They did the same with Matt's previous video. He specifically said that was a representation of a search algorithm, not a simulation of lightning, and the video title was "the lightning algorithm". Clickbait titles are bad enough, but why misrepresent (and directly contradict) what the guest says?
@@RFC-3514 It's his job to get views, and these titles do that. Don't fault him; fault the algorithm, and the people who the algorithm is built to serve.
I was teaching about frame of reference in my physics classes recently. This video will be a perfect follow up showing how the description of a planet's motion changes depending on your frame of reference. Thanks!
Hi, I'm an old quantum chemist and currently also turnung my focus of interest away from electrons orbiting nuclei to the Milky way and galaxies. You can also very nicely illustrate orbits with the Gravity Simulator /all scenarios (freely accessible on the internet). For me very fascinating switching the view to comoving systems and working with different camera views. Please let me know if this is interesting for you. PS: I have to admit, my spatial imagination is not that excellent and it sometimes takes time to comprehend it. These things are so important for astrophysics.
@@godsbeautifulflatearth i will make sure that we will be able to send people like you to space in the near future so you can see the round earth with your own eyes. you arent special. you didnt discover something "big earth" doesnt want you to know about. you just want to think that so you can have a shred of meaning in a world where you otherwise have none.
video: "has been referred to earth's 'second moon' but that's just sensationalist kind of thing" video title: The Strange Orbit of Earth's Second Moon :D
I'm more interested in this strange kidney bean orbit than another moon, strange oddities like this would be useful in determining the subatomic scale of the laws of attraction and repulsion
I love when abstract maths and science is translated through an artistic lens. Whenever I teach maths I try to use the “A picture is worth a million words” philosophy and show the reason behind the maths. This was Beautiful. Bravo.
that 0:33 moment when the mathematical model shifts perspective (as earth as the center of the universe), and how it was represented visually is so beautiful.
These are in fact the beautiful spirographic patterns that astronomers ACTUALLY observe when they look at binary star systems and their moons and 'exoplanets'. My TYCHOS model (inspired by Tycho Brahe's geoheliocentric system) demonstrates that the Sun and Mars are binary companions - and that our planets truly orbit around Earth just like shown in this video.
@@godsbeautifulflatearth quick question: why would the government try to hide earths true shape? whats the reason? there has to be a reason to spend the trillions or whatever it costs to keep the round earth "conspiracy" running.
Fun fact: Those patterns, created by orbiting bodies orbiting other orbiting bodies, are called epicycles. Before astronomers knew that the sun was at the center of our solar system, many astronomers were baffled by those strange patterns that result from assuming the earth is at the center. In order to model the patterns, they would keep adding epicycles to create a system that followed those paths. However, its been proved mathematically that you can keep adding epicycles over and over again to create a continuous path of any kind, so they could keep using them without ever noticing that a heliocentric model would be much simpler and accurate. Because of this, "adding epicycles" has become a joke phrase to mean "adding more and more fixes and details to a bad design/theory instead of ditching it for a simpler more robust one"
The Earth is the center of the universe. The Sun goes around the Earth. The planets also go around the Earth, following strange epi-cyclic patterns because they are strongly influenced by the gravity of the Sun and of one another. This is completely consistent with Einstein's notion that every reference frame is equally as valid as any other reference frame. A heliocentric model may be simpler for calculations but it is not "more accurate" - nor is it less accurate. Every reference frame is equally as valid as any other reference frame. This idea may seem non-intuitive to you but it is reality.
All reference frames are valid, but they are not all equal. Inertial reference frames play a special part in Newtonian physics and General Relativity (although they are defined differently in the two cases). In fact, both theories are created with those reference frames, and changing to others is little more than an addon. For understanding things, writing physical laws, and solving problems, inertial frames are vastly superior. So yes, one could rewrite all of physics to work in a weird reference frame where the earth is stationary, but at huge cost in both computation and intuition. At the end of the day, science isn't about some sense of absolute truth, it's about making predictions, testing their accuracy, and using this to make better predictions. If you're changing things to make predictions harder (and also improving prediction-making harder) then you've made it worse. That means all reference frames are not equal when it comes to doing science.
"They call it second moon but that's just sensationalist" Video title: "Astronomers hate him! Local mathematician finds the secret of Earth's second moon"
@@lailasharlincholet Cruithne is an asteroid at only 5km across, so calling it a moon can be considered sensationalistic (making it out to be something greater than what it is). On a completely different note, did anyone notice that Matt mentioned the numbers 5 and 13? They are part of the Fibonacci sequence which are numbers commonly found throughout nature.
@@lailasharlincholet It's not a moon/satellite of Earth, it's a satellite of the Sun, it's in orbit around the Sun. But it's known well by that name, Earth's second moon. Incidentally it was found by an Australian who named it after his pet sheep. True. :-)
Principia for KSP allows you to display these trails as well - one of the most interesting ones is the Pluto System with the bigger of the 4 smaller moons form a nearly triangular orbit and the outer one a pentagonal orbit.
Fun to see retrograde motion from an overhead perspective. It's amazing that ancient astronomers worked this out by tracing the lines of the planets across the sky on a night by night, week by week, month by month, year by year basis.
The code at 0:03 is definitely Mathematica. Many common programming languages (e.g., C++, Java, Python) are a bit annoying to do graphics with, but Mathematica and Julia are very nice for this kind of thing.
You could even do it in C, and if you know a bit of mathematics and know how to google stuff you can make your own. I posted a video on my channel showing a sphere rotating around, having little programming language experience at all, and learning as an adult.
This boy is going somewhere great. There is a shape for everything and he's noticed. The changing water droplet. The snow flake. The "emotional" influence (thought) that can change everything. This one needs to continue and be aided.
I dont think it has a choice but to continue. Its continuing right now. Could you imagine the trouble we would be in if it didnt?Oh yeah...we just left that reality. Shew...that was close lol *looks around* uh oh...
The Mars animation does a great job showing why there’s specific windows when we need to launch Mars missions, because it does get SO close (relatively) to earth for short times, and other times it is exceptionally far away. It can be very easy to imagine planets staying roughly the same distance away from each other at all times
Reminds me of a great trivia question: What planet is, on average, the closest to Earth? The answer is Mercury. And by the way, Mercury is, on average, the closest planet to EVERY planet.
@@jimmyh2137 yep. And on average, the sun is closer to the Earth than any other planet. Say you are standing near a carousel. Measure your average distance to one of the horses. Sometimes the horse is near you, but sometimes it’s on the other side of the carousel. Compare that to your distance to the center point of the carousel. Your distance to the center point is, on average, less since the horse spends more time being further away from you than the center point.
