This one certainly took a lot longer to put together than I originally anticipated - hope you found it worth the wait! As far as I'm aware, there hasn't been a high quality and complete version of this derivation made available to the public in video form before (so maybe this video is a first on that front). Looking forward to your feedback, questions and comments as always!
+Derpy Gaming I'll be part of a scientist panel discussing terraforming in-depth in Edinburgh in April: www.sciencefestival.co.uk/event-details/terraforming--terrifying-or-terrific
Please try a question for me as I cannot get the answer in the back of the book. Aphelion = 150 AU, Perihelion = 0.4 AU. Speed at Aphelion is 7000 m/s. Find speed at Perihelion.
I just watched a 50 minute video while only understanding the first 10 minutes. You, my man, have some talent to explain topics even though its way above my level. Well done!
Your derivation is great! Most of the others I’ve found rely on the principles of conservation of energy and angular momentum. I understand those principles were postulated more recently in science history, so this approach seems more “pure” to me. Thanks a lot!!!
Getting back into Physics after spending almost 10 years in tech, had the idea to start with Kepler. Your presentation really helped me wrap my head around his results. Thank you!
Holy smokes, that is some serious maths. At least for me and my rusty maths knowledge. Now I know why Sal Khan always mentions "mastery based learning". I have quite some gaps in my math skills and find it quite impressive how you "play" with it due to your profound knowledge. Respect. I'm blown away by what Kepler, Newton, Gauss & co. came up with in the distant past.
Martian Colonist I’m currently reading “Seven Brief Lessons on Physics” by Carlo Rovelli and he wrote about both the topics you mentioned. Agree on the relativity part - haven’t read the quantum mechanics chapter yet, so it’s still a black box. :)
I highly recommend Leonard Susskind's 'The Theoretical Minimum' courses (all free online) if you would like to develop a deep conceptual understanding of modern Physics: theoreticalminimum.com/courses
Thanks for the recommendation. I'll put it on my watchlist. Funny Kerbal Space Program lured me into the physics rabbit-hole. My initial question was only if it's possible to calculate the Hohmann transfer window to a planet with an eccentric orbit. I still don't have the answer to that, but a ton more question :)
Hi Martin, nice video, one quick question. How did you get from d^2r/dt^2-h^2/r^3+G(Mp+MS)/r^2 = 0 to d^2u/dtheta^2+u=G(Mp+Ms)/h^2. I understand all of it, except this part right here. Hope you explain.
Great video! but I have a couple items of advice: First it is way too long, break it up into 5 parts if you have to; you will get far more views and watch time over all. Second did you know that you can add more ads to thees long form videos and make more money? If the video is more then ten minutes you can add commercial breaks in the middle or end of the video. just go to the monitization page in the "info and settings" and you will be able to change it.
+Cody'sLab This IS the broken apart version :) I chose not to subdivide this video as the middle parts would be meaningless in such a long derivation. I instead opted for overall coherence, as finding this entire derivation in one place has been annoyingly difficult to date. This video was made at special request, so I don't expect too many views beyond dedicated orbital mechanics enthusiasts. Equally, with such a small intended audience I wanted to reward those who elect to listen to the entire thing by not subjecting them to ads.
I actually chose to watch this one precisely *because* it had a decent length. Way too many little crap nothing videos on UA-cam. People used to have an attention span longer than two minutes.
That's a simple relationship for a circular orbit, but it is very complicated for an elliptical orbit, which is most of them. I iterated through an animation with r varying from apohelion to perihelion like an oval clock face, but we can approximate each step-wise iteration based on each angle being time times relative velocity and the angle plugged into three equations, one for the radius of the ellipse at that angle and the other two giving x and y based on the radius and the angle, which is good enough for plotting a simple animation, but not good enough for getting to, say, the Moon, Mars or Pluto
13:19 the proportionality don't create the law. F would need to be directly proportional to the square radius or inversely proportional to the mass product, all that assuming of course that the constants are different, which the inclusion of G dictates is not the case. Equal constants cancel
Greetings Martian! With due respect, please help me out! I'm stucked. At 34:30 you mentioned, that " If we want to define a two dimension coordinate system, we also define a direction at right angles to this vector r, so that we have a well defined coordinates, so we can define a unit vector theta, at righ angles to the vector r." Martian! Please explain this so called coordinate system to me, because I have no idea where I can see, how I can see on the related diagram / drawing the 2 dimensional coordinate system. Maybe I'm blind or I just can't visualise it. If vector r will going to move in the respect of time, then theta hat also forced to move to keep the right angle. So we talk about a fix or a moving 2D coordinate system? I can't figure out. I want to smile on my question, after the answer will crystal clear for me. But I want the answer. Please help! Sincerely yours! Great video!!!
hi Martian your explanation is quite clear to understand. your knowledge about the subject is really quite deep. thanks for explaining planets orbit in such a beautiful way.
Great video with great subject. Great that the lecture can go without adverts which disturbs attention and concentration. It was also great for my exam on Orbital mechanics, very good way of understanding the Kepler and Newton’s Law Of orbits.
Q: When a planet moves a around a star, with different velocities at it’s perihelion and it’s aphelion, does that mean that time on that planet goes slower or faster, because time goes slower when an object moves faster?
You never really explained why the e at the beginning is the same as the e at the end, it looks like you've arbitrarily just called it e so that the algebra cancels out
The eccentricity serves the mathematical role of controlling the shape of the ellipse. We are always free to define a new constant, then verify it has the prescribed behaviour (in this case that on a conic section). You can also quite readily show the physical basis of e in terms of the orbit's energy by working in a Lagrangian framework (my preferred approach) - though that would require a side diversion into the calculus of variations in order to explain it from first principles.
+Martian Colonist you don't make that point however. Go watch the video-- you establish the e as being eccentricity of the ellipse, and then we forget it, then way later you just arbitrarily create a new variable, label it e and then start interchanging this with the old variable e. You are free to define a variable, but not to attach it to variable which has already been defined, unless you state that they are defining the same value. Go watch the video, it really does appear to be a "here's one I prepared earlier" with that e variable ( I hate using lower case e to denote anything which isn't Euler's constant, but that's the convention). I really had to go away and satisfy myself that you hadn't pulled a fast one on me. Otherwise, awesome video!
Establishing e as the eccentricity in the prelude was to provide physical intuition for how it controls the shape of an ellipse. I agree that more formally I could have defined a variable e' and then showed that it is precisely equivalent to the e as defined earlier, though I thought that to be evident from the form of the solution that came out of solving the differential equation. For further clarity, you may find this useful: arxiv.org/pdf/1009.1738
I'm plagued by my previous comments--I hope you didn't take offence from my comments on a pretty trivial matter really. Your video is brilliant, and I get my students to watch this.
yep it is indeeed well organised website ...but dont u think it is bit more basical i mean it started asking me Q .OF MATH OF 5TH GRADE ..LINEAR PAIR OF ANGLES!!
The unit vector theta is perpendicular to the unit vector in the direction of r. The easiest way to work out theta hat is to differentiate the components of r hat with despect to theta. Since r hat = cos(theta) x hat + sin(theta) y hat, the derivate is theta hat = - sin(theta) x hat + cos(theta) y hat. You can verify this is perpendicular by taking the dot product of r hat and theta hat, which is zero for perpendicular vectors.
