@empty

- Astrophysics

@empty

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- Astrophysics

I made a post cause I had odd number questions asked and that looked gross

- Empty

cool let's check it out

- Astrophysics

Now find the force law for a central force field that allows a particle to move in a logarithmic spiral orbit given by \[r = k e^{\alpha \theta}\], where k and alpha are constants

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## More answers

- Astrophysics

I guess I should give you some things that will help you lol, \[\frac{ d^2 }{ d \theta ^2 } \left( \frac{ 1 }{ r } \right)+\frac{ 1 }{ r } = -\frac{ \mu r^2 }{ l^2 }F(r)\] it's pretty easy actually

- Empty

lol what is all of this I've never seen this before

- Astrophysics

O

- anonymous

This is a university physics I assume?

- anonymous

Fansy stuff hitting the fan

- Astrophysics

This has to do with central force motion, I just assume you know everything

- anonymous

empty like my soul

- anonymous

I know the centripetal acceleration but never heard of central force

- Astrophysics

Err this will take some time to explain

- anonymous

I say we shoot each other with physics knowledge

- anonymous

I am although a classical physicist

- Empty

I could probably figure this out but I feel like there's some method of doing this or reason for doing this.

- anonymous

There is reason for everything

- anonymous

Especially physics is a process of becoming a god

- Empty

Haha cool so what about chemistry?

- anonymous

Chemistry is more earthy application based study

- anonymous

there is nothing theoretical about it whereas physics most are

- Empty

Oh what do you know about chemistry?

- anonymous

empirical vs theoretical

- anonymous

Chemistry is all knowable

- Empty

What does that mean?

- anonymous

Everything is empirical in chemistry

- anonymous

Physics mostly rely on the unreasonable effectiveness of mathematics at explaining the physical phenomena.

- anonymous

anyway let's get down to the central force business

- Empty

Hahaha "Everything is empirical in chemistry"

- Empty

I'll be damned if there aren't 8 things listed here: https://en.wikipedia.org/wiki/Theoretical_chemistry#Branches_of_theoretical_chemistry

- anonymous

central force depends on the distance between spherically symmetric object and the object being pondered

- Astrophysics

It has to do with the motion of a system consisted of two bodies affected by a force that is directed along the line connecting the centres of the two bodies, this is the central force. |dw:1438444424125:dw|

- Astrophysics

This sort of requires you to understand lagrangian

- Astrophysics

actually no

- anonymous

According to the theory everything with a mass has central force to it however minuscule they are

- anonymous

that equation digs up my nostalgia on universal gravitation

- Astrophysics

Actually, since I'm too lazy to derive it as it takes too long xD, just read this, if you want...http://www.astro.uwo.ca/~houde/courses/PDF%20files/physics350/Central_force.pdf

- Empty

I can derive the euler-lagrange equation with calculus but that's just math and I get that the action gets minimized L=T-U pretty clearly. I guess the question is how do you find the kinetic and potential energy of this system in the first place?

- Astrophysics

Yeah, pretty much

- Astrophysics

Quit giving each other medals

- Empty

lolwhat

- Astrophysics

lol

- nincompoop

try to draw a path of the log central force

- nincompoop

I can't see the log playing out, just yet

- Astrophysics

\[\frac{ d }{ d \theta } \left( \frac{ 1 }{ r } \right) = \frac{ d }{ d \theta } \left( \frac{ e^{- \alpha \theta} }{ k } \right) = \frac{ - \alpha e^{-\alpha \theta} }{ k }\]
\[\frac{ d^2 }{ d \theta^2 } \left( \frac{ 1 }{ r } \right) = \frac{ \alpha^2 }{ r }\]
\[F(r) = \frac{ -l^2 }{ \mu r^2 }\left( \frac{ \alpha ^2 }{ r } +\frac{ 1 }{ r }\right) = \frac{ - l^2 }{ \mu r^3 }(\alpha ^2+1)\]

- nincompoop

true

- Astrophysics

The force law is attractive inverse cube

- nincompoop

isn't it r^2 tho?

- Astrophysics

If you want to do something for fun find r(t) and theta (t)

- Astrophysics

Nope

- Astrophysics

Originally \[\frac{ d^2 }{ d \theta ^2 } \left( \frac{ 1 }{ r } \right)+\frac{ 1 }{ r } = -\frac{ \mu r^2 }{ l^2 }F(r)\]

- nincompoop

looks mathematically legit

- nincompoop

I am a little hurt when you said chemistry is more earthly-based :(

- Astrophysics

How is chemistry earthly based

- Astrophysics

It all started from helium and hydrogen being composed in stars, don't get me started please...

- nincompoop

oh that was another dude hahaha nvm

- Astrophysics

xD

- nincompoop

FOUND IT
http://www.dartmouth.edu/~phys44/lectures/Chap_4.pdf

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