done as being completely "physical", even though still done using approximations. And the three-body calculation shown in the follow-up video is "proof" (in a sense) that everything works out as expected.
In the follow-up video, we begin by assuming the same approximations. I mean, why not, it worked great the first time? This approach then leads to the idea of moons upon moons and Fourier series, and allows us to "solve" the problem. But, I am careful to point out that the approximations do NOT hold in this case so that the final result is "unphysical." So while it is true that *I* knew in advance that the final result would be unphysical, I think the story would be much less compelling to the viewer if approached it by saying, "here's something that doesn't work, but let's do it anyway so I can talk about Fourier series."
I think it's pretty clear by the end that this was (more-or-less) a "ruse" to talk about Fourier series, but I did it in a way that an actual physicist might have approached such a problem without knowing the answer in advance. And I would argue there's real value in that!
This channel is great, the quality of the animations really impresses me. Keep it up!
Thanks, will do!
With just the right mass and speed, definitely plausible. However improbable, the universe has infinite times to try to make it happen which means its almost certain such a orbit actually occurs somewhere.
It certainly wouldn't be stable. Things would soon get out of sync, due to the numbers not being perfect, and if not that, then due to the effects of other objects and if not that, then due to the relativistic effects which would ultimately ruin it by gravitational radiation if nothing else.
@@medexamtoolscom You're right, but I don't think a minimum orbital count was specified.
Now that I think about it, calculating the orbital derivative with respect to each orbital distance would be an interesting problem, as well.
This would be a nice introduction to a lecture on the fourier series
That's essentially what it is. Stay tuned for part 2!