Very good demonstration - is there a Part 2 - I cant find it on channel? Very interested in proving the time Period T of orbit is same as that for circular orbit.
I'm afraid I didn't get around to making a part 2 (mainly due to a lack of demand), but I'll try to dig up a reference for proving the 3rd law holds for non-circular orbits for you...
Absolutely fantastic treatise on the subject; thank you so much. I was trying to do a deep dive into Satellite Communications. Coming from an EE background, I was stymied by the first chapter about orbital mechanics in a book on SatComm, which threw in the final expression above and terms such as "anomaly" which made no sense. Elsewhere I could only find superficial explanations, and even worse, peppered with comments such as "as is well known in standard calculus" or "as you would have learned in school". Your description is so precise and comprehensive, which I did not find anywhere else; thank you again.
The question is why, not how you think it works because of math. Babble for a whole hour without answering a simple question. Is it off balance from where it would be to make a circle or because a planet and sun are both moving towards the other?
The math gives you the how and the why, you probably just don’t understand it i’m guessing, and i don’t even mean that as an insult. To say it simply, the elliptical shape is true because in order to get a perfect circle shape for an orbit, the forces involved and the velocity of the orbiting objects have to be in a balance. Most planets won’t get the exact right trajectory and speed, etc, to maintain a perfect circle shape. And since a circle is really just a special case of an ellipse, it would make sense for planetary orbits to be generally many different kinds of ellipses and not just one rare special case. This video is more about the mathematical proof of it being an elliptical shape, but maths will give you the answers you’re looking for if you’re willing to delve into it.
I read other comments...."Great Explanation!" etc..so I believe it IS a great explanation.........so I need a refresher course in EVERYTHING!! I guess my age doesn't help either, but after the first 5 minutes, this video wound up sounding like waves breaking on the beach and I found myself thinking about things I need from the store.
I would imagine that it would be much more difficult to do a future calculation for ae, r and your angles due to the interference from the other planets. I would guess that we do basic calculations for the positions of the sun and planets all the time just to make sure that our computers don't blow up? I would imagine that other celestial bodies may exert some influence on us as well. Maybe Alpha Centari, the black hole at the center of the galaxy, other local stars and black holes. Exoplanets. I know Gravity is the weakest of the four forces but exactly how weak is it?
SuperNorstShow Well this is general relativity not newtonian mechanics, but the “speed” of gravity is the speed of light. In other words, gravity is not a force that acts upon on objects instantaneously, it takes time for objects to gravitationally affect each other. So when you ask about how much other planets/stars/galaxies affect our calculations, they would really only have a measurable effect if they were sufficiently close or enough time had passed for the gravitational force to reach it (since the force travels at the speed of light). I presume gravitational waves are detected by us waiting enough time for the gravitational waves from distant celestial bodies to reach the earth, as the gravitational interaction is not instantaneous as newton thought.
I have a question....as per I know, Kepler's Laws of motion was published before Newton's law of gravity............Rather, Newton unified Kepler's Laws of Planetary motion and his own third law of motion to come up with the law of gravitation.....So how can you derive Kepler's law from Newton's Law of gravitation???????????? Johannes Kepler published his first two laws about planetary motion in 1609 and third law was published in 1619. Isaac Newton showed in 1687 that relationships like Kepler's would apply in the Solar System to a good approximation, as a consequence of his own laws of motion and law of universal gravitation.
Kepler's laws were first derived empirically by looking for patterns in observed planetary motion data collected by Tycho Brahe. Kepler basically 'guessed' that planetary orbits are elliptical, because that fit the data. But it wasn't until Newton that it was proven *why* Kepler's laws are true.
I wanted to explain this to my lil brother in 2 grade, Einstien said"If you can't explain it to a six year old, you don't understand it yourself", I dont think i can make him understand by this.
It's ultimately a philosophical point about what it means to ask 'why' something is true. If you want to rigourously know the reason behind phenomena in nature, there unfortunately isn't an alternative to delving into the relative mathematics that the laws of nature are written in. Einstein always endeavoured to make the maths behind his equations as simple as possible, but that still poses a minimum level of algebra for Special Relativity and Tensor Calculus + Differential Geometry for General Relativity. So if you are looking for a simple 'why' then you could talk about how the force of gravity changes with distance and it 'turns out' this implies an ellipse. I don't think this explanation adequately explains why the orbit isn't some other shape though.
+Martial Colonist i get this derivation and what you derived made sense but can you give me a more theoretical explanation (reasoning not proving) for the same. Links are also helpful. Thanks
On a fundamental level, it is due to two principles: 1) The equivalence of inertial mass and gravitational mass (i.e. the m in F=ma is the same m as in W=mg). 2) The force of gravity following an inverse square law (i.e. F=Gm1m2/r^2). Both 1) and 2) holding lead to elliptical orbits. For an interesting demonstration of this, in Einstein's theory of General Relativity 1) holds in generality, but 2) is only approximately true. The consequence is that in areas with strong gravitational fields orbits are not perfectly elliptical and undergo precession. For example, this effect causes the orbit of Mercury to deviate (very slightly) from that of an ellipse.
OK, then why not a circular orbit (technically speaking circle is also an ellipse, so can a circular orbit also exist ?) with sun at the center and centrifugal force equal to gravitational force ? (like in atomic model where coulombs force is equal to centrifugal force )
Strictly speaking, no perfectly circular orbits exist in the Universe (as even an orbit with eccentricity = 0.00000000000001 is an ellipse, even though it would appear remarkably circular). Also, bear in mind that electron orbits in atoms aren't circular either (electrons are better thought of as 'probability clouds', known as orbitals).
If i consider no other force (except for the one force between the star and the planet) by this same derivation we can see that circular orbits exist. (actually even if we take all the forces shouldn't randomness of these forces cancel each other out somewhere in the universe but then again this is completely hypothetical) and e=[1-(b^2/a^2)]^(1/2) so in a case where a=b ; e=0 that means this will be a circle and again circle is just a case of ellipse in which the foci are coinciding or have a infinitesimal distance between them. So I ask again can circular orbits really not exist. And thanks for answering my last question.
12:57 what is interesting is Newton never figured out what value of his universal gravitational constant was. Herny Cavendish did that after Newton's death 71 years later. Too bad. Newton would have been delighted.
The elliptical orbit of the planets are caused by the onward motion of the sun/star. similarly the advance of the perihelion of the planet mercury is caused by the curved path of the sun in space,which is circle the milky way galaxy.
So your first sentence states the common sense reason why the planets move in elliptical orbits. And the above video the long tedious, not necessary to know unless an astrophysicist, proof. Thank you, that's why I clicked on the link.
_"Ryan MacDonald - a Theoretical Astrophysicist based at Cambridge University - proves from first principles Kepler's laws of planetary motion_ *_(Part 1 of 2)"_* what about Part 2?