And in the previous one Matt said "this is an animation showing how a search algorithm works, it looks a bit like lightning but obviously it's not trying so simulate real lightning", and the title was "the lightning algorithm". I think I'm about one misleading clickbait title away from unsubscribing.
Wow, 1st time here. So in fact our solar system is like a tube vortex with our planets chasing the sun creating these lovely geometric patterns behind them with energy through the galaxy of the Milky Way? Facinating Didn’t know there was an asteroid that also rotates around earth. This would explain several ISS videos showing a very rocky looking small planet pass by them from time to time!
What would the epicycles of Earth look like with Mars viewed as stationary? Similarly, what would the epicycles of Mercury look like with Venus viewed as stationary?
I can’t believe this! I’ve always been taught that Tolemaic/Aristotelian astronomy was “ugly” and complicated… now, complicated it looks for sure, but actually the patterns of epicycles of sun and planets “around the Earth” are beautiful! Astronomers before Copernicus would have had nightmares trying to calculate planetary orbits, but what a mathematical insight they must have had if they could do it without computers! Thank you 🙏 for showing this incredibly fascinating world from Earth’s perspective!!! By the way how is it possible that the planets all have such an amazingly symmetrical apparent orbit around the Earth? What if you were watching from any other planet? Would you get similar patterns? And what if you were watching from any random moon? Would you still see anything similar? Can you make your next videos on these topics? 🙏👏
I find it fascinating how similar the patterns look like windings on electric motors. Even more fascinating was the fact I didn’t get to see the pattern the Earth makes in full? Now that would have been interesting
@@maggieme8220 we dont need any more proof that earth IS special. We need more ppl to see those proofs that Earth IS special. If i worded that correctly it will make perfect sense. If not this should be your third attempt to try to make sense of it. Seeing how simple things are complicated to hide true meaning our trained brains overlook the complications set in place to complicate things. That pattern isnt natural. Thats why it feels like it does. Js
@@onthelvl8291 Just because you see a pleasing pattern, does not mean it isn't natural. Nature is filled with pleasing designs, and most are modeled with surprisingly simple mathematics. The fact that we find them pleasing does not make them unnatural or imply design.
My TYCHOS model (inspired by Tycho Brahe's geoheliocentric system) demonstrates that the Sun and Mars are binary companions - and that our planets truly orbit around Earth just like shown in this video.
Thank you for letting those orbits play out. If there's video of that for each of the planets, or somewhere people can play with the tool themselves, I'd love a link to it.
I would love to see the Lagrange points and see what they look like spatially along with (gravitational cancellation boundaries) and how that changes with the orbits.
Shouldn't Lagrange points be rotating in a circular orbit around Earth, like the Sun? They stay at a fixed distance and are at a fixed angle relative to the line between Earth and the Sun
1:56 Those shapes traced out are called epitrochoids which are very similar to epicycloids, except epicycloids have sharp points instead of the little loops like these ones have.
This is cool. Wish I could play with this program. A few possible improvements: 1. Exact placement of planets on a specific date so that their orbits coincide with what we see outside. 2. Tighter control of precise relationships. (The 8 to 13 ratio could be fine tuned.) The 5 pointed Venus orbit would not be so perfect. 3. The asteroid's orbit is shown with BOTH the earth and sun shown stationary. They can't both be stationary.
Something that I think is worth mentioning is @5:07 to 5:08 in the video when comparing the orbits of Earth and Venus you can see that they trace out a Cardioid that you can also see emerge within the Mandelbrot Set.
One of the philosophical implications of Einstein's "Relativity" is that, since every reference frame is as valid as every other reference frame, it is perfectly acceptable to consider the Earth the center of the universe. That may make the mathematics rather complicated sometimes (as seen in the beautiful but complex orbital simulation graphic) but it's perfectly valid. I very much like thinking of the Earth as the center of the universe. There are no observations to dispute the notion.
@@SimonFoster63 - Can we not consider the Earth as standing still and that all other astronomical bodies are in motion? (just as in the narrator's spirograph animation - the Earth is the center of the spirograph.) That would make us an inertial reference frame. ("hypotrochoid" and "epitrochoid" are so hard to pronounce and such unfamiliar terms, I just call them "spirographs.")
@@SimonFoster63 - The Earth is not accelerating in relation to the Earth. You are standing (or sitting) on the Earth. You are not accelerating in relation to the Earth and you are the observer. Therefore, the Earth is an inertial reference frame for you. (If this is a new idea to you then you are in store for great joy when you wrap your head around it. One of those "a-ha" moments.)
@@rubiks6 Actually, you are accelerating vs. the Earth. What do you think keeps your feet sticking to the ground? (Hint: look up "equivalence principle"). The surface of a massive body is by no means an 'inertial reference frame' from the standpoint of General Relativity. What you are discussing - and it's a perfectly valid approximation, given the speeds and precision involved - is Galilean Relativity. Don't need Einstein for that.
My sentiments are about the same as everyone else here. I love watching Numberphile, and am subscribed to it, so I mostly ignore the titles. Still, it's a disservice to both your guests and your viewers to blatantly misrepresent the video. I love the channel for it's topics on maths and sciences, not for propagating conspiracy theories.
Our current understanding of universe is like a narrow gap, I’m not talking about technologies, to be able to see the whole picture first we need to become one inside, otherwise everything around us can not go any further than magic, you are also a part of the universe
Yeah go outside and verify your reality. It won't match with any first hand evidence. We're now told cool stories in school about earth and the universe. Lots of unverifiable subjective claims that are never experienced.
The visible spirograph where the lines are densely drawn is called an envelope. And it's a weird world out there (no pun intended) when it comes to just lines being traced multiple times.
Amazing job. It really helps to visualize how important timing is when launching a spacecraft to another planet. Stunning pattern imagery. The music is perfect as are the colors. Thoroughly enjoyed this.
This video reminds me of a great bit on the TV show QI about how mercury is actually the planet that spends the most time closest to earth, but you wouldn't think that because most people don't take into account our "nearest" neighbors' orbit patterns and lengths. It just so happens that Mercury orbits the sun relatively quickly so it spends more time close to earth than Venus or Mars.
