Its how two huge masses influences other smaller objects with its gravity. Those white dots are Lagrange points (points that an object can stay in the same position in relation to the two huge objects)
@@allualex2606 haha I know you’re not nearly as smart as you think Alex🤣🤣 it’s more of your identity than it is a true relative description. If it wasn’t you wouldn’t be so foolish.
@@bryan1377 probably just an Euler method sim of orbital motion, or maybe Runga-Kutta. Very cool and interesting, but you don't need anything as in depth as machine learning for this kind of simulation. Only deterministic physics.
This is an amazing Sim.. I would like to know more about what you do? Is the project you are working on a part of astronomy and machine learning..? Just thinking loud..
Hi, thank you for the question. Actually this simulation is just a small project I do with personal interest. The simulation's main goal is actually trying to demonstrate how centrifugal force, Coriolis force and gravity works in rotating frame (as shown by arrows in the other 2 videos in the playlist). There is nothing too facy here :)
Check this! commons.wikimedia.org/wiki/File:L4_diagram.svg L4 and L5 exist because on those points, the total force from the two body would point directly to their center of mass and the magnitude is just enough to provide the centrifugal force required for the satellite to do circle around it with the same period.
Hi! Thank you for this wonderful simulation. Please tell me, can you share a link to the source code of this simulation? What did you use to create it?
At these distances, any weird gravitational affects due to the odd planet geometry would be unnoticably small. Like an object at the L4 point wouldn't notice much difference between a star-planet system where the planet is a toroid vs just a sphere of equivalent mass. The icons representing each object have been massively scslled up in size so that we can see what's happening, in reality at this perspective you would not be able to see anything other than the sun, maybe a tiny bright spot for the planet but it'd have to be a pretty massive planet.
@@maxk4324 I think he means what would the Lagrange points be in an earth-moon system where earth is donut shaped. My guess is that there would be an extra L in the baricenter
Because L4 and L5 are the mountain top of the gravitational potential! So they will repel the particles instead of attract them. The reason these particles can orbit around L4 and L5 is not because they are potential well. It's because in this frame, Coriolis force can provide the "centripetal force".
I guess your "strictly speaking physical" refers to the fact that we apply Coriolis force and centrifugal force on the particle, and people often says centrifugal force "does not exist". About this, you might want to check the discussion on physics exchange: physics.stackexchange.com/questions/109500/does-centrifugal-force-exist In short, the answer depends on how you define whether a force exist or how you define "un-physical". Nevertheless, the physical picture we used in the simulation is valid and robust.
@@EASYEarthSciences I meant particle trajectories in the simulation. I'm just trying to understand what the simulation is showing. I guess it's demonstrating the shape of the potential surface only?
@@JanPBtest the simulation is done in a rotating reference frame is what he's saying. If the "camera" were to be stationary you would see the blue planet orbiting the sun and all the tiny satellite dots would initially be orbiting the sun at the same speed as the planet. But then trying to picture how Lagrange point stability works would be impossible for the human brain to decipher. Instead, by assuming the entire frame of reference is rotating at the same speed as the planet's orbit, the objects of interest all initially start "stationary" despite them actually circling the Sun. To account for the fact that the reference frame is rotating the sim needs to factor in fictitious forces, or forces don't actually exist from a stationary view point, but which appear to exist from the rotating viewpoint. For example, imagine you are on a spinny carnival ride that spins fast enough to stick you to the wall. From your rotating point of view it feels like you are being pressed into the wall. But it's not like there's actually something pushing you against the wall, because that would be magic. Instead, from my stationary perspectivd outside the ride I can see what's actually happening. In actuality, your body is trying to move in a straight line, for an object in motion always 'wants' to maintain that motion, both in how fast and in what direction it's traveling. However the round walls of the spinning ride are constantly acting to redirect your motion by exerting a pulling force towards the center of of rotation, thus keeping you moving in a circle rather than careening in a straight line right into a hot dog stand. You could imagine if the walls around you suddenly vanished, to me I would suddenly see you travel in a straight line tangent to the circle you once traveled. From your view you are being pushed away from the center, this is a fictitious force that is experiemced only if we assume the emtire reference frame is rotating. From my view you are being pulled towards the center of the ride the walls, which act to constantly redirect your momentum. This is the true force that exists from a stationary reference frame. For this sim, to make it easier to visualize, he selected a rotating reference frame and so had to account for this by adding in the fictitious centripetal forces (the one I described in the carnival example), and also the Coriolis force which is a bit more complex to describe so I'll let you look that up on your own.
