Kepler's First Law DERIVATION

Get ready to walk circles⁠-*ahem* I mean ellipses⁠-around this derivation.
0:00 The Law
0:25 Defining an Ellipse
0:49 Energy
1:33 Angular Momentum
2:43 Introducing Constants
3:17 Combing Equations
3:40 Voila!
Sources:
-www.physicsclassroom.com/clas...
-Proof of Kepler’s first law from Newtonian dynamics. A1 Dynamical Astronomy
Intro and Outro:
"Astronaut in the Ocean" by Masked Wolf, beats by FaMusic

[@centinelroads]

You are so underrated. No words can describe how concise and clear you are.

[@astronaughtpov]

Thank you very much :)

[@sussybaka3420]

Thank you so much! now I finally know the derivation

[@astronaughtpov]

I appreciate the comment!

[@rhettallain]

These videos are legit good. Just wanted to let you know that.

[@astronaughtpov]

Thanks, I really appreciate it!

[@Reinhardt965]

This was very helpfull, thanks!!

[@planets9102]

As a physics student, you are amazing.

[@astronaughtpov]

Thank you!

[@MinionNil]

Ósom!!

[@griffithfimeto3387]

One thing you defined l & e , how did you get l/m root (e/l)^2_(ri_1/l)^2 , what operation did you do i won't memorize something i don't understand this video is not full until you explain why to me , from saudia 😂❤

[@astronaughtpov]

Hi, thanks for the question! Absolutely-it is always better to understand a concept than to try to memorize it. The equation you are referencing comes from a combination of substituting the definitions of e and l into the equation before and algebraic manipulation. If you'd like me to write out a more detailed step-by-step explanation, feel free to email [e-mail] or perhaps I can add it to the "community" section on this channel.

[@griffithfimeto3387]

@astronaughtpov do it in the community so everyone get to know it , thank , God bless you ? I am waiting

[@astronaughtpov]

Apologies for the delay. I just added some notes in the community of this channel. I did not go through every step, but all the key steps are listed. I hope it helps!

[@qedmath1729]

if you could have explained the purple equation at 1:16 that would be great. I think I was able to justify it, but that involved squaring vectors, and it was weird.

[@SajidPajid]

x=r cos, y=r sin
calculate x'^2+y'^2 (derivative then square) to get the velocity components

[@delfieelfie]

Hey I have a question. How did you reach the yellow inverse equation at 3:29? Incredible video btw

[@Im.Sterben]

This is a formula:
∫1/(a^2-x^2)dx=arcsin(x/a)+C
And we also know that:
-arcsin(x)=arccos(x)-pi/2
Hence, I think you can they are equal because of C, the constant in the integral.

[@saywhat1078]

Is the proof not complete unless you show that what you assigned to e is actually equal to the eccentricity of a conic section?

[@astronaughtpov]

In general, it is a good idea to justify why you've chosen a particular value. One easy way to do this is by plugging in a specific value.
For example, if we look at our ellipse when theta = 180 degrees, r becomes the semi-major axis and cos(theta) becomes -1. That will give you an expression for the ellipse that is likely much more familiar.

[@gamingwithlegends7006]

Very good vdos

[@griffithfimeto3387]

You got a subscriper

[@vimalramachandran]

Since Kepler came before Newton, how can you do this without using the gravitational constant?

[@astronaughtpov]

That is an excellent question. The derivation in this video relies on modern physics, but here is a link that shows the derivation without the gravitational constant: math.berkeley.edu/~robin/Kepler/index.html#:~:text=Also%2C%20Kepler%20was%20able%20to,traced%20out%20was%20an%20ellipse.&text=Thus%2C%20c%3De%2C%20which,of%20planetary%20motion%20was%20born.

[@autf2_6]

Emin abiden geldik

[@ashutoshmandal6611]

Will not it be GMm/r.r ?

[@astronaughtpov]

Hello, thanks for the question! -GMm/r comes from the gravitational potential energy. You may be thinking of gravitational force, which is indeed GMm/r^2.

[@AaBb-km2yf]

But I like your channel

[@AaBb-km2yf]

I don’t understand 💔💔💔

[@astronaughtpov]

Let me know if I can help answer any questions.