QI actually covered Cruithne on QI!! Stephen Dry even called it Earth's second moon on the show. However they eventually came back and said that Earth has multiple tiny tiny objects that orbit it. But they never mentioned that Cruithne wasn't actually orbiting Earth...gasp
HUH? You saw the surface of Pluto? The one with the cartoon Pluto on the cartoon planet? Do you mean Devon Island when you say the surface of Mars? They say Viking 1 landed in 1976. Oh wait, I get it, you are just happy that everyone is fooled today that couldn't be fooled back in the '80's. NASA has been going nowhere for 60 years. All of NASA's "images" are computer generated graphics. The hubble telescope is really sophia. No planes hit the towers. There is no killer virus. Wake up, you are special. The earth is flat.
To think of the discoveries made by Kepler, Copernicus, etc. Who would've drawn out their models by hand. To now be able to plot out visual representations in seconds on a computer. We are so lucky!
Yep, its also why humans have 5 skeletal nodes from the body. 4limbs+1head. and why each of those nodes have 5 fingers/toes, or 5 sensory systems on one node.
@@DerpMuse I'm pretty sure the golden ratio isn't related to the number of fingers you have. After all, most animals don't have 5 fingers. We have 5 fingers for better stability wielding tools and gripping, not cause of a number from the Fibonacci sequence.
@@pranavkondapalli9306 When people say in their slightly condescending way that "I'm pretty sure...". Those people should remember that all of us don't know everything. My question is have you thought outside of the box enough to realize that the golden ratio isn't the only Fibonacci ratio, that is notched in to the ratio relationships, of which .618 is only one point? Using a trajectory as an example (for a natural formation). Since a Golden Ratio trajectory that expands and contracts does so in a spiral shape. At any point on the spiral shape, there will be a ratio relationship, that can be neatly gotten to in steps, from the .618. In fact, there will be an increment effect that would appear like the famous Russian dolls with the same set, within itself in smaller and smaller versions. However, only the same scale, major milestone ratios would need to be plotted to manifest an expanding or a contracting spiral trajectory, that is based on versions of the golden ratio. So, whatever number of fingers an animal has. Can be measured by ratio, to the rest of it's body proportions or similar species proportions. (This is a bit far afield, but actually if you look at the skeletons of mammals. The template is the same, and I'd say the one to best illustrate this is the skeleton of bats. We're all that template, just in different proportions.)
@@Lexivor Well the opening comment (Pravnav's) to that this thread is based on names Fibonacci. Then, the rest of the comments mention Fibonacci. And, a small amount of Googling should show lots of body measurements that are spaced and fit with the the ratios. I hope you know that the progression (or reduction) of the Fib ratios is not just a fixed number of .618. There are many points along this scale. Extra credit for your homework. Google might also tell you that lots of plants have their appendages and flowers arranged in line with Fib. math.
I wonder if there's any correlation between this and Randall Carlson's ideas on Sacred Geometry. I'd love to hear his thoughts on this video, AND the thoughts of your team on his SG videos. Very cool stuff here!
Freemasons talking about Venus-Earth 5 pointed symmetry: *_Golden Ratio. Incomplete Five-Pointed Star (not to be confused with Sirius). We already knew that!_* 2000+ years old Geto-Dacians from Sarmizegetusa: *_8 years of 366 days plus 13 years of 364 days) divided by 21 years = 1 year average of 365,2381. The firwood cone has 8 and 13 spirals on it. We already knew that!_*
I finally saw how the loops in orbits are created. Earth centric motion. I always wanted a Spirograph when I was a kid but never got one. This was cool math.
I had heard that the five pointed star was actually “The Star of Venus”. To actually see how Venus sketches out this five pointed star pattern in the night sky is really neat.
omg I've been playing with this stuff in sound. can you treat distance(planet, planet) as a synth signal and get interesting harmony? I'll bet you can!
I swear I watched a video like this within the last year, but my youtube history says it's never heard of it. But I sWEAR that video is out there, it's about harmonics and space and it's cool. I've tried everything I can to find it on my lunch break here with no luck. If you find it, can you link it back here?
This couldn't have been recommended to me at a better time , i have to write and present an essay on the 3 body problem and this seems to describe it beautifully.
Great to see it from this perspective. Reminds me of the 15th-century attempts to account for the motions of the planets in a geocentric universe. Strange to see the planets run clockwise. Although this is perfectly legitimate, the general convention is to view the solar system from the north side of the ecliptic, and have them run counterclockwise.
Those old explanations of how the earth could still be at the centre, and the convolutions needed to explain how the other celestial bodies moved makes me think of the current theories of dark matter/dark energy. It **might** be that the theories are correct (like the old idea that the earth was at the centre) and that general relativity still holds up.......but it requires the belief in a, so far, entirely undetected new form of matter and of energy (and no strong idea of what they would be formed out of) and requires a 1900% increase in the mass of the universe. Or......there is something missing in the general theory of relativity ('maybe the earth isn't at the centre' ) and we don't need to imagine (literally, since we can't detect them) new energy/matter.
@@peaceonearth8693 Indeed 😄! Lay a cold resistant clock on the north pole, its dial facing upwards, and the sun and stars move in the same direction as the hands of the clock. Do the same experiment on the south pole and you see them running in the other direction.
@@koenth2359 I'd say it's the other way around: in the northern hemisphere, clocks go sun-wise, imitated after sundials (skeuomorphism way before the iphone). Then it was exported all over the world because luck of the draw would have it that people from the northern hemisphere became the dominant force in the world.
Current title: The Strange Orbit of Earth's Second Moon (plus The Planets) Is it clickbait? Yes. It's clearly Earth's infant step-brother. Also says nothing about what the video is actually about.
Wow, I'm actually surprised. I saw the "spirograph" gif of "The dance between Venus and the Earth" a while ago online, and never knew it came from someone just doing it for fun on Tumblr. That's pretty cool! The newer animations are very well put together, too. Makes it easier to understand all that's happening, and takes out a major possibility of misunderstanding it just by the visuals.
"And in the year 2021, a collector of mathematical curiosities, known today only by their pseudonym 'Number Phile,' single-handedly revived the geocentric model of the universe."
I like how he uses Spirograph as an aid to explaining the circle interactions. It makes perfect sense to someone who played with it growing up (I did in Canada). But I suspect many people wouldn’t have the foggiest idea what he is referring to.
He was probably one of the precious few sane, not hostile people on Tumblr. I can't imagine this wonderful person seeing someone else's math based gif and trying to raise a hate mob to convince them to off themselves.
As we know the same thing happens with a weight on a wire pendulum, it makes nice predictable patterns . If the pendulum was in the vacuum of space it would do the same without decay..
