Central Forces and the 2 Body Problem - Two Ways to Model the Motion.

My goal was to make a cleaner and shorter version. Well, that didn't happen. This one is longer - but BETTER. In this video, I include a numerical model for a binary star system and compare it to an effective one dimensional potential.

Here are some resources that I mention in the video.

Python code for the potential graph:

Python code for the binary star system:

Binary Star tutorial - finding stable circular orbits

Introduction to Lagrangian Mechanics

Let me know if I'm missing any other links.

[onionbroisbestwaifu]

When you said, “we are all grownups here.” My first thought was no I’m not, and then I realized that I’m 18 as of a few days ago and I can’t believe that hit me while watching a classical two-body problem.

[scottish_cafe]

One of the best videos that I found about using in non trivial way Lagrange mechanics with great python animation at the end <3 Nice!

[Keeykey]

This is a much better lecture than the one I had on classical mechanics in college. Thank you!

[fizixx]

I think this is a great video....things like reduced mass need to be explained instead of all the hand-waving textbooks want to do.

[niranjanm]

great video as always. its also a scare free introduction to simulation

[kotikunja]

The explanation is crystal clear.
thank you for the video

[Santa-qzmu]

Thank you soooo much for this. I was looking for a thorough explanation for this, as I'm 13 and working on the iPHO.

[Cloudserious]

OMG I finally figure out the two body problem, thank you much.your video is always very logical and understandable. I’m so glad to find your channel.

[danielricardogermain]

The best explanatory physics video I have seen online. I wish I was your student.

[comicrelief]

At 8:46 are you not missing m2Rdot^2 ?

[porit]

Thank you so much! It was really helpful

[HitAndMissLab]

Thanks for a great video. I've learned so much from this, it's amazing. Please make more videos like this.

[jacobharris]

This is an amazing video. I think this derivation was probably outside the scope of what I was looking for but I got so excited at the end when you got the orbits to work and created that effective potential plot. I definitely want to try this in my free time. Using the numerical method you used, would it be possible to do something similar to this for 3 bodies or more and how hard would to show the orbits on screen, if not all the bodies are in the same orbital plane?

[hariharani]

I'm from India,
One of the best video, Sir
Thank you so much, it's really helpful, make more video's like this,
Thank you Sir

[ripmartin]

To add to my comment about elliptical orbits. The Lagrangian T=T-U=1/2MR'*2+1/2^r'*2-U(r) when you assume R's velocity is constant it oversimplifies and ignores the acceleration I want to isolate. If r vector is oscillating with a sin wave acceleration the center of mass has to be oscillating with m/M*sin wave acceleration. The system is going to get the potential to a minimum. This is the mechanism that induces entropy. We need to add a component that equates the loss of acceleration in the bodies with the loss of change in potential energy. This is a very important fundamental mechanism of energy. If we solve for the acceleration of R can you, we isolate a clean answer.

[lautaroignaciocabezasferre]

muy buen video, me ayudo muchísimo para la facultad :)
saludos desde argentina

[ripmartin]

I have been working on a derivation of the acceleration on the center of mass that you hold to zero in order to constrain the system. In an elliptical orbit the gravitational force and centrifugal force are out of balance and the imbalance is in one direction. The force exerted on the center of mass is not zero. Some of the acceleration in the orbiting body must be transferred to the orbited body, conservation of energy requires it. This would mean an elliptical orbit slowly accelerates the whole system and forms a stable circular orbit given sufficient time. This is the mechanism that keeps the solar system intact. At the point you apply the Lagrange, instead of holding the acceleration of the center of mass to zero how about isolating the acceleration in the large mass. I have what I think is the answer 1/2ma=MA, a is the acceleration added to a circular orbit to induce an elliptical orbit. 1/2 comes from the final stable circular orbit being the mean velocity between the two orbits.
This makes the formation of the solar system completely different. this is also the basis I will propose a unified theory. Give me a clean derivation and we could win a Nobel.
Rip L Martin

[cptfordo]

At 11:25, you mention that the potential energy function U(r) only takes in "r" as in the relative position between the two masses, and not R as the position of the center of mass. Why does the potential energy only depend on the relative location between the two bodies? Thank you :)

[pawelo]

at 42:52 there must be a wrong formula for F2 - when we divide norm(r) by mag(r)**2 this is no longer inverse square law. That norm(r) seems inappropriate because as far as i know it does the same as mag(r).

[markostojanovic]

Great video. Thank you! But why can we solve an open integer without getting a constant? 26:23