Yes that's correct! This is usually called "co-rotating frame". And because we are doing the simulation in co-rotating frame, we need to consider centrifugal and Coriolis force when calculating the particles' acceleration. You can see this in more detail in the other two videos of this series.
is this in a rotating frame of reference or are the two mass bodies fixed? In some parts of the simulation, the movement of the massless particles seems odd, so my initial guess was that this is due to the frame of reference rotating and thus not being inertial.
Hi, thank you for the question. Indeed, the term "massless" is somewhat misleading. We call them massless because their mass is so much smaller than the other two main body (e.g. Sun and Earth), not meaning their rest mass is zero (like photon). Nonetheless, whether massless particles like photon would be affected by gravity is also an interesting topic. You might want to see some discussion as shown below: aapt.scitation.org/doi/pdf/10.1119/1.13435 www.researchgate.net/post/How-can-Newtons-gravity-theory-predict-that-light-is-bent-when-passing-close-to-a-star
Mathematically its the origin or the limit where suns_grawith- earths_grawith=< grawith_of_flyingobject :P atleast thats what i guess from graph ;p so no one pulls the flyig object to somewhere atleast not that noticeable ;p
Close. You missed the fictitious forces due to rotation. You can't tell visually, but if you read (or watch) up on Lagrange points you'll realize that the "camera" looking down on this simulated system is rotating at the same speed that the blue planet orbits the sun, thus making both appear stationary. That makes this entire system a rotating reference frame roughly centered on the sun. So you need to also account for the centripetal (or centrifugal, whichever is the fictitious force, I always much those up) and Coriolis forces. Alternatively you could have the planet actually orbit the sun and thus have the reference frame be a stationary inertial one and then you'd be right in only accounting for gravitational forces and inertia (if I understand correctly). Although I might be misunderstanding what "grawith" means in your original equation as I have not seen this term before and assumed you meant gravity.
L4 and L5 are stable, doesn't mean any particle around them will always be able stay there. Your orbital parameters still need to lie within some particular regime in order to circulate around them. Also, not all the restricted 3 body system has stable Lagrange points. As shown in the two other simulations in the series, only those system with mass ratio > 24.97 can create stable L4 and L5.
@@GoblinAlchem A year late, but I'll answer anyway. See, when people say that L4 and L5 points are stable, that isn't always true. There is a certain condition that must be satisfied, namely that the mass ratio between the primary and secondary is greater than 24.96 (if you do the math behind it, you'll see that the actual exact value is (25 + 3 * sqrt(69)) / 2). If the mass ratio is less than that threshold, the L4 and L5 points become unstable, just like L1, L2, and L3. For example, the mass ratio for Sun-Earth, Sun-Jupiter, and Earth-Moon is around 333000, 1000, and 81 respectively, all of which are greater than 24.96, so their L4 and L5 points are stable (if you ignore gravitational effects from other bodies, because for Earth-Moon they're technically not stable due to effects from the Sun). On the other hand, Pluto-Charon has a mass ratio of only 8, which is less than 24.96, so their L4 and L5 points are unstable. For this simulation, either the points are simply too far away (which I doubt, since some of them got pretty close to it but still unstable regardless) or the maker set the mass ratio below 24.96.
Kinda meaningless with such a short timeframe. Hard to say, but it looks like you ended up with a Hilda-type orbit for at least one of them. Again, had to say in such a short timeframe.
That's true. This video is, scientifically speaking, quite meaningless. I actually wrote the code and made the two other videos in the playlist to demonstrate how centrifugal force, Coriolis force and gravity works in rotating frame. For this "Ring" simulation, I just want to mess around. But somehow people love it 😂.
Wish it could go for longer to see what settles in L4 and L5
nothing does
i have no idea what this is but kewl :D
Its how two huge masses influences other smaller objects with its gravity. Those white dots are Lagrange points (points that an object can stay in the same position in relation to the two huge objects)
How simple minded are you?
@@allualex2606 I would say that was uncalled for....
@@allualex2606 haha I know you’re not nearly as smart as you think Alex🤣🤣 it’s more of your identity than it is a true relative description. If it wasn’t you wouldn’t be so foolish.
@@allualex2606 Looks like you need the lesson here
This helped me finally understand langrange points thank you
Fascinating! What software program do you use?
Might be python ? ... beautiful work by EASY天文地科小站 anyway.
Thank you! The code is indeed written in python~
@@EASYEarthSciences wow… is this machine learning or something else?
@@bryan1377 this is gravity between the sun and earth and their respective Lagrange points
@@bryan1377 probably just an Euler method sim of orbital motion, or maybe Runga-Kutta. Very cool and interesting, but you don't need anything as in depth as machine learning for this kind of simulation. Only deterministic physics.
This is an amazing Sim..
I would like to know more about what you do? Is the project you are working on a part of astronomy and machine learning..? Just thinking loud..