@@blinkerfluid7988 It wouldn't "swing" in space, you're right. It would travel in a straight line until acted upon by gravity to change its velocity or direction. It would probably orbit something in the patterns shown in the video.
What Earth's second moon? 1:48 these patterns made me feel like our universe is way more complex than we think. Kepler's law assume it to be ellipse but the trajectories are way more complex
Is the 5 pointed symmetry of the earth and Venus really because 13 - 8 is 5? If the ratio was 2 and 3, would it have 1 point? Without doing any work, I'm pretty sure it would have 3. 5:42
Consider two planets, inner planet M and outer planet N. Suppose M makes m revolutions in the same period of time that N makes n revolutions, where m>n. Planet then N is overtaken by M how many times in this period of time? I think the answer to that is m-n (also counting 'catching up' as overtaking). The closest distance between M and N is the moment when M and N are on a straight line (I like the word syzygy) where M is between the Sun and N. So this closest distance also happens m-n times.
@@koenth2359 I like this explanation. So applying it to Stuart's example, where the ratios are 2:3, if we start timing when the two planets are closest, by the time the inner planet has made 1 orbit, the outer planer has travelled 2/3rds of an orbit. By the time inner planet completes its second orbit, outer planet has travelled 4/3rds (one orbit + 1/3 of its second) - always 'ahead' of the inner planet. Inner planet only catches up with the outer planet at the end of its third orbit (and as outer planet completes it's second orbit). This catch point is the same as the starting point. So one 'spike' only.
2:22 Matt: That’s just sensationalism
Numberphile: I found the title of the video
🤣
They did the same with Matt's previous video. He specifically said that was a representation of a search algorithm, not a simulation of lightning, and the video title was "the lightning algorithm". Clickbait titles are bad enough, but why misrepresent (and directly contradict) what the guest says?
@@RFC-3514 It's his job to get views, and these titles do that. Don't fault him; fault the algorithm, and the people who the algorithm is built to serve.
@@RFC-3514 If it gets more people into watching maths stuff, then it's totally worth it.
Numberphile doesn't know how to do clickbait, but he's learning.
I was teaching about frame of reference in my physics classes recently. This video will be a perfect follow up showing how the description of a planet's motion changes depending on your frame of reference. Thanks!
The Earth is Flat, Stationary and Non-Rotating.
@@godsbeautifulflatearth i want whatever you are smoking
@@godsbeautifulflatearth what would cause the seasons?
Hi, I'm an old quantum chemist and currently also turnung my focus of interest away from electrons orbiting nuclei to the Milky way and galaxies. You can also very nicely illustrate orbits with the Gravity Simulator /all scenarios (freely accessible on the internet). For me very fascinating switching the view to comoving systems and working with different camera views. Please let me know if this is interesting for you. PS: I have to admit, my spatial imagination is not that excellent and it sometimes takes time to comprehend it. These things are so important for astrophysics.
@@godsbeautifulflatearth i will make sure that we will be able to send people like you to space in the near future so you can see the round earth with your own eyes. you arent special. you didnt discover something "big earth" doesnt want you to know about. you just want to think that so you can have a shred of meaning in a world where you otherwise have none.
video: "has been referred to earth's 'second moon' but that's just sensationalist kind of thing"
video title: The Strange Orbit of Earth's Second Moon :D
Ahahah i was about to comment the same exact thing...a bit of clickbaiting...
Greatful for the clickbait. We all get manipulated by it. If not for this i wouldn't see this inspiring video.
@@goomiac numberphile can have little a clickbait, as a treat
Cruinthe-Bait
I'm more interested in this strange kidney bean orbit than another moon, strange oddities like this would be useful in determining the subatomic scale of the laws of attraction and repulsion
I love when abstract maths and science is translated through an artistic lens. Whenever I teach maths I try to use the “A picture is worth a million words” philosophy and show the reason behind the maths. This was Beautiful. Bravo.
Proud to say I knew that 8+5=13 before this episode.
Only on Earth. Here on Mars we have 8 fingers so it’s 10+5=15
It is also numbers of the Fibonacci series
I, too, suspected something like that. But I wasn't sure.
@@christianadam2907 ...which means that 5/8 = 8/13 almost exactly. It is also known as the Golden Ratio.
@Autodidactic Peasant Let the argument begin 😅👍
that 0:33 moment when the mathematical model shifts perspective (as earth as the center of the universe), and how it was represented visually is so beautiful.
A minute in and I'm getting all nostalgic for Spirograph.
How cool was Spirograph. I was forever on that thing. Spent my pocket money just on pencils alone.
These are in fact the beautiful spirographic patterns that astronomers ACTUALLY observe when they look at binary star systems and their moons and 'exoplanets'.
My TYCHOS model (inspired by Tycho Brahe's geoheliocentric system) demonstrates that the Sun and Mars are binary companions - and that our planets truly orbit around Earth just like shown in this video.
I'm hesitant to say it... but I want a 3D printer so I can make my own Spirographs...
Till now, I thought spirograph is just an interesting thing and never think this can occur in nature too
@@simonshack1 yes, Tycho Brahe and Spirographic orbits. not just a toy.
This was actually cool. Never thought to look at the rotations from that perspective. Well done.
It's all fantasy and wild speculation.
@@godsbeautifulflatearth quick question: why would the government try to hide earths true shape? whats the reason? there has to be a reason to spend the trillions or whatever it costs to keep the round earth "conspiracy" running.
Fun fact: Those patterns, created by orbiting bodies orbiting other orbiting bodies, are called epicycles.
Before astronomers knew that the sun was at the center of our solar system, many astronomers were baffled by those strange patterns that result from assuming the earth is at the center. In order to model the patterns, they would keep adding epicycles to create a system that followed those paths.
However, its been proved mathematically that you can keep adding epicycles over and over again to create a continuous path of any kind, so they could keep using them without ever noticing that a heliocentric model would be much simpler and accurate.
Because of this, "adding epicycles" has become a joke phrase to mean "adding more and more fixes and details to a bad design/theory instead of ditching it for a simpler more robust one"
The Earth is the center of the universe. The Sun goes around the Earth. The planets also go around the Earth, following strange epi-cyclic patterns because they are strongly influenced by the gravity of the Sun and of one another. This is completely consistent with Einstein's notion that every reference frame is equally as valid as any other reference frame. A heliocentric model may be simpler for calculations but it is not "more accurate" - nor is it less accurate.