18- #Planetary Orbits All stars and planets have orbits. For centuries it was believed that Earth is fixed and the sun, moon and planets revolve around it. However 1400 years ago the Quran said that not only the sun and moon but also Earth moves in a designated path: [Quran 39.5] [Allah] Created the heavens and the Earth in truth. He overlaps the night over the day and overlaps the day over the night, and enslaved the sun and the moon, ALL MOVE (كل يجري) to a prerecorded destiny. Is He not the Exalted, the Forgiver? Here the Quran is referring to ALL MOVING: not only the sun and moon but also Earth. In Arabic grammar there is difference between the singular (one), binary (two) and plural (three or more). The reference to binary is "Kulahuma Yajreean كلاهما يجريان" however the Quran said "Kullon yajree كل يجري" referring to the plural (three or more). Since the sun and moon are just two but the Quran is referring to three or more then according to the Quran all the three move sun, moon and Earth. [Quran 86.11] And the sky that returns. "Al-rajeh الرَّجْعِ" means returns to the same location. Today we know that all planets return to the same locations in their respective orbits. How could an illiterate man who lived 1400 years ago have known that planets return to their original locations? Mistranslations: Quran 18.86 sun setting in a spring. (The Christian Bible says that Earth is a 2 dimensional flat disk and the heaven is like a canopy solid like bronze: Isaiah 40:22)
Kepler found the laws empirically by studying years of observations. It wasn't until Newton that it was theoretically understood *why* Kepler's laws hold.
Wow!! This worked better than Ambien!! *** Note to self....stick to videos with "Hubble Images" in title!! Watched it for a while, but way over my head at this point. Definitely going back to school if I hit the lottery!!! LOL!!!
Thanks a lot! I had another doubt as well. At around 23 mins into it, you mentioned that r=r2-r1 Assuming the angle made by the lines r2 and r1 is = 90 degrees, shouldn't r = the square root of r1^2 + r2^2? I understand that the Pythagoras Theorem works with the angle being 90 degrees, but I didn't seem to understand how r2 was greater than r. Thanks again! Loved this!
If you look at the diagram at 22:00 you can see than the vector r1 starts at the origin ('O') and points towards the star, whilst r2 starts at the origin and points towards the planet. Now imagine you are stood on the star and want to go to the planet. You would travel from the star to the origin, travelling in the opposite direction to r1 (-r1) and then travel from the origin to the planet (+r2), so the overall (vector) equation for the distance between the star and the planet is r=-r1 + r2 = r2-r1. Hope that helps!
Scientific fact and scientific law are totally different things. You have to look up the meaning of the word law and the meaning of the words scientific law in that order.
Ty for the video and the good effort from your part but it is very confusing and too long! I have watched tons of vids about the motion of the planets and all ellipses but there is no video yet that explains with clarity and without glitches the elliptic orbits! So why the planets orbit stars in ellipses!? I see lot of comments from ppl here and it seems that most of them understand the issue but when you ask them to explain to you they know sh!t and they are more confused than ever! Im asking ppl who knows on the matter can someone just in two words explain the ellipses!? Martian Colonist with all the respect ty for ur time and ur dedication! Cheers!
I watched the whole thing, and i do not see where you answered the question. I know you did, but my math skills are not on this level. not even close. perhaps do a very specific example? like say how to observe Mars position, and then use what we know to derive it's orbit, and why it is elliptical. though i find the math interesting, i can't follow with substituting real numbers, and this would take me several days to research what the actual numbers are in order to plug them in. yes the formula is more important, but it makes my brain hurt. haha. just a few more videos and i will have seen all your videos up to 3 years ago. in the immortal words of Spock "Fascinating"
I do like the video and am glad for fewer ads, but i would have watched it even with more ads. I know what effort goes into even very simple videos, and creators deserve the rewards they have earned. just my free unsolicited .5 cents
The succinct answer is that an elliptical orbit is the inevitable consequence of two fundamental laws: 1. The gravitational force falls off as the inverse square of distance. 2. Net force is directly proportional to acceleration. All the mathematics in this video is just proving that if these two laws hold, bound orbits must have an elliptical shape.
@@martiancolonist is this fundamental, or more to do with other bodies acting within the system? IE Jupiter pulls on the sun and thus upsets the earths (Barry center) orbit? happy holidays, just a few videos left and i will be in the les than 3 years old content you have created.
@@jadefinchscene5644 it is fundamental for two-body interactions. If you have multiple bodies, the sum over the competing forces changes the distance-dependence, so more complicated orbits can result. These additional interactions (such as from Jupiter) act to perturb the orbits of the planets over long timescales.
@@martiancolonist excellent. thank you so much for helping me understand. the math is very cool, and i wish i had teachers back in school who would have shown me real world applications of the math instead of just saying trust me. I would have actually found it useful, instead of just confusing. seeing no use for it all i just ignored it. 25 years later I am looking back and am finding it all fascinating. because i can actually apply it to something. I will continue to learn these things as best i can. I have a physics graduate living with me, and another that is finishing his PHD thesis living across the street, so i have some help. thank you for taking the time to reply.
Please make a video on proving that the expression you got at the end is actually an ellipse by showing that it produces a shape that satisfies the geometric definition of an ellipse. That would complete this proof.
Loved this video. I had that question several times before - as to how can one say that planets will follow an elliptical orbit just using Newton's Gravity equation... and seeing this video was very satisfying. Btw, I was not expecting the solution to be so complicated, but nevertheless I was able to follow it fully. One thing you should have mentioned I think is that if e has greater than or equal to 1 then it becomes a parabola or hyperbola. (correct?)
grkhetan Glad you liked the video! Yes, the complicated nature of the derivation is why it took a fair amount of time before Newton first showed it. In this video I was taking 'orbit' to explicitly mean bound periodic trajectories (sometimes parabolic or hyperbolic trajectories are called 'unbound orbits'). You are correct that conic sections with e=1 are parabolic and e>1 are hyperbolic.
Did Newton also show that his gravity equation and laws of motion implies elliptical orbits? Did he use a similar proof? I somehow feel that there might be a simpler way to prove this than this method? What do you think?
grkhetan Newton used a quite convoluted geometric proof, which is quite difficult to follow compared to this one (as calculus was quite new back then, he proved it without using calculus so that most readers could follow it).
Yes but Newton didn't have vector calculus so he couldn't do it that way. He couldn't even calculate the value of G used in his equations, that was accomplished over one hundred years later by sharper minded people.
So, I find the description of this video interesting. "Of all the possible shapes..., why ellipses?" Well, what else would it be? What shape seems more likely? One could say circle, but in all of the salient ways that matter a circle *is* an ellipse. You certainly wouldn't expect a shape with corners. What is some other smooth closed shape that would be a viable candidate? Just by starting with that type of reasoning one could have almost *guessed* that it needed to be either an ellipse or a circle. Also, you know historically this ran the other way. We started with the ellipses, and then inferred inverse square behavior for the force law from that. Anyway, I suspect that an ellipse is the simplest shape you can come up with (except for the circle special case) that provides a smooth (no corners) trajectory. And we could reject the circle as a *required* shape just based on the independence of orthogonal directions. If behaviors in x and y have to be independent of each other, then a circle is too tight a requirement. Next you come to the ellipse. It's a simple harmonic oscillator in each direction - absolutely the simplest thing it can possibly be.
