Your Daily Equation #17: Planetary Orbits: Kepler, Newton, and Gravity

Episode 17 #YourDailyEquation: Newton's law of gravitation determines the trajectories of the planets and explains the patterns in their motion found by Kepler. In this episode, Brian Greene explains the basics of planetary orbits, while also giving a nod to conic sections and the dimensionality of space.
Even if your math is a bit rusty, join Brian Greene for brief and breezy discussions of pivotal equations and exciting stories of nature and numbers that will allow you to see the universe in a new way.
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[@martijn130370]

Beautiful, especially the conical sections, and the reverse quadratic law intuitively explained!

[@xspotbox4400]

Got to love Newton, it's a rocket science what he did.

[@shaolin89]

It is always such a delight to listen to Professor Greene. I am, as a layman, learning so much over here. Greetings from Denmark.

[@joshyoung81]

Man do I love these. I watch them every night going to sleep. And that’s not a knock! Thanks Brian!!

[@marciliosantos898]

The best subject physics on planetary motion that I see. Thanks a lot Dr. Brian!

[@neonblack211]

So glad you picked this as a topic, even though it’s probably my favourite topic on physics so far I would have thought to ask for it

[@petergreen5337]

Thank you very much for this lecture.

[@friedrichn7767]

I just came straight out to a book upon this subject... this is amazing😀🤗😍

[@theodoresweger4948]

Very well done exolained in a way easy to understand, especially the shaped of the orbits at different speeds, I especialy like the formula A=V^2/R , when driving around curves I have an understanding of the speed limits for curves...Thank you very much.

[@andreaswagner6022]

Love this series.

[@gedlangosz1127]

A fascinating episode. I had not realised the five cases or planetary motion and how they fit with the conic sections. I will have to derive the maths for this as my homework!

[@ch7310]

It sucks that I can givz it only one thumbs up. Kepler, Newton and conic sections all rolled into one deserve at least 3

[@toddvolyn9137]

Well done! Thank you

[@Archaeometal]

Thank you, Prof. Greene! This series, the WSF lectures, and your books have expanded my mind and understanding. So fortunate to be able to learn directly from you. Wishing you well. -- Nova Scotia, Canada

[@ranapratap9230]

Thank you sir

[@jhumphre]

Excellent and very clear explanation. Beautiful planetary motion! If Brahe had not been so accurate and precise with his measurements, Kepler wouldn't have derived his three laws (at least until such measurements were available).

[@paulneeds]

Already REALLY looking forward to a derivation of Newton’s 2nd symphony.. haha, of course I mean Law. Fascinating stuff - especially as I couldn’t manage higher level high school maths!

[@realcygnus]

Superb content

[@rushi1306]

Sir can you discuss conservative force or field in any of your QnA chat. And thanks for making these videos, they are great. And the animation of trajectories was great.

[@rishavagrawal6347]

Love these episodes, sir!!!!If you ever come across these comments plz do consider about making a video on F= ma .

[@lsuarez2007]

Great video Brian. Greetings from Buenos Aires Argentina

[@terryparry2339]

Thank you, thank you ....

[@aryanbhatt5835]

I'd love to see a video about coupled harmonic oscillators, like the pendula connected by a spring. Thank you so much for this series!

[@luisfelipe7351]

wonderful

[@semmering1]

Hi Brian, I would have had such an excellent teaching during my university education.... Would be glad to see you some time in a lecture here in Europe...

[@brendawilliams8062]

Thankyou

[@elizabethmoyer4235]

I studied this at A Level, UK. Love it. I love physics and you are a great teacher. Could you please explain how we can see the Big Bang through gravitational waves? Thank you so much. I am watching all the WSF videos, so interesting to hear from cutting edge scientists, yourself included. Ps I love your voice too!

[@NoahWolfe]

Thank you so much for this series and your time. Fantastic stuff.

[@johnkechagais7096]

Dropping an Apple pen in program about orbital mechanics and finishing with the Ancient Greeks with conic sections :)

[@Bigandrewm]

I find it pretty interesting to look at older mathematical solutions, as how people solved problems without having access to our powerful modern tools. Relating to this episode, for example -Archimedes' surviving documents relating to his study of conic sections. It also makes it frustrating to know that so much of the original work people have done is destroyed by history, and that we will never really know how some of these concepts came into being, in terms of the thought processes of the people who did it.

[@christianmaxschafer8696]

Really great sequel !!! My question for Q&A: how could the universe expand after the big bang instead of collapsing into a black hole ?

[@dls6068]

Christian Max Schäfer because of entropy (sorry, my science English is not really good, but nature always goes for bigger entropy).

[@simonmeier5222]

Thank you for this amazing videos!

[@gifropan]

Hi Brian I enjoyed listening and watching your video. I’m curious there must be a speed below which one wouldn’t even get an orbit. What is the minimum speed required to achieve some kind of an orbit.