Every reference frame is equally as valid as any other reference frame. This idea may seem non-intuitive to you but it is reality.
@@rubiks6 if you say something with enough confidence it doesn't mean you're right lol
Guess I'm an outsider. I've never been to a party where a joke's punchline was "adding epicycles". Ha ha hahaha
@@thebeast5215 He's not wrong, though
All reference frames are valid, but they are not all equal. Inertial reference frames play a special part in Newtonian physics and General Relativity (although they are defined differently in the two cases). In fact, both theories are created with those reference frames, and changing to others is little more than an addon. For understanding things, writing physical laws, and solving problems, inertial frames are vastly superior.
So yes, one could rewrite all of physics to work in a weird reference frame where the earth is stationary, but at huge cost in both computation and intuition. At the end of the day, science isn't about some sense of absolute truth, it's about making predictions, testing their accuracy, and using this to make better predictions. If you're changing things to make predictions harder (and also improving prediction-making harder) then you've made it worse. That means all reference frames are not equal when it comes to doing science.
1: 00 hence, why there is precession.
Very interesting, never heard of this before.
Smart guy !
"They call it second moon but that's just sensationalist"
Video title: "Astronomers hate him! Local mathematician finds the secret of Earth's second moon"
I assumed that all 460 flat earthers showed up to give it a thumbs-down.
Can you explam what is sensationalist pls
@@lailasharlincholet Cruithne is an asteroid at only 5km across, so calling it a moon can be considered sensationalistic (making it out to be something greater than what it is).
On a completely different note, did anyone notice that Matt mentioned the numbers 5 and 13? They are part of the Fibonacci sequence which are numbers commonly found throughout nature.
@@lailasharlincholet It's not a moon/satellite of Earth, it's a satellite of the Sun, it's in orbit around the Sun. But it's known well by that name, Earth's second moon. Incidentally it was found by an Australian who named it after his pet sheep. True. :-)
@@GymRowboat 3,6and9aswell!!
Principia for KSP allows you to display these trails as well - one of the most interesting ones is the Pluto System with the bigger of the 4 smaller moons form a nearly triangular orbit and the outer one a pentagonal orbit.
KSP should be a mandatory part of all middle school science curriculums.
@@RK-252 Yeah exactly. KSP is the best space simulator.
Fun to see retrograde motion from an overhead perspective. It's amazing that ancient astronomers worked this out by tracing the lines of the planets across the sky on a night by night, week by week, month by month, year by year basis.
They weren't distracted by Seinfeld and twitter.
Was going to say "they must not have jad a TV but yea,..u beat me to it...
It also helps to believe you are charting literally divine patterns.
@@questioneverything4633 What's Seinfeld?
*astrologers*
Fascinating. Bring him back for more episodes ya.
I really enjoy what Matt Henderson is doing, makes me want to learn a programming language!
The code at 0:03 is definitely Mathematica. Many common programming languages (e.g., C++, Java, Python) are a bit annoying to do graphics with, but Mathematica and Julia are very nice for this kind of thing.
I made such a program a couple of years ago in C#. It was quite easy to make, using C# in visual studio.
You could even do it in C, and if you know a bit of mathematics and know how to google stuff you can make your own. I posted a video on my channel showing a sphere rotating around, having little programming language experience at all, and learning as an adult.
"Hello World!"
Do yourself a favor: start with either Ubuntu or C; they're the most forgiving of their language groups
This boy is going somewhere great.
There is a shape for everything and he's noticed.
The changing water droplet. The snow flake.
The "emotional" influence (thought) that can change everything.
This one needs to continue and be aided.
I dont think it has a choice but to continue. Its continuing right now. Could you imagine the trouble we would be in if it didnt?Oh yeah...we just left that reality. Shew...that was close lol *looks around* uh oh...
The Mars animation does a great job showing why there’s specific windows when we need to launch Mars missions, because it does get SO close (relatively) to earth for short times, and other times it is exceptionally far away. It can be very easy to imagine planets staying roughly the same distance away from each other at all times
The specific windows are even more apparent when the orbits are correctly depicted as elliptical
It's not really about the closeness of the planets themselves but rather what path a Hohmann transfer between them will take.
Reminds me of a great trivia question: What planet is, on average, the closest to Earth? The answer is Mercury. And by the way, Mercury is, on average, the closest planet to EVERY planet.
@@fredact it can't be, cmon, you're telling me Mars is on average closer to Venus than Mercury?
@@jimmyh2137 yep. And on average, the sun is closer to the Earth than any other planet.
Say you are standing near a carousel. Measure your average distance to one of the horses. Sometimes the horse is near you, but sometimes it’s on the other side of the carousel. Compare that to your distance to the center point of the carousel. Your distance to the center point is, on average, less since the horse spends more time being further away from you than the center point.
Reminds me of the patterns I would make with the toy/art tool Spirograph.
@J Errety Calm yourself, man.
thanks for sharing this info with the universe!
“That’s sensationalist” * uses it in the video title *
And in the previous one Matt said "this is an animation showing how a search algorithm works, it looks a bit like lightning but obviously it's not trying so simulate real lightning", and the title was "the lightning algorithm". I think I'm about one misleading clickbait title away from unsubscribing.
Wow, 1st time here. So in fact our solar system is like a tube vortex with our planets chasing the sun creating these lovely geometric patterns behind them with energy through the galaxy of the Milky Way? Facinating
Didn’t know there was an asteroid that also rotates around earth. This would explain several ISS videos showing a very rocky looking small planet pass by them from time to time!
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This video is uploaded at 3:14 PM IST! Coincidence?
Yes
@@pranavkondapalli9306 Coincidence? I think so.
What would the epicycles of Earth look like with Mars viewed as stationary?
Similarly, what would the epicycles of Mercury look like with Venus viewed as stationary?
I'm almost certain that I've seen something about this somewhere in the past. I'll see if I can dig it up.
Or with Venus as reference point? We need another episode or four!
I would definitely be interested in seeing how Earth's path differs from the perspective of each planet.
This is so creative. Looks beautiful and so is to learn those orbits with it. This is great way to present knowledge.
I can’t believe this! I’ve always been taught that Tolemaic/Aristotelian astronomy was “ugly” and complicated… now, complicated it looks for sure, but actually the patterns of epicycles of sun and planets “around the Earth” are beautiful!
Astronomers before Copernicus would have had nightmares trying to calculate planetary orbits, but what a mathematical insight they must have had if they could do it without computers!
Thank you 🙏 for showing this incredibly fascinating world from Earth’s perspective!!!
