The Shortcut that Lets You Write Down the Orbit of a Planet in One Line: Physics Mini Lesson

You can find the orbit of a planet by solving a tough differential equation (like I showed you in my last video), or you can do with one (or two) lines of algebra thanks to the "Runge-Lenz" vector! Get the notes for free here: courses.physicswithelliot.com...
Get all the links here: www.physicswithelliot.com/run...
How to solve the differential equation for the orbit: • DERIVING the Orbit of ...
How to understand the orbits from the effective potential: • The Trick that Makes U...
Tutoring inquiries: www.physicswithelliot.com/tut...
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About physics mini lessons:
In these intermediate-level physics lessons, I'll try to give you a self-contained introduction to some fascinating physics topics. If you're just getting started on your physics journey, you might not understand every single detail in every video---that's totally fine! What I'm really hoping is that you'll be inspired to go off and keep learning more on your own.
About me:
I’m Dr. Elliot Schneider. I love physics, and I want to help others learn (and learn to love) physics, too. Whether you’re a beginner just starting out with your physics studies, a more advanced student, or a lifelong learner, I hope you’ll find resources here that enable you to deepen your understanding of the laws of nature. For more cool physics stuff, visit me at www.physicswithelliot.com.

[@trigocuantico]

Just watched the previous video, I'm very thankful that this content exists

[@chaitanyakhamar6527]

Wow, this concept helped me so much in my introductory university physics class! Great video that simplifies orbital mechanics!

[@PhysicswithElliot]

Thanks Chaitanya!

[@physicshuman9808]

12:54
You should not put exclamation point find a zero because it looks like a factorial and zero factorial is equal to one

[@sea34101]

I don't know what to think about this. On the one hand, this is something I have never heard about and the derivation was very clear, so thanks for this.
On the other hand, I can't figure out if this was a calculation trick or if there is a deeper meaning behind this. When I was an undergraduate student, our physics professor enjoyed showing us "modern physics" where the standard textbook stuff was derived using principles which looked at first sight very remote from the concepts we were supposed to learn (like force, energy, etc..). In particular, I remember him deriving many equations involving the magnetic potential A whose physical meaning has always been pretty nebulous to me (instead of appying the cross product to a "physical" vector like a force or a movement, he was applying it to the nabla operator ...). To put it differently, if I were in a physics exam, how can I come up with the idea of introducing by myself a constant quantity which involves a unit vector?
I imagine that the answer involves getting a master degree in theoretical physics, but I would have appreciated if you had given a hint to explain where this idea was coming from.

[@RalphDratman]

Elliot, by my lights you are a wonderful physicist as well as a superb teacher. Thank you for these videos.
Yet even more impressive to me, watching this, is physics itself as our species has come to understand it.
What a gem it is, what a shining synthesis of mathematics and the natural world in its infinitely beautiful, infinitely impressive reality.

[@JasonAStillman]

Here here!!

[@JasonAStillman]

That is a thing of beauty, thanks..

[@augustisalman8027]

Im commenting here for you to see. Thank you so much for your efforts and time.

[@eminhaskic6019]

Wow! BEST CHANNEL ON CZcams

[@diniaadil6154]

I remember being introduced to this operator in a college exam. Does this operator show up anywhere else in physics, or just in the case of newtonian interactions and determining orbits?

[@PhysicswithElliot]

Yes in the quantum mechanics of the hydrogen atom!

[@jonatanpaschoal7362]

Olá, como vai? Você poderia deixar legenda em português para seus vídeos?

[@yuchuanwei]

I wanna to exchange my idea on the 2D isotropic oscillator. Its trajectory is also an ellipse. I think I got the associate ''Runge Lenz" vector. If you have interests, I am glad to tell you and get your comments.

[@MessedUpSystem]

Why did nobody teach this in my Classical Mechanics class?

[@librealgerien]

This is the first time I hear eccentricity pronounced with as “essentricity”, but always as “eKSentricity.” Good job though and thanks for these videos.

[@rajuadhikari4777]

At 6:09 I didn't understand where did u multiply 'r' in the numerator?

[@PhysicswithElliot]

The unit vector (r with a hat on it) turned into the position vector (r with an arrow on top): \vec{r} = r \hat{r}

[@rajuadhikari4777]

@@PhysicswithElliot thank you

[@satenikansryan9201]

I don’t understand how epsilon can be smaller than 1

[@joseprocyon7526]

The Energy can be negative

[@rv706]

I read somewhere that there's a link between the Runge-Lenz vector and a subtle SO(4) (yes, 4 not 3) symmetry of the system... Do you have any idea of what that could be? -- Edit: I looked it up on Google and it has to do with the hydrogen atom, so quantum stuff, so off-topic here. Sorry.

[@PhysicswithElliot]

Yep that's the symmetry in the classical case too!

[@robinhillyard6187]

Can we also derive the RL vector from least action?

[@bbartt80]

When taking dt of: r_hat=theta*theta_hat yields dr_hat/dt=dtheta/dt*theta_hat - where did theta*dtheta_hat/dt go?

[@PhysicswithElliot]

I don't quite follow, what makes you say \hat{r} = \theta \hat{\theta}?