I didn't click "Dislike" because I realize that the source of my complaint could be my own ignorance. I listened to the whole presentation, and I think that the only thing that was explained is the geometry of an ellipse. I didn't come away understanding why an orbit would be elliptical rather than circular. I thought that I understood that the concept of an orbit is that the orbiting object is in constant free fall. I was expecting to expand my understanding of that, but it wasn't addressed. It seemed like I was listening to a high school teacher that understands a complicated concept, but lacks ability to communicate it to others. Just speaking out loud what you're writing is not teaching. Again, I know my ignorance level is high. If someone that understands this subject better than me disagrees with my analysis of the video, please respond to my comment so that it won't keep others from watching the video.
Thanks for your feedback. The essential reason for elliptical orbits is the combination of a force (in this case, gravity) that follows an inverse square law and force being directly propertional to acceleration (F=ma). Interestingly, these two conditions are actually only true for speeds slow relative to the speed of light (F=ma changes, as if the mass, m, increases) and `weak' gravitational fields. For example, this means that Mercury follows a slightly `non-elliptical' orbit (due to the gravitational field of the Sun altering the geometry of space-time), which requires Einstein's General Relativity to explain. Thus elliptical orbits are essentially a prediction of Newtonian gravity and Newton's 2nd law (as I emphasise at the beginning of the video). My approach here was to explain the key reason (Newton's law of gravity + Newton's 2nd law) qualitatively at the beginning, before showing quantitatively how these ideas lead to an ellipse as the unique solution. The maths was then intended as an appendix for those who were interested, as it is hard to find this online (I didn't want people to have to just accept it was true). As to your question about circles, a circle is an ellipse (it is an ellipse where the eccentricity parameter is exactly 0). As no bound orbit in the Universe will have exactly zero eccentricity, every bound orbit will be an ellipse, with circular orbits simply convenient for thought experiments (as the maths is easier). I hope that helps, please let me know if you have more questions!
Newton's proof was a quite convoluted geometric proof (as calculus was still being developed at the time), which is quite archaic and difficultt to follow compared to the one presented here.
Please help !!. (1)"Why is the above so complicating, are we "missing" something ??" (2)"Why did the knowledgeable Isaac Newton create 3 laws instead of one law ??" (3)"Did he hide the meaning of the single formula by inferring to it with 3 laws ??" (4)"If so why ??" * * [Note] Sadly an injustice was done in 1729 by the honorable Andrew Motte, when he translated "viribus(Latin)" meaning "strength" to "force".* * Much will be come clear when corrected.
The orbits are elliptical because gravity is an inverse square law (to a close approximation). Google "Feynman's Lost Lecture" on UA-cam; it's a 3Blue1Brown video. He works it all out.
The essential reason is given at the beginning: it is due to Newton's law of gravity being an inverse square law, coupled with Newton's 3 laws of motion. The rest of the video is proving that this statement is correct, rather than simply expecting people to accept it on faith.
What a whole lot of crap. Speed can never compete with acceleration. Unless it's initial values is.... infinite... Fire a bullet vertically up with the speed of a gps satellite, 14000 km/h. Within 15 minutes it sits theoretically 500 km under sealevel! O wait, I should fire the bullet horizontally, that's my bug! Ha ha ha ha ha! Orbital science, what a bullshit. The moon circles the earth. Ok. But NOT due to gravity.
Jan Spreen: Simple trolling is the best trolling. But in case you're for real, Khan Academy offers free physics classes. That bullet...it's acceleration drops to nil. The duration of the acceleration is very very important. Its KINETIC ENERGY is shit because it doesn't hardly weigh anything. Learn some kinematics, and it will all make sense. en.wikipedia.org/wiki/Kinematics
You know your stuff but you do have many problems 1. You use the word THIS too many times and the viewer do not know where this is. 2. You do not progress left to right and top to bottom which we all use when answering a question instead of scribbling all over like graffiti Watch the Dr Physics how he does it. It is said that those who csnt teach. You are the opposite you can buy cant Teach. You need to go to teachers training school to teach. I used to think those schools are irrelevant but now I know you need it
![How the Bizarre Path of Mars Reshaped Astronomy [Kepler's Laws Part 1]](http://i.ytimg.com/vi/Phscjl0u6TI/mqdefault.jpg)
![How the Bizarre Path of Mars Reshaped Astronomy [Kepler's Laws Part 1]](/img/tr.png)
This one certainly took a lot longer to put together than I originally anticipated - hope you found it worth the wait!
As far as I'm aware, there hasn't been a high quality and complete version of this derivation made available to the public in video form before (so maybe this video is a first on that front).
Looking forward to your feedback, questions and comments as always!
I have a question for you (It might be a little off topic of this video :) ) What is your opinion on terraforming of Mars?
+Derpy Gaming
I'll be part of a scientist panel discussing terraforming in-depth in Edinburgh in April:
www.sciencefestival.co.uk/event-details/terraforming--terrifying-or-terrific
+Martian Colonist awesome! I'll be looking forward to that! :)
Please try a question for me as I cannot get the answer in the back of the book. Aphelion = 150 AU, Perihelion = 0.4 AU. Speed at Aphelion is 7000 m/s. Find speed at Perihelion.
I just watched a 50 minute video while only understanding the first 10 minutes. You, my man, have some talent to explain topics even though its way above my level. Well done!
Thanks for the kind words!
We need time to get familiar, nothing is above anyone’s level.
Go watch some khan academy videos. And go play some Kerbal space program. You can learn anything
Your derivation is great! Most of the others I’ve found rely on the principles of conservation of energy
and angular momentum. I understand those principles were postulated more recently
in science history, so this approach seems more “pure” to me. Thanks a lot!!!
Getting back into Physics after spending almost 10 years in tech, had the idea to start with Kepler. Your presentation really helped me wrap my head around his results. Thank you!
Holy smokes, that is some serious maths. At least for me and my rusty maths knowledge.
Now I know why Sal Khan always mentions "mastery based learning". I have quite some gaps in my math skills and find it quite impressive how you "play" with it due to your profound knowledge. Respect.
I'm blown away by what Kepler, Newton, Gauss & co. came up with in the distant past.
The beauty of relativity and quantum mechanics completely blows this out of the water!
Martian Colonist I’m currently reading “Seven Brief Lessons on Physics” by Carlo Rovelli and he wrote about both the topics you mentioned. Agree on the relativity part - haven’t read the quantum mechanics chapter yet, so it’s still a black box. :)
I highly recommend Leonard Susskind's 'The Theoretical Minimum' courses (all free online) if you would like to develop a deep conceptual understanding of modern Physics: theoreticalminimum.com/courses
Thanks for the recommendation. I'll put it on my watchlist. Funny Kerbal Space Program lured me into the physics rabbit-hole. My initial question was only if it's possible to calculate the Hohmann transfer window to a planet with an eccentric orbit. I still don't have the answer to that, but a ton more question :)
@@martiancolonist Thanks a lot for this!! Now my summer is going to be good.
Hi Martin, nice video, one quick question. How did you get from d^2r/dt^2-h^2/r^3+G(Mp+MS)/r^2 = 0 to d^2u/dtheta^2+u=G(Mp+Ms)/h^2. I understand all of it, except this part right here. Hope you explain.