By the way how is it possible that the planets all have such an amazingly symmetrical apparent orbit around the Earth?
What if you were watching from any other planet? Would you get similar patterns?
And what if you were watching from any random moon? Would you still see anything similar?
Can you make your next videos on these topics? 🙏👏
This needs to become a full hour documentary.
There have been several. The point of these TH-cam channels is precisely to give people a shorter version.
I find it fascinating how similar the patterns look like windings on electric motors. Even more fascinating was the fact I didn’t get to see the pattern the Earth makes in full? Now that would have been interesting
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Wonder if Matt has done any of these from the perspective of the other planets. What would the patterns of the inner planets look like from Jupiter?
this, I am curious about this aswell, this is the main question we should have the answer for since that would prove earth is really special.
@@maggieme8220 we dont need any more proof that earth IS special. We need more ppl to see those proofs that Earth IS special. If i worded that correctly it will make perfect sense. If not this should be your third attempt to try to make sense of it. Seeing how simple things are complicated to hide true meaning our trained brains overlook the complications set in place to complicate things. That pattern isnt natural. Thats why it feels like it does. Js
maybe from the perspective of the asteroid belt... if it was a planet was it full of a maddening night's sky *BWUAEHAHUAEHAHAAA!!*
It’s not terribly difficult to animate ;) try it
@@onthelvl8291 Just because you see a pleasing pattern, does not mean it isn't natural. Nature is filled with pleasing designs, and most are modeled with surprisingly simple mathematics. The fact that we find them pleasing does not make them unnatural or imply design.
PLEASE make a wallpaper of the inner planets complete cycles... That graphic looks aaaaaaaaaaamazing....
Great job, Matt :-)
I agree. Where can we get these images?
the music when we watch the planet orbiting makes the whole thing perfect
My TYCHOS model (inspired by Tycho Brahe's geoheliocentric system) demonstrates that the Sun and Mars are binary companions - and that our planets truly orbit around Earth just like shown in this video.
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Thank you for letting those orbits play out. If there's video of that for each of the planets, or somewhere people can play with the tool themselves, I'd love a link to it.
More of Matt! More of Matt! More of Matt!
After failing in being a king Robb Stark decides to dedicate his life to astronomy
After failing to save the world Superman decides to become an astromathematician.
Hopefully he decides to stay home for his uncle's wedding this time
Amazing am going to use this. Thank you so much. MacKenzie
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I would love to see the Lagrange points and see what they look like spatially along with (gravitational cancellation boundaries) and how that changes with the orbits.
Shouldn't Lagrange points be rotating in a circular orbit around Earth, like the Sun? They stay at a fixed distance and are at a fixed angle relative to the line between Earth and the Sun
This is really cool!
1:56 Those shapes traced out are called epitrochoids which are very similar to epicycloids, except epicycloids have sharp points instead of the little loops like these ones have.
Wish he'd done Pluto. Don't @ me, purists; its large oblong orbit that cuts in front of Neptune would have been fascinating to see in this context.
I was thinking the same thing.
The animation of the shift in perspective looks really cool.
I like it too. Yet all the animation does is just speeding up to match the earth's rotation and zooming in :)
This is cool. Wish I could play with this program.
A few possible improvements:
1. Exact placement of planets on a specific date so that their orbits coincide with what we see outside.
2. Tighter control of precise relationships. (The 8 to 13 ratio could be fine tuned.) The 5 pointed Venus orbit would not be so perfect.
3. The asteroid's orbit is shown with BOTH the earth and sun shown stationary. They can't both be stationary.
"but that's just sensationalist" - Brady puts it in the title.
Something that I think is worth mentioning is @5:07 to 5:08 in the video when comparing the orbits of Earth and Venus you can see that they trace out a Cardioid that you can also see emerge within the Mandelbrot Set.
Yes, and a funny thing is that Venus is now even more connected to love ♥ Btw. 5+8=13... that Golden something Fibonacci guy, huh?
A very complicated way to play spirographs. Love it!
Amazing to see different perspectives. Ive never seen the orbits displayed like this.
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One of the philosophical implications of Einstein's "Relativity" is that, since every reference frame is as valid as every other reference frame, it is perfectly acceptable to consider the Earth the center of the universe. That may make the mathematics rather complicated sometimes (as seen in the beautiful but complex orbital simulation graphic) but it's perfectly valid.
I very much like thinking of the Earth as the center of the universe. There are no observations to dispute the notion.
Isn't that only true for inertial reference frames?
@@SimonFoster63 - Can we not consider the Earth as standing still and that all other astronomical bodies are in motion? (just as in the narrator's spirograph animation - the Earth is the center of the spirograph.) That would make us an inertial reference frame.
("hypotrochoid" and "epitrochoid" are so hard to pronounce and such unfamiliar terms, I just call them "spirographs.")
@@rubiks6 I'm not an expert here but I don't think an inertial frame can accelerate. The Earth is definitely accelerating.
@@SimonFoster63 - The Earth is not accelerating in relation to the Earth. You are standing (or sitting) on the Earth. You are not accelerating in relation to the Earth and you are the observer. Therefore, the Earth is an inertial reference frame for you.
(If this is a new idea to you then you are in store for great joy when you wrap your head around it. One of those "a-ha" moments.)
@@rubiks6 Actually, you are accelerating vs. the Earth. What do you think keeps your feet sticking to the ground? (Hint: look up "equivalence principle"). The surface of a massive body is by no means an 'inertial reference frame' from the standpoint of General Relativity.
What you are discussing - and it's a perfectly valid approximation, given the speeds and precision involved - is Galilean Relativity. Don't need Einstein for that.
Magic. Beautifully explained. Thank you.
My sentiments are about the same as everyone else here. I love watching Numberphile, and am subscribed to it, so I mostly ignore the titles. Still, it's a disservice to both your guests and your viewers to blatantly misrepresent the video. I love the channel for it's topics on maths and sciences, not for propagating conspiracy theories.
I'm with you up until the last clause. Not every incorrect thing is a conspiracy theory, and not all conspiracy theories are incorrect.
Our current understanding of universe is like a narrow gap, I’m not talking about technologies, to be able to see the whole picture first we need to become one inside, otherwise everything around us can not go any further than magic, you are also a part of the universe
Yeah go outside and verify your reality. It won't match with any first hand evidence. We're now told cool stories in school about earth and the universe. Lots of unverifiable subjective claims that are never experienced.
Orbitgazing.