Hi, thank you for the question.
Actually this simulation is just a small project I do with personal interest. The simulation's main goal is actually trying to demonstrate how centrifugal force, Coriolis force and gravity works in rotating frame (as shown by arrows in the other 2 videos in the playlist). There is nothing too facy here :)
@@EASYEarthSciences thank you for the response..appreciate it👍
I get why L1,L2.L3 exist but why do L4 and L5 exist?
Check this!
commons.wikimedia.org/wiki/File:L4_diagram.svg
L4 and L5 exist because on those points, the total force from the two body would point directly to their center of mass and the magnitude is just enough to provide the centrifugal force required for the satellite to do circle around it with the same period.
The picture is pretty. An explanation using words would be better.
Hi! Thank you for this wonderful simulation. Please tell me, can you share a link to the source code of this simulation? What did you use to create it?
Internal Lagrange points of Earth, if Indian Ocean is low gravity point, where are the other Lagrange points within our planet?
Very cool simulation! What python packages did you use to create this custom animation? Looks stylish :)
Hi, the animation is produced by python package matplotlib. The color style is manually adjusted by the author.
if this is a sim, do one for ringworlds and donut planets
At these distances, any weird gravitational affects due to the odd planet geometry would be unnoticably small. Like an object at the L4 point wouldn't notice much difference between a star-planet system where the planet is a toroid vs just a sphere of equivalent mass. The icons representing each object have been massively scslled up in size so that we can see what's happening, in reality at this perspective you would not be able to see anything other than the sun, maybe a tiny bright spot for the planet but it'd have to be a pretty massive planet.
@@maxk4324 I think he means what would the Lagrange points be in an earth-moon system where earth is donut shaped.
My guess is that there would be an extra L in the baricenter
Why are the particles being repulsed by L4 and L5 rather being attracted to them here?
Because L4 and L5 are the mountain top of the gravitational potential! So they will repel the particles instead of attract them.
The reason these particles can orbit around L4 and L5 is not because they are potential well. It's because in this frame, Coriolis force can provide the "centripetal force".
@@EASYEarthSciences So the motions shown in the video are not strictly speaking physical?
I guess your "strictly speaking physical" refers to the fact that we apply Coriolis force and centrifugal force on the particle, and people often says centrifugal force "does not exist".
About this, you might want to check the discussion on physics exchange:
physics.stackexchange.com/questions/109500/does-centrifugal-force-exist
In short, the answer depends on how you define whether a force exist or how you define "un-physical". Nevertheless, the physical picture we used in the simulation is valid and robust.
@@EASYEarthSciences I meant particle trajectories in the simulation. I'm just trying to understand what the simulation is showing. I guess it's demonstrating the shape of the potential surface only?
@@JanPBtest the simulation is done in a rotating reference frame is what he's saying. If the "camera" were to be stationary you would see the blue planet orbiting the sun and all the tiny satellite dots would initially be orbiting the sun at the same speed as the planet. But then trying to picture how Lagrange point stability works would be impossible for the human brain to decipher. Instead, by assuming the entire frame of reference is rotating at the same speed as the planet's orbit, the objects of interest all initially start "stationary" despite them actually circling the Sun. To account for the fact that the reference frame is rotating the sim needs to factor in fictitious forces, or forces don't actually exist from a stationary view point, but which appear to exist from the rotating viewpoint.
For example, imagine you are on a spinny carnival ride that spins fast enough to stick you to the wall. From your rotating point of view it feels like you are being pressed into the wall. But it's not like there's actually something pushing you against the wall, because that would be magic. Instead, from my stationary perspectivd outside the ride I can see what's actually happening. In actuality, your body is trying to move in a straight line, for an object in motion always 'wants' to maintain that motion, both in how fast and in what direction it's traveling. However the round walls of the spinning ride are constantly acting to redirect your motion by exerting a pulling force towards the center of of rotation, thus keeping you moving in a circle rather than careening in a straight line right into a hot dog stand. You could imagine if the walls around you suddenly vanished, to me I would suddenly see you travel in a straight line tangent to the circle you once traveled. From your view you are being pushed away from the center, this is a fictitious force that is experiemced only if we assume the emtire reference frame is rotating. From my view you are being pulled towards the center of the ride the walls, which act to constantly redirect your momentum. This is the true force that exists from a stationary reference frame. For this sim, to make it easier to visualize, he selected a rotating reference frame and so had to account for this by adding in the fictitious centripetal forces (the one I described in the carnival example), and also the Coriolis force which is a bit more complex to describe so I'll let you look that up on your own.
I'm guessing that the planet is orbiting the star, and the camera is just following it?
Yes that's correct!