[@jamestrexler6329]

Oh! Circular restricted three-body problem, please? CR3BP became an in-joke between one of my friends and I during our interplanetary astrodynamics course for some reason, and I think he'd get a kick out of seeing it here. Plus, it's an absolutely amazing problem. I remember plotting results and watching them turn into glorious space spirographs.

[@7Earthsky]

I studied Keplers laws during my Nat Science degree...I actually really enjoyed it and i'm not very mathematical at all.

[@nikko_301]

For us who encounter these formulas getting explained the first time and perhaps want to dig in deeper, do you have any suggestions on litterature that is worth looking into? You could put them in the description of the video. Thanks again for this great initiative. Kind regards from Sweden.

[@DKFX1]

My personal preference is to go straight to the main source first, then you can read additional modern explanations afterwards. In this case that would be Sir Isaac Newton's papers on celestial mechanics and gravity, published in the late 16th hundreds. You can definitely find those on Google Ngram with a little effort.

[@azhannayeem4030]

Great series Dr. Green! Keep it up. Thank you :)

[@rfbertelli]

But isn't there a velocity V

[@michaelsommers2356]

Yes, but that's boring.

[@annmcguiremitchell5846]

Would love to hear your thoughts on the Fibonacci Sequence

[@jeffwells1255]

A really nice review of high school math here, and why mathematics was my college minor. You have an excellent way with words, sir, and I only wish there were more of you in the world.

[@bluefinance153]

can you please explain Renormalization in QFT?

[@BruinChang]

Does the direction of the imposed speed matter when considering the trajectory of the moving earth? I mean if the applied velocity is in the radial direction, will the earth still follow the four different curves?

[@cesarflores1395]

oh by the way, which table is that you’re using ? Blessings to you and family 🙏🏻

[@hrishikeshchanekar9846]

Beautiful tribute to sir Isaac Newton in the begining 🥺

[@jimm123]

It's awesome that you are doing this series . Many thanks from Sault Ste. Marie, Canada.

[@alanmarston8612]

I attempted to watch your live opening. Now the sound is in sync.

[@jimtwisted1984]

So which planets are > than Vc and which are

[@husseinkhalife8817]

Please can you elaborate more on Quantum Field Theory according to Paul Dirac in a separate episode?

[@hawzhinblanca]

thanks, my favorite episode so far.

[@Usman-eg8se]

I love how he wrote the P in ‘Planetary’. It looks like the one from the logo of the Planetary Society

[@Valdagast]

So this episode is just going through the motions?

[@paulneeds]

Valdagast haha!

[@swindler1570]

I am mad now

[@ManWhoUsesComputer]

Amazing, Thanks! *Question: Since the motions are all conic, is it safe to assume the gravity "well" is conic - of a cone shape? PS: How does 4-dimensional spacetime deform/curve (e.g. as in form a "well")? Does it do this in a 5th dimension?

[@frede1905]

Question 1: I am not sure what you mean by the "gravity well", so you have to be more specific. Question 2: No, spacetime doesn't need a 5th dimension to curve in. Curvature is an intrinsic property of a space (which means it is something you as a being in the space can "detect" or measure yourself by doing some very specific experiments. For instance, if you were a 2-dimensional being living on the surface of a sphere, then you could detect the curvature of the sphere, even though you don't have access to the third dimension that the sphere is embedded in, so you can't see the sphere from the "outside" in a birds-eye view, like we can). A curved spacetime is simply a spacetime with non-Euclidean geometry, in other words a geometry where the usual rules of geometry that you learn at high school do not work anymore.

[@ahelalley]

wha about some thermodynamics or heat exchange equations ? i think it would be great

[@johnfarris6152]

The difference of the difference, is always something strange.

[@mikeclarke952]

You might as well do circular motion/angular momentum and gyroscopic precession next? Regards.

[@jayatigoyal8103]

I think sun and orbit of earth make a cone with the centre of galaxy, that's why we get conic section shape trajectories of earth around the sun.

[@johnfarris6152]

👽Your a Man's man Brian Greene👽

[@toddjoseph2412]

Could you explain how the sun centered and earth centered models both work mathematically but the sun centered model is a lot simpler.

[@jacopocarnimeo3443]

Hi Brian. Since I think that without the basic knowledge (by knowledge I mean the comprension of the simpler formulas, where they come from, and how to derive them from a natural observable phenomena) it's harder to understand the complex processes, could you walk us from the basic concept and formulae (givin space also to the easy one which might be also advanced in the history of maths and physics) in order to let us more appreciate what you're are explaining. PS: I'm really thankful for what you're doing here.

[@kishores99]

Can't believe Brian greene is teaching newton mechanics.

[@devikab.s.3613]

Could you explain simple harmonic equation someday

[@cesarflores1395]

Thanks for your lectures … 10 to the 30 power is a nonillion (quintillion)

[@paai74]

Where can i send a q&a video?