Lovely music going with that cosmic waltz.
Sounds a lot like Orlin's Theme
Video Idea: Veblen Functions and Buchholz psi functions
The visible spirograph where the lines are densely drawn is called an envelope. And it's a weird world out there (no pun intended) when it comes to just lines being traced multiple times.
What do you get for that friend who has everything? Antibiotics.
Sounds like a GoT episode, but is indeed an astronomic phenomenon: "The Dance of the Bean and the Drop"
Alan Davies is angrily shouting at this video right now!
this is beautiful maths, from beautiful real life
Amazing job. It really helps to visualize how important timing is when launching a spacecraft to another planet. Stunning pattern imagery. The music is perfect as are the colors. Thoroughly enjoyed this.
I would loooove to have merch with those graphs, it could even make for this incredible wall art
This video reminds me of a great bit on the TV show QI about how mercury is actually the planet that spends the most time closest to earth, but you wouldn't think that because most people don't take into account our "nearest" neighbors' orbit patterns and lengths. It just so happens that Mercury orbits the sun relatively quickly so it spends more time close to earth than Venus or Mars.
QI actually covered Cruithne on QI!! Stephen Dry even called it Earth's second moon on the show. However they eventually came back and said that Earth has multiple tiny tiny objects that orbit it. But they never mentioned that Cruithne wasn't actually orbiting Earth...gasp
I feel so fortunate to be living at this time. I was able to see the surface of Mars & Pluto, which was an impossibility back in the 80's.
HUH? You saw the surface of Pluto? The one with the cartoon Pluto on the cartoon planet? Do you mean Devon Island when you say the surface of Mars? They say Viking 1 landed in 1976. Oh wait, I get it, you are just happy that everyone is fooled today that couldn't be fooled back in the '80's. NASA has been going nowhere for 60 years. All of NASA's "images" are computer generated graphics. The hubble telescope is really sophia. No planes hit the towers. There is no killer virus. Wake up, you are special. The earth is flat.
Interesting indeed ! It took a while for early astronomy to get away from geocentrism, but artistically, it is intriguingly beautiful !
Whenever I forget which order to tighten the 5 lugs on my car's wheels, I just superimpose the orbits of Earth and Venus. Easy.
Then changing the spark plugs would require an astrolabe or an orrery?
I always remember the pattern, I just never remember which lug nut to start with.
@@Monty_BeGoodToEachOther Always start with the third one...
@@haroldwilkes6608 Nope. It's the second one. 🤪
The first thing it came to my mind when I saw the thumbnail was a microscopic living thing, lol.
Wow, what an amazing time to be alive.
Four Thousand years from now: "Those poor savages back then, with just the one lifespan."
To think of the discoveries made by Kepler, Copernicus, etc. Who would've drawn out their models by hand. To now be able to plot out visual representations in seconds on a computer. We are so lucky!
@@matthewreynolds8068 Have you ever seen old people try to work a computer?
@@peaceonearth8693 Yes. I also have seen a lot of young people who are no better at it.
*I NEED MORE OF THESE*
8 and 13 are also Fibonacci numbers, and the ratio btw the Fibonacci numbers approaches φ, which is known for having 5-fold symmetry
Yep, its also why humans have 5 skeletal nodes from the body. 4limbs+1head. and why each of those nodes have 5 fingers/toes, or 5 sensory systems on one node.
@@DerpMuse I'm pretty sure the golden ratio isn't related to the number of fingers you have. After all, most animals don't have 5 fingers. We have 5 fingers for better stability wielding tools and gripping, not cause of a number from the Fibonacci sequence.
@@pranavkondapalli9306 When people say in their slightly condescending way that "I'm pretty sure...". Those people should remember that all of us don't know everything. My question is have you thought outside of the box enough to realize that the golden ratio isn't the only Fibonacci ratio, that is notched in to the ratio relationships, of which .618 is only one point?
Using a trajectory as an example (for a natural formation). Since a Golden Ratio trajectory that expands and contracts does so in a spiral shape. At any point on the spiral shape, there will be a ratio relationship, that can be neatly gotten to in steps, from the .618. In fact, there will be an increment effect that would appear like the famous Russian dolls with the same set, within itself in smaller and smaller versions. However, only the same scale, major milestone ratios would need to be plotted to manifest an expanding or a contracting spiral trajectory, that is based on versions of the golden ratio.
So, whatever number of fingers an animal has. Can be measured by ratio, to the rest of it's body proportions or similar species proportions. (This is a bit far afield, but actually if you look at the skeletons of mammals. The template is the same, and I'd say the one to best illustrate this is the skeleton of bats. We're all that template, just in different proportions.)
@@peaceonearth8693 I'm pretty sure the Fibonacci ratio is not relevant in this situation.
@@Lexivor Well the opening comment (Pravnav's) to that this thread is based on names Fibonacci. Then, the rest of the comments mention Fibonacci. And, a small amount of Googling should show lots of body measurements that are spaced and fit with the the ratios. I hope you know that the progression (or reduction) of the Fib ratios is not just a fixed number of .618. There are many points along this scale.
Extra credit for your homework. Google might also tell you that lots of plants have their appendages and flowers arranged in line with Fib. math.
I wonder if there's any correlation between this and Randall Carlson's ideas on Sacred Geometry.
I'd love to hear his thoughts on this video, AND the thoughts of your team on his SG videos.
Very cool stuff here!
Freemasons talking about Venus-Earth 5 pointed symmetry:
*_Golden Ratio. Incomplete Five-Pointed Star (not to be confused with Sirius). We already knew that!_*
2000+ years old Geto-Dacians from Sarmizegetusa: *_8 years of 366 days plus 13 years of 364 days) divided by 21 years = 1 year average of 365,2381. The firwood cone has 8 and 13 spirals on it. We already knew that!_*
I finally saw how the loops in orbits are created. Earth centric motion. I always wanted a Spirograph when I was a kid but never got one. This was cool math.
5:05 it makes the start of the Mandelbrot set. I assume that has to do with the fact that the 8:13 ratio is made of Fibonacci numbers?
The Pope: "The Earth is the center of the universe!"
Copernicus: "Wanna play Spirograph?"
I had heard that the five pointed star was actually “The Star of Venus”. To actually see how Venus sketches out this five pointed star pattern in the night sky is really neat.
And to think that ancient people plotted the planets' courses and found Venus' unique pattern thousands of years ago.
Matt should really sell merch with this stuff printed on it. I would buy the heck out of that!