This is usually called "co-rotating frame". And because we are doing the simulation in co-rotating frame, we need to consider centrifugal and Coriolis force when calculating the particles' acceleration. You can see this in more detail in the other two videos of this series.
is this in a rotating frame of reference or are the two mass bodies fixed? In some parts of the simulation, the movement of the massless particles seems odd, so my initial guess was that this is due to the frame of reference rotating and thus not being inertial.
NVM, you answered this in the comments already. :)
The frame of reference do be rotating
What are the moving blue dots?
I do know where the lagrange points are but the blue dots are mysterious to me.
@تريكي (رئيس جلد الشحاتين) and they aren't real asteroids right, just some referential ones?
the objects are asteroids?
Not necessarily.
I did not understand one damn thing, how many are of the same view?
I couldn’t find the Lagrange Point until about my 3rd or 4th girlfriend back then...
L1 is tough the first time, but it gets easier after thatt. L4 & L5 are a breeze. So to speak.
How does gravity act on a massless particle?
Hi, thank you for the question. Indeed, the term "massless" is somewhat misleading. We call them massless because their mass is so much smaller than the other two main body (e.g. Sun and Earth), not meaning their rest mass is zero (like photon).
Nonetheless, whether massless particles like photon would be affected by gravity is also an interesting topic. You might want to see some discussion as shown below:
aapt.scitation.org/doi/pdf/10.1119/1.13435
www.researchgate.net/post/How-can-Newtons-gravity-theory-predict-that-light-is-bent-when-passing-close-to-a-star
@@EASYEarthSciences Thank you for answering my question. Very good simulation.
Mathematically its the origin or the limit where suns_grawith- earths_grawith=< grawith_of_flyingobject :P
atleast thats what i guess from graph ;p so no one pulls the flyig object to somewhere atleast not that noticeable ;p
Close. You missed the fictitious forces due to rotation. You can't tell visually, but if you read (or watch) up on Lagrange points you'll realize that the "camera" looking down on this simulated system is rotating at the same speed that the blue planet orbits the sun, thus making both appear stationary. That makes this entire system a rotating reference frame roughly centered on the sun. So you need to also account for the centripetal (or centrifugal, whichever is the fictitious force, I always much those up) and Coriolis forces. Alternatively you could have the planet actually orbit the sun and thus have the reference frame be a stationary inertial one and then you'd be right in only accounting for gravitational forces and inertia (if I understand correctly). Although I might be misunderstanding what "grawith" means in your original equation as I have not seen this term before and assumed you meant gravity.
What?
I don't know what their actual properties... But i do know that out there, there is a big party going on.. 😂😂
我不明白。
關於拉格朗日點，可以來看看我們在「泛科學」上對 JWST 的介紹文章！
pansci.asia/archives/332819
What
Apparently something is wrong with the simulation? Nothing is stable even in the stable L4 and L5 points
L4 and L5 are stable, doesn't mean any particle around them will always be able stay there. Your orbital parameters still need to lie within some particular regime in order to circulate around them.
Also, not all the restricted 3 body system has stable Lagrange points. As shown in the two other simulations in the series, only those system with mass ratio > 24.97 can create stable L4 and L5.
@@EASYEarthSciences , what is the mass ratio here?
@@GoblinAlchem
A year late, but I'll answer anyway.
See, when people say that L4 and L5 points are stable, that isn't always true. There is a certain condition that must be satisfied, namely that the mass ratio between the primary and secondary is greater than 24.96 (if you do the math behind it, you'll see that the actual exact value is (25 + 3 * sqrt(69)) / 2). If the mass ratio is less than that threshold, the L4 and L5 points become unstable, just like L1, L2, and L3.
For example, the mass ratio for Sun-Earth, Sun-Jupiter, and Earth-Moon is around 333000, 1000, and 81 respectively, all of which are greater than 24.96, so their L4 and L5 points are stable (if you ignore gravitational effects from other bodies, because for Earth-Moon they're technically not stable due to effects from the Sun). On the other hand, Pluto-Charon has a mass ratio of only 8, which is less than 24.96, so their L4 and L5 points are unstable.
For this simulation, either the points are simply too far away (which I doubt, since some of them got pretty close to it but still unstable regardless) or the maker set the mass ratio below 24.96.
Kinda meaningless with such a short timeframe. Hard to say, but it looks like you ended up with a Hilda-type orbit for at least one of them. Again, had to say in such a short timeframe.
That's true. This video is, scientifically speaking, quite meaningless. I actually wrote the code and made the two other videos in the playlist to demonstrate how centrifugal force, Coriolis force and gravity works in rotating frame. For this "Ring" simulation, I just want to mess around. But somehow people love it 😂.
Explain Better pls