33:40. Got a little lost here regarding the unit vector theta.
Good Day Mr Ryan, could you please share the links of video for this next video you mentioned before about 2nd and 3rd laws of Kepler?..... Thanks.. 👌
Great video! but I have a couple items of advice: First it is way too long, break it up into 5 parts if you have to; you will get far more views and watch time over all. Second did you know that you can add more ads to thees long form videos and make more money? If the video is more then ten minutes you can add commercial breaks in the middle or end of the video. just go to the monitization page in the "info and settings" and you will be able to change it.
+Cody'sLab
This IS the broken apart version :)
I chose not to subdivide this video as the middle parts would be meaningless in such a long derivation. I instead opted for overall coherence, as finding this entire derivation in one place has been annoyingly difficult to date.
This video was made at special request, so I don't expect too many views beyond dedicated orbital mechanics enthusiasts. Equally, with such a small intended audience I wanted to reward those who elect to listen to the entire thing by not subjecting them to ads.
Alright sounds good.
+Cody'sLab
Thanks for the advice Cody!
I actually chose to watch this one precisely *because* it had a decent length. Way too many little crap nothing videos on UA-cam. People used to have an attention span longer than two minutes.
how do you calculate the orbital position with respect to time (or angle)?
That's a simple relationship for a circular orbit, but it is very complicated for an elliptical orbit, which is most of them. I iterated through an animation with r varying from apohelion to perihelion like an oval clock face, but we can approximate each step-wise iteration based on each angle being time times relative velocity and the angle plugged into three equations, one for the radius of the ellipse at that angle and the other two giving x and y based on the radius and the angle, which is good enough for plotting a simple animation, but not good enough for getting to, say, the Moon, Mars or Pluto
13:19 the proportionality don't create the law. F would need to be directly proportional to the square radius or inversely proportional to the mass product, all that assuming of course that the constants are different, which the inclusion of G dictates is not the case. Equal constants cancel
Greetings Martian! With due respect, please help me out! I'm stucked. At 34:30 you mentioned, that " If we want to define a two dimension coordinate system, we also define a direction at right angles to this vector r, so that we have a well defined coordinates, so we can define a unit vector theta, at righ angles to the vector r." Martian! Please explain this so called coordinate system to me, because I have no idea where I can see, how I can see on the related diagram / drawing the 2 dimensional coordinate system. Maybe I'm blind or I just can't visualise it. If vector r will going to move in the respect of time, then theta hat also forced to move to keep the right angle. So we talk about a fix or a moving 2D coordinate system? I can't figure out. I want to smile on my question, after the answer will crystal clear for me. But I want the answer. Please help! Sincerely yours! Great video!!!
hi Martian your explanation is quite clear to understand. your knowledge about the subject is really quite deep. thanks for explaining planets orbit in such a beautiful way.
did you wrote third law wrong? I read on Feynman's lectures on physics it says 3/2 power of diameter. which is a 3/2
Pen tip needs to have a pointer to see where you are/move on the screen.
Great video with great subject. Great that the lecture can go without adverts which disturbs attention and concentration.
It was also great for my exam on Orbital mechanics, very good way of understanding the Kepler and Newton’s Law Of orbits.
Q: When a planet moves a around a star, with different velocities at it’s perihelion and it’s aphelion,
does that mean that time on that planet goes slower or faster,
because time goes slower when an object moves faster?
No, the speeds of the planets are too small to be affected by any noticeable time dilation effect.
You never really explained why the e at the beginning is the same as the e at the end, it looks like you've arbitrarily just called it e so that the algebra cancels out
The eccentricity serves the mathematical role of controlling the shape of the ellipse. We are always free to define a new constant, then verify it has the prescribed behaviour (in this case that on a conic section). You can also quite readily show the physical basis of e in terms of the orbit's energy by working in a Lagrangian framework (my preferred approach) - though that would require a side diversion into the calculus of variations in order to explain it from first principles.
+Martian Colonist you don't make that point however. Go watch the video-- you establish the e as being eccentricity of the ellipse, and then we forget it, then way later you just arbitrarily create a new variable, label it e and then start interchanging this with the old variable e. You are free to define a variable, but not to attach it to variable which has already been defined, unless you state that they are defining the same value.
Go watch the video, it really does appear to be a "here's one I prepared earlier" with that e variable ( I hate using lower case e to denote anything which isn't Euler's constant, but that's the convention).
I really had to go away and satisfy myself that you hadn't pulled a fast one on me.
Otherwise, awesome video!
Establishing e as the eccentricity in the prelude was to provide physical intuition for how it controls the shape of an ellipse. I agree that more formally I could have defined a variable e' and then showed that it is precisely equivalent to the e as defined earlier, though I thought that to be evident from the form of the solution that came out of solving the differential equation. For further clarity, you may find this useful: arxiv.org/pdf/1009.1738
I'm plagued by my previous comments--I hope you didn't take offence from my comments on a pretty trivial matter really. Your video is brilliant, and I get my students to watch this.
No problem, being pedantic and questioning is always a great way to probe the understanding of a topic.
What do you teach?
Hi, could you please tell me what is the velocity on circular orbit and on elliptical orbit I need the formula.
Does any of this preclude e=0?
You appeared to say (at about 10:48) that if 'e' is zero it is a circular orbit. A circular orbit is characterized by a=b and not by the parameter 'e.
Given that we define the eccentricity "e" as: e = SQRT(1-(b^2/a^2)), to say that e=0 or to say that a=b is exactly the same.
e is c/a.
c is the focal distance from the center.
e is also sqrt(1-(b^2/a^2))
so when b=a, e=0
hey ..i want to know abt sources or material or boooks to learn calculus
+RAHUL PATIL
www.khanacademy.org/
yep it is indeeed well organised website ...but dont u think it is bit more basical i mean it started asking me Q .OF MATH OF 5TH GRADE ..LINEAR PAIR OF ANGLES!!
RAHUL PATIL
It covers calculus up to university level vector calculus, just go to the right sections.
Martian Colonist okkk thanks man for insisting
u really explain things very well ...hey man but we arent phd holders like u sooo ..i insist u to speak english rather than science
How to plot the equation at the end for r(theta)?
You can substitute in r = sqrt(x^2 + y^2), x = r cos(theta) and y = r sin (theta) to go into cartesian coordinates.
@@martiancolonist thanks
Colonist as in colony or colon ?
I really want to learn calculus and vectors , please guide me
Crickey mate, listening to you makes me regret spending my childhood ( and adult life) reading the Beano.
Great video, thank you! How does theta hat equal -sin(theta) cos(theta)?
The unit vector theta is perpendicular to the unit vector in the direction of r. The easiest way to work out theta hat is to differentiate the components of r hat with despect to theta. Since r hat = cos(theta) x hat + sin(theta) y hat, the derivate is theta hat = - sin(theta) x hat + cos(theta) y hat.
You can verify this is perpendicular by taking the dot product of r hat and theta hat, which is zero for perpendicular vectors.
does planetary acceleration depend on its orbital eccentricity?
The greater the eccentricity the more rapid the change in velocity. The greatest rate of change occurs at closest approach.