[@davidbarnett1740]

Who is the better physicist? I relied on (loosely) on George Gamow. Maybe it was the "Biography Of Physics" but one of Gamow's books had about 75 pages about Newton's discoveries, about 1/4 of the book. Much more than the part about Einstein's discoveries, so I would call Newton the better physicist. --- I lie your answer MUCH better. Both are so far above anyone else, who cares. They worked on different topics and both lead 'the world' to a better understanding of the world.

[@michaelwhalan9783]

The earth just moved for me

[@martintopinka8295]

Why a cone and a plane? Do the cone and the plane have any physical meaning like potential vs kinetic energy? I naively guess that the angle by which you cut the cone is related the speed and eccentricity.

[@DeepakChauhan-lc7xe]

Can anyone explain me why the denominator of Newtonian force of gravity is square of distance behalf of 3D space, I did not understand it

[@keithmitchell99]

Can a quantum model explain why those sconce lights are askew?

[@jamieoglethorpe]

Now we need the rocket equation where the mass is not a constant!

[@merlepatterson]

2C or not to see?

[@localtitans4166]

That G is not Newton's constant.. he didn't even knew it's value.. its value was found about a century later by Henry Cavendish maybe..

[@rickandelon9374]

yep correct

[@vijay_r_g]

Ok,the velocities of the planets determine the shape of their orbits around the sun.But how does these planets get that velocity?

[@tonib5899]

Who was the best physicist,Both.

[@kopbeni]

there is also a smaller velocity where the earth will fall into the sun

[@chritophergaafele8922]

How did Newton prove the inverse square law

[@phayezrc]

The Sun is big even though viewing the optical illusion which makes it look small is misleading, it is huge. For a size comparison the length of the radius of the Sun is equal to two and one half times the distance of the moon to the earth.

[@craigkesack2866]

Assuming I didn't make a bad math error, I get that earth's velocity is less than V-circular, just plugging into the equations.

[@sagemaster3408]

It’s Isaac Newton !!

[@donnahaynes8766]

7:20 OMG!! I just commented on the previous episode about how I hated to hear Dr Krishna Kumar say in class "and immediately we see". Now Dr Greene uses EXACTLY the same phrase!! Dude! it is not always "immediate" to some of us! We will catch up; we are not stupid! We just need a few moments to catch up with you. Give us a moment or two and we WILL have our AHA moment! I know your time is limited and you are so generous to give us all of this education. But please try not to leave many of us in the dust with that "immediately we see that" stuff. perhaps say something like "we see from this calculus rule (or the other) that..." That would at least tell us which calculus semester (or in my case, quarter) we should review in order to catch up. Your "immediately we see" does nothing for me.

[@HebaruSan]

25:10 - Oh no, an elliptical orbit with two periapses 90 degrees from where the real one would be! :(

[@michaelsommers2356]

You do realize that the Sun is not drawn to scale, don't you?

[@CliqueSpace]

Brian, you should foster another career as a calligrapher.

[@HimanshuSharma-xn6uc]

r=(l²/uC)/1-√1+(2El²/uC²)sin(∅-∅º)

[@brookestephen]

If you cut the cone at one angle you get a HYPERBOLE?!?!?! That is a lie.

[@ricardodelzealandia6290]

Fo-sai??

[@pinkfloydhomer]

Foci = the two focuses of an ellipse

[@adityajha9665]

Physics.....is my most favourite subject in entire cosmos

[@johnfarris6152]

It doesn't matter.

[@PetraKann]

I wouldn't put Einstein in Newton's league. Certainly Einstein is in the top 12

[@dankuchar6821]

I would put Einstein right there was Newton. They are two of the greatest because they had insights no one else came up with. they both looked at things from a completely different perspective than anyone else had at the time. Personally I think that's what makes them so great.

[@PetraKann]

@@dankuchar6821 I generally agree with you. However I consider 23 scientists/Philosophers/Mathematicians as more important than Einstein, with respect to their contributions and the context of their discoveries. It's only an opinion. I wish that I could be ranked in the top 20 or 30 million - but alas, I just havent performed well enough of the years. CHeers

[@areliablesource2848]

@@dankuchar6821 Dan, I agree with you. The other aspect about Newton and Einstein that raises them up is that they "opened the door" to the changes in how to view the world for hundreds of years. Another amusing "wow" thing is the age of Newton and Einstein when these insights occurred (Newton, 23 and Einstein, 26).

[@dnstone1127]

Newtonn was the better mathematician as he did all the calculations alone.

[@JeffTyndall]

No one comes close to Newton.

[@Jackie-wn5hx]

He lived during the era of the bubonic plague and quarantines, so there's a reason no one came close to him.

[@iainmaclean4770]

-1/12

[@dwightcollman4917]

Weird face color

[@bluefinance153]

can you please explain Renormalization in QFT?

[@bluefinance153]

can you please explain Renormalization in QFT?

[@bluefinance153]

can you please explain Renormalization in QFT?

[@bluefinance153]

can you please explain Renormalization in QFT?

[@paulneeds]

Quantum Maths once was enough..