This is fascinating. Beautiful patterns presented beautifully. The heavens were very well made, and this opens them up a bit to us. Thanks, Math!
2:15 Ngl, these should be the symbols for our future planetary federation
omg I've been playing with this stuff in sound. can you treat distance(planet, planet) as a synth signal and get interesting harmony? I'll bet you can!
I swear I watched a video like this within the last year, but my youtube history says it's never heard of it. But I sWEAR that video is out there, it's about harmonics and space and it's cool. I've tried everything I can to find it on my lunch break here with no luck. If you find it, can you link it back here?
This was probably one of the most interesting videos i have seen for a long time. So thank you.
I didn’t know Andy Murray had a PhD in Astro Physics. You learn something everyday…
I'm glad someone else thought he likes like him
Well, Bryan May (Queen's guitarist) has one, so why not?
@@SebWilkes Not just looks. Their accents are clearly from the same part of Scotland.
And also a wicked first serve!🎾
This couldn't have been recommended to me at a better time , i have to write and present an essay on the 3 body problem and this seems to describe it beautifully.
Great to see it from this perspective. Reminds me of the 15th-century attempts to account for the motions of the planets in a geocentric universe.
Strange to see the planets run clockwise. Although this is perfectly legitimate, the general convention is to view the solar system from the north side of the ecliptic, and have them run counterclockwise.
Those old explanations of how the earth could still be at the centre, and the convolutions needed to explain how the other celestial bodies moved makes me think of the current theories of dark matter/dark energy.
It **might** be that the theories are correct (like the old idea that the earth was at the centre) and that general relativity still holds up.......but it requires the belief in a, so far, entirely undetected new form of matter and of energy (and no strong idea of what they would be formed out of) and requires a 1900% increase in the mass of the universe.
Or......there is something missing in the general theory of relativity ('maybe the earth isn't at the centre' ) and we don't need to imagine (literally, since we can't detect them) new energy/matter.
So, if you stand in Antartica the universe rotates counter-clockwise?
:-D
@@peaceonearth8693 Indeed 😄! Lay a cold resistant clock on the north pole, its dial facing upwards, and the sun and stars move in the same direction as the hands of the clock.
Do the same experiment on the south pole and you see them running in the other direction.
@@koenth2359 I'd say it's the other way around: in the northern hemisphere, clocks go sun-wise, imitated after sundials (skeuomorphism way before the iphone). Then it was exported all over the world because luck of the draw would have it that people from the northern hemisphere became the dominant force in the world.
@@daanwilmer Of course, totally agree!
Looking again at this what a lovely demonstration
Current title: The Strange Orbit of Earth's Second Moon (plus The Planets)
Is it clickbait? Yes. It's clearly Earth's infant step-brother. Also says nothing about what the video is actually about.
I could watch these animations all day
So relaxing
Thank you for visualizing the beautiful patterns of the planets of our solar system and practically showing some fun application of mathematics.
Wow, I'm actually surprised. I saw the "spirograph" gif of "The dance between Venus and the Earth" a while ago online, and never knew it came from someone just doing it for fun on Tumblr. That's pretty cool! The newer animations are very well put together, too. Makes it easier to understand all that's happening, and takes out a major possibility of misunderstanding it just by the visuals.
"And in the year 2021, a collector of mathematical curiosities, known today only by their pseudonym 'Number Phile,' single-handedly revived the geocentric model of the universe."
I used to draw epicycloids all the time in high school computer science. This brings me back.
I like how he uses Spirograph as an aid to explaining the circle interactions. It makes perfect sense to someone who played with it growing up (I did in Canada). But I suspect many people wouldn’t have the foggiest idea what he is referring to.
Did you know that there's a direct correlation between the decline of Spirograph and the rise in gang activity? Think about it.
Cosmic poetry. This was beautiful.
He was probably one of the precious few sane, not hostile people on Tumblr. I can't imagine this wonderful person seeing someone else's math based gif and trying to raise a hate mob to convince them to off themselves.
When your opinion of a rival social media platform is colorued entirely by what you read on reddit, you get takes like this one.
Amazing! and the music couldn't have been more fitting!
As we know the same thing happens with a weight on a wire pendulum, it makes nice predictable patterns . If the pendulum was in the vacuum of space it would do the same without decay..
A pendulum relies on Earth's gravity to work. I'm not so sure it would swing at all in space.
@@blinkerfluid7988 It wouldn't "swing" in space, you're right. It would travel in a straight line until acted upon by gravity to change its velocity or direction. It would probably orbit something in the patterns shown in the video.
You have added greatly to my comprehension of the relative movements of celestial bodies.
Just looked at Matt Henderson's credentials and it's safe to say he's a genius.
It's refreshing to hear someone pronounce 'Cruithne' correctly. Thank-you. 🙂👍
What Earth's second moon? 1:48 these patterns made me feel like our universe is way more complex than we think. Kepler's law assume it to be ellipse but the trajectories are way more complex
You were clickbaited
Cruithne
More complicated than we think?
Is there anybody out there who thinks the universe is uncomplicated?
Those patterns look so beautiful
Is the 5 pointed symmetry of the earth and Venus really because 13 - 8 is 5? If the ratio was 2 and 3, would it have 1 point? Without doing any work, I'm pretty sure it would have 3. 5:42
Consider two planets, inner planet M and outer planet N. Suppose M makes m revolutions in the same period of time that N makes n revolutions, where m>n. Planet then N is overtaken by M how many times in this period of time? I think the answer to that is m-n (also counting 'catching up' as overtaking). The closest distance between M and N is the moment when M and N are on a straight line (I like the word syzygy) where M is between the Sun and N. So this closest distance also happens m-n times.
@@koenth2359 I like this explanation. So applying it to Stuart's example, where the ratios are 2:3, if we start timing when the two planets are closest, by the time the inner planet has made 1 orbit, the outer planer has travelled 2/3rds of an orbit. By the time inner planet completes its second orbit, outer planet has travelled 4/3rds (one orbit + 1/3 of its second) - always 'ahead' of the inner planet. Inner planet only catches up with the outer planet at the end of its third orbit (and as outer planet completes it's second orbit). This catch point is the same as the starting point. So one 'spike' only.
That’s amazing, I never visualised orbital movement like this before.
That's interesting. On "QI" they said it was a second moon, but it really isn't.
But then again, QI is known for being fallible quite often.
They've actually said there are 2, 1 or 5, lots, none.
"The Strange Orbit of Earth's Second Moon"
Please don't call my mom that