@@martiancolonist can you make a video about this relationship and do the maths for it too? It would be really helpful for my high school paper
Very good demonstration - is there a Part 2 - I cant find it on channel? Very interested in proving the time Period T of orbit is same as that for circular orbit.
I'm afraid I didn't get around to making a part 2 (mainly due to a lack of demand), but I'll try to dig up a reference for proving the 3rd law holds for non-circular orbits for you...
Thanks. I have found a proof on maths stack - needed to t substitution for the integration. But thanks for the offer!
Why don't both have the ecllips they do
Absolutely fantastic treatise on the subject; thank you so much. I was trying to do a deep dive into Satellite Communications. Coming from an EE background, I was stymied by the first chapter about orbital mechanics in a book on SatComm, which threw in the final expression above and terms such as "anomaly" which made no sense. Elsewhere I could only find superficial explanations, and even worse, peppered with comments such as "as is well known in standard calculus" or "as you would have learned in school". Your description is so precise and comprehensive, which I did not find anywhere else; thank you again.
what ( eccentricity) depend on? as every planet has its own eccentricity and what is the factors that eccentricity depend on?
The question is why, not how you think it works because of math. Babble for a whole hour without answering a simple question. Is it off balance from where it would be to make a circle or because a planet and sun are both moving towards the other?
The math gives you the how and the why, you probably just don’t understand it i’m guessing, and i don’t even mean that as an insult.
To say it simply, the elliptical shape is true because in order to get a perfect circle shape for an orbit, the forces involved and the velocity of the orbiting objects have to be in a balance.
Most planets won’t get the exact right trajectory and speed, etc, to maintain a perfect circle shape. And since a circle is really just a special case of an ellipse, it would make sense for planetary orbits to be generally many different kinds of ellipses and not just one rare special case.
This video is more about the mathematical proof of it being an elliptical shape, but maths will give you the answers you’re looking for if you’re willing to delve into it.
Sir can you make about the satellites too , from the launch . Or anyone can recommend some video , it would be great help.
I read other comments...."Great Explanation!" etc..so I believe it IS a great explanation.........so I need a refresher course in EVERYTHING!!
I guess my age doesn't help either, but after the first 5 minutes, this video wound up sounding like waves breaking on the beach
and I found myself thinking about things I need from the store.
I would imagine that it would be much more difficult to do a future calculation for ae, r and your angles due to the interference from the other planets. I would guess that we do basic calculations for the positions of the sun and planets all the time just to make sure that our computers don't blow up? I would imagine that other celestial bodies may exert some influence on us as well. Maybe Alpha Centari, the black hole at the center of the galaxy, other local stars and black holes. Exoplanets. I know Gravity is the weakest of the four forces but exactly how weak is it?
SuperNorstShow Well this is general relativity not newtonian mechanics, but the “speed” of gravity is the speed of light. In other words, gravity is not a force that acts upon on objects instantaneously, it takes time for objects to gravitationally affect each other.
So when you ask about how much other planets/stars/galaxies affect our calculations, they would really only have a measurable effect if they were sufficiently close or enough time had passed for the gravitational force to reach it (since the force travels at the speed of light). I presume gravitational waves are detected by us waiting enough time for the gravitational waves from distant celestial bodies to reach the earth, as the gravitational interaction is not instantaneous as newton thought.
cool.liked the derivation.thanks
also why is there a launch window for launching satellites from earth to LEO?
I have a question....as per I know, Kepler's Laws of motion was published before Newton's law of gravity............Rather, Newton unified Kepler's Laws of Planetary motion and his own third law of motion to come up with the law of gravitation.....So how can you derive Kepler's law from Newton's Law of gravitation????????????
Johannes Kepler published his first two laws about planetary motion in 1609 and third law was published in 1619.
Isaac Newton showed in 1687 that relationships like Kepler's would apply in the Solar System to a good approximation, as a consequence of his own laws of motion and law of universal gravitation.
Kepler's laws were first derived empirically by looking for patterns in observed planetary motion data collected by Tycho Brahe. Kepler basically 'guessed' that planetary orbits are elliptical, because that fit the data. But it wasn't until Newton that it was proven *why* Kepler's laws are true.
I wanted to explain this to my lil brother in 2 grade, Einstien said"If you can't explain it to a six year old, you don't understand it yourself", I dont think i can make him understand by this.
It's ultimately a philosophical point about what it means to ask 'why' something is true. If you want to rigourously know the reason behind phenomena in nature, there unfortunately isn't an alternative to delving into the relative mathematics that the laws of nature are written in. Einstein always endeavoured to make the maths behind his equations as simple as possible, but that still poses a minimum level of algebra for Special Relativity and Tensor Calculus + Differential Geometry for General Relativity.
So if you are looking for a simple 'why' then you could talk about how the force of gravity changes with distance and it 'turns out' this implies an ellipse. I don't think this explanation adequately explains why the orbit isn't some other shape though.
I do not know calculus or vectors..kindly recommend appropriate reading material.
Very good till about 50:00.. too long it will be better if you use blackboard
+Martial Colonist i get this derivation and what you derived made sense but can you give me a more theoretical explanation (reasoning not proving) for the same. Links are also helpful. Thanks
On a fundamental level, it is due to two principles:
1) The equivalence of inertial mass and gravitational mass (i.e. the m in F=ma is the same m as in W=mg).
2) The force of gravity following an inverse square law (i.e. F=Gm1m2/r^2).
Both 1) and 2) holding lead to elliptical orbits. For an interesting demonstration of this, in Einstein's theory of General Relativity 1) holds in generality, but 2) is only approximately true. The consequence is that in areas with strong gravitational fields orbits are not perfectly elliptical and undergo precession. For example, this effect causes the orbit of Mercury to deviate (very slightly) from that of an ellipse.
OK, then why not a circular orbit (technically speaking circle is also an ellipse, so can a circular orbit also exist ?) with sun at the center and centrifugal force equal to gravitational force ? (like in atomic model where coulombs force is equal to centrifugal force )
Strictly speaking, no perfectly circular orbits exist in the Universe (as even an orbit with eccentricity = 0.00000000000001 is an ellipse, even though it would appear remarkably circular). Also, bear in mind that electron orbits in atoms aren't circular either (electrons are better thought of as 'probability clouds', known as orbitals).
If i consider no other force (except for the one force between the star and the planet) by this same derivation we can see that circular orbits exist. (actually even if we take all the forces shouldn't randomness of these forces cancel each other out somewhere in the universe but then again this is completely hypothetical) and e=[1-(b^2/a^2)]^(1/2) so in a case where a=b ; e=0 that means this will be a circle and again circle is just a case of ellipse in which the foci are coinciding or have a infinitesimal distance between them. So I ask again can circular orbits really not exist. And thanks for answering my last question.
12:57 what is interesting is Newton never figured out what value of his universal gravitational constant was. Herny Cavendish did that after Newton's death 71 years later. Too bad. Newton would have been delighted.
"times by"?
Excellent. I think I need to watch a few more times!.
The elliptical orbit of the planets are caused by the onward motion of the sun/star.
similarly the advance of the perihelion of the planet mercury is caused by the curved path of the sun in space,which is circle the milky way galaxy.
So your first sentence states the common sense reason why the planets move in elliptical orbits. And the above video the long tedious, not necessary to know unless an astrophysicist, proof. Thank you, that's why I clicked on the link.
What does orbit mean ??
This would be a good video to start: ua-cam.com/video/VGcQhgkXPx0/v-deo.html
Very good explanation! Thank you!
What other orbit could there be? Square? :-) The circle is also a possibility as a member of the family but with zero probability. im(half ass)o
_"Ryan MacDonald - a Theoretical Astrophysicist based at Cambridge University - proves from first principles Kepler's laws of planetary motion_ *_(Part 1 of 2)"_*
what about Part 2?
18- #Planetary Orbits
All stars and planets have orbits.
For centuries it was believed that Earth is fixed and the sun, moon and planets revolve around it. However 1400 years ago the Quran said that not only the sun and moon but also Earth moves in a designated path:
[Quran 39.5] [Allah] Created the heavens and the Earth in truth. He overlaps the night over the day and overlaps the day over the night, and enslaved the sun and the moon, ALL MOVE (كل يجري) to a prerecorded destiny. Is He not the Exalted, the Forgiver?
Here the Quran is referring to ALL MOVING: not only the sun and moon but also Earth. In Arabic grammar there is difference between the singular (one), binary (two) and plural (three or more). The reference to binary is "Kulahuma Yajreean كلاهما يجريان" however the Quran said "Kullon yajree كل يجري" referring to the plural (three or more). Since the sun and moon are just two but the Quran is referring to three or more then according to the Quran all the three move sun, moon and Earth.
[Quran 86.11] And the sky that returns.
"Al-rajeh الرَّجْعِ" means returns to the same location. Today we know that all planets return to the same locations in their respective orbits.
How could an illiterate man who lived 1400 years ago have known that planets return to their original locations?
Mistranslations: Quran 18.86 sun setting in a spring.
(The Christian Bible says that Earth is a 2 dimensional flat disk and the heaven is like a canopy solid like bronze: Isaiah 40:22)
The video is awesome, very well explained, but how did Kepler found it, he didn't have Calculus nor Newton's laws
Kepler found the laws empirically by studying years of observations. It wasn't until Newton that it was theoretically understood *why* Kepler's laws hold.
Wow!! This worked better than Ambien!! *** Note to self....stick to videos with "Hubble Images" in title!! Watched it for a while, but way over my head at this point. Definitely going back to school if I hit the lottery!!! LOL!!!
I got lost after you said "Calculus" xP Could you recommend some material?
The Khan Academy is an excellent free online Maths resource.
Thanks a lot!
I had another doubt as well. At around 23 mins into it, you mentioned that r=r2-r1
Assuming the angle made by the lines r2 and r1 is = 90 degrees, shouldn't r = the square root of r1^2 + r2^2?
I understand that the Pythagoras Theorem works with the angle being 90 degrees, but I didn't seem to understand how r2 was greater than r. Thanks again! Loved this!
If you look at the diagram at 22:00 you can see than the vector r1 starts at the origin ('O') and points towards the star, whilst r2 starts at the origin and points towards the planet. Now imagine you are stood on the star and want to go to the planet. You would travel from the star to the origin, travelling in the opposite direction to r1 (-r1) and then travel from the origin to the planet (+r2), so the overall (vector) equation for the distance between the star and the planet is r=-r1 + r2 = r2-r1.
Hope that helps!
I have several questions
Scientific fact and scientific law are totally different things. You have to look up the meaning of the word law and the meaning of the words scientific law in that order.
Really nice explanation. Great.
this aint a fine art y'all stop talking like it is........it is helpful (the video)
Ty for the video and the good effort from your part but it is very confusing and too long! I have watched tons of vids about the motion of the planets and all ellipses but there is no video yet that explains with clarity and without glitches the elliptic orbits! So why the planets orbit stars in ellipses!?
I see lot of comments from ppl here and it seems that most of them understand the issue but when you ask them to explain to you they know sh!t and they are more confused than ever! Im asking ppl who knows on the matter can someone just in two words explain the ellipses!?
Martian Colonist with all the respect ty for ur time and ur dedication! Cheers!
In short, it is due to Newton's law of gravity being an inverse square law and Newton's three laws of motion.
Then why the orbit is not circle?
Centripetal acceleration!
I watched the whole thing, and i do not see where you answered the question. I know you did, but my math skills are not on this level. not even close. perhaps do a very specific example? like say how to observe Mars position, and then use what we know to derive it's orbit, and why it is elliptical. though i find the math interesting, i can't follow with substituting real numbers, and this would take me several days to research what the actual numbers are in order to plug them in. yes the formula is more important, but it makes my brain hurt. haha.
just a few more videos and i will have seen all your videos up to 3 years ago. in the immortal words of Spock "Fascinating"
I do like the video and am glad for fewer ads, but i would have watched it even with more ads. I know what effort goes into even very simple videos, and creators deserve the rewards they have earned. just my free unsolicited .5 cents
The succinct answer is that an elliptical orbit is the inevitable consequence of two fundamental laws:
1. The gravitational force falls off as the inverse square of distance.
2. Net force is directly proportional to acceleration.
All the mathematics in this video is just proving that if these two laws hold, bound orbits must have an elliptical shape.
@@martiancolonist is this fundamental, or more to do with other bodies acting within the system? IE Jupiter pulls on the sun and thus upsets the earths (Barry center) orbit?
happy holidays, just a few videos left and i will be in the les than 3 years old content you have created.
@@jadefinchscene5644 it is fundamental for two-body interactions. If you have multiple bodies, the sum over the competing forces changes the distance-dependence, so more complicated orbits can result. These additional interactions (such as from Jupiter) act to perturb the orbits of the planets over long timescales.
@@martiancolonist excellent. thank you so much for helping me understand. the math is very cool, and i wish i had teachers back in school who would have shown me real world applications of the math instead of just saying trust me. I would have actually found it useful, instead of just confusing. seeing no use for it all i just ignored it. 25 years later I am looking back and am finding it all fascinating. because i can actually apply it to something. I will continue to learn these things as best i can. I have a physics graduate living with me, and another that is finishing his PHD thesis living across the street, so i have some help. thank you for taking the time to reply.
Please make a video on proving that the expression you got at the end is actually an ellipse by showing that it produces a shape that satisfies the geometric definition of an ellipse. That would complete this proof.
Loved this video. I had that question several times before - as to how can one say that planets will follow an elliptical orbit just using Newton's Gravity equation... and seeing this video was very satisfying. Btw, I was not expecting the solution to be so complicated, but nevertheless I was able to follow it fully.
One thing you should have mentioned I think is that if e has greater than or equal to 1 then it becomes a parabola or hyperbola. (correct?)
grkhetan
Glad you liked the video!
Yes, the complicated nature of the derivation is why it took a fair amount of time before Newton first showed it.
In this video I was taking 'orbit' to explicitly mean bound periodic trajectories (sometimes parabolic or hyperbolic trajectories are called 'unbound orbits'). You are correct that conic sections with e=1 are parabolic and e>1 are hyperbolic.
Did Newton also show that his gravity equation and laws of motion implies elliptical orbits? Did he use a similar proof? I somehow feel that there might be a simpler way to prove this than this method? What do you think?
grkhetan
Newton used a quite convoluted geometric proof, which is quite difficult to follow compared to this one (as calculus was quite new back then, he proved it without using calculus so that most readers could follow it).
If want to take it further - check story on Medium (almost no math): Mercury Precession without Space Bending Illusion
Wonderful explanation
Planets are elliptical because of pull and repelling of the sun
how can kepler be german when there was no germany at this time
+MeNeXzPnz
He was in a subsidiary country of the Holy Roman Empire that was part of the German cultural group of the time period.
Thanks for your big effort and time to make these well explained video... 👍👍....you must have a master degree in physic i guess
Great explanation but it is too long and confusing
There is no royal road to science
Because squared inverse law
Very good
Hi dude, I'm a big fan of yours and I hope you can go to Mars I would love to come I'm 14 I read which partition do you recommend?
Not sure what you mean by 'partition', can you clarify?
University departments , Mr. Ryan
+Martian Colonist University departments , Mr. Ryan
Science / Engineering. Identify which subject you enjoy the most, then commit yourself wholeheartedly to its pursuit.
Mars One :) Thank you
Yes but Newton didn't have vector calculus so he couldn't do it that way. He couldn't even calculate the value of G used in his equations, that was accomplished over one hundred years later by sharper minded people.
So, I find the description of this video interesting. "Of all the possible shapes..., why ellipses?" Well, what else would it be? What shape seems more likely? One could say circle, but in all of the salient ways that matter a circle *is* an ellipse. You certainly wouldn't expect a shape with corners. What is some other smooth closed shape that would be a viable candidate? Just by starting with that type of reasoning one could have almost *guessed* that it needed to be either an ellipse or a circle. Also, you know historically this ran the other way. We started with the ellipses, and then inferred inverse square behavior for the force law from that. Anyway, I suspect that an ellipse is the simplest shape you can come up with (except for the circle special case) that provides a smooth (no corners) trajectory. And we could reject the circle as a *required* shape just based on the independence of orthogonal directions. If behaviors in x and y have to be independent of each other, then a circle is too tight a requirement. Next you come to the ellipse. It's a simple harmonic oscillator in each direction - absolutely the simplest thing it can possibly be.
I see, thank you for the help :)
Thanks!
Great. Thanks
I didn't click "Dislike" because I realize that the source of my complaint could be my own ignorance. I listened to the whole presentation, and I think that the only thing that was explained is the geometry of an ellipse. I didn't come away understanding why an orbit would be elliptical rather than circular.
I thought that I understood that the concept of an orbit is that the orbiting object is in constant free fall. I was expecting to expand my understanding of that, but it wasn't addressed. It seemed like I was listening to a high school teacher that understands a complicated concept, but lacks ability to communicate it to others. Just speaking out loud what you're writing is not teaching.
Again, I know my ignorance level is high. If someone that understands this subject better than me disagrees with my analysis of the video, please respond to my comment so that it won't keep others from watching the video.
Thanks for your feedback. The essential reason for elliptical orbits is the combination of a force (in this case, gravity) that follows an inverse square law and force being directly propertional to acceleration (F=ma). Interestingly, these two conditions are actually only true for speeds slow relative to the speed of light (F=ma changes, as if the mass, m, increases) and `weak' gravitational fields. For example, this means that Mercury follows a slightly `non-elliptical' orbit (due to the gravitational field of the Sun altering the geometry of space-time), which requires Einstein's General Relativity to explain. Thus elliptical orbits are essentially a prediction of Newtonian gravity and Newton's 2nd law (as I emphasise at the beginning of the video).
My approach here was to explain the key reason (Newton's law of gravity + Newton's 2nd law) qualitatively at the beginning, before showing quantitatively how these ideas lead to an ellipse as the unique solution. The maths was then intended as an appendix for those who were interested, as it is hard to find this online (I didn't want people to have to just accept it was true). As to your question about circles, a circle is an ellipse (it is an ellipse where the eccentricity parameter is exactly 0). As no bound orbit in the Universe will have exactly zero eccentricity, every bound orbit will be an ellipse, with circular orbits simply convenient for thought experiments (as the maths is easier).
I hope that helps, please let me know if you have more questions!
mind blowing
bravo, thanks for explaining
I think Newton did it in a simpler way.
Newton's proof was a quite convoluted geometric proof (as calculus was still being developed at the time), which is quite archaic and difficultt to follow compared to the one presented here.
I love you man.
Please help !!. (1)"Why is the above so complicating, are we "missing" something ??" (2)"Why did the knowledgeable Isaac Newton create 3 laws instead of one law ??" (3)"Did he hide the meaning of the single formula by inferring to it with 3 laws ??" (4)"If so why ??" * * [Note] Sadly an injustice was done in 1729 by the honorable Andrew Motte, when he translated "viribus(Latin)" meaning "strength" to "force".* * Much will be come clear when corrected.
head blasting..
What is HEYCH???? It's H. ( phonetically- AEICH.. i.e like Eight but with an h at the end!) BUT AMAZING DERIVATION & EXPLANATION!
Please print because you on screen handwriting is nearly illegible. As is mine. My handwriting on paper is much better.
Too elementary for me. Got anything else?
It was veryyyy goood
The orbits are elliptical because gravity is an inverse square law (to a close approximation). Google "Feynman's Lost Lecture" on UA-cam; it's a 3Blue1Brown video. He works it all out.
Omg! I just wanted to know why planets orbit in an ellipse!!! What's dis 1 hour of other crap!??
The essential reason is given at the beginning: it is due to Newton's law of gravity being an inverse square law, coupled with Newton's 3 laws of motion. The rest of the video is proving that this statement is correct, rather than simply expecting people to accept it on faith.
What a whole lot of crap. Speed can never compete with acceleration. Unless it's initial values is.... infinite... Fire a bullet vertically up with the speed of a gps satellite, 14000 km/h. Within 15 minutes it sits theoretically 500 km under sealevel! O wait, I should fire the bullet horizontally, that's my bug! Ha ha ha ha ha! Orbital science, what a bullshit. The moon circles the earth. Ok. But NOT due to gravity.
Jan Spreen
So what is it
Jan Spreen: Simple trolling is the best trolling. But in case you're for real, Khan Academy offers free physics classes. That bullet...it's acceleration drops to nil. The duration of the acceleration is very very important. Its KINETIC ENERGY is shit because it doesn't hardly weigh anything. Learn some kinematics, and it will all make sense.
en.wikipedia.org/wiki/Kinematics
Jan, I want to know why you're writing posts like that. How's that any fun? You're just wasting time of naive people, there is no humor to it.
You know your stuff but you do have many problems
1. You use the word THIS too many times and the viewer do not know where this is.
2. You do not progress left to right and top to bottom which we all use when answering a question instead of scribbling all over like graffiti
Watch the Dr Physics how he does it. It is said that those who csnt teach. You are the opposite you can buy cant Teach. You need to go to teachers training school to teach. I used to think those schools are irrelevant but now I know you need it
Just awful