## Astrophysics one year ago @empty

1. Astrophysics

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

2. Empty

cool let's check it out

3. 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

4. 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

5. Empty

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

6. Astrophysics

O

7. anonymous

This is a university physics I assume?

8. anonymous

Fansy stuff hitting the fan

9. Astrophysics

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

10. anonymous

empty like my soul

11. anonymous

I know the centripetal acceleration but never heard of central force

12. Astrophysics

Err this will take some time to explain

13. anonymous

I say we shoot each other with physics knowledge

14. anonymous

I am although a classical physicist

15. Empty

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

16. anonymous

There is reason for everything

17. anonymous

Especially physics is a process of becoming a god

18. Empty

Haha cool so what about chemistry?

19. anonymous

Chemistry is more earthy application based study

20. anonymous

there is nothing theoretical about it whereas physics most are

21. Empty

Oh what do you know about chemistry?

22. anonymous

empirical vs theoretical

23. anonymous

Chemistry is all knowable

24. Empty

What does that mean?

25. anonymous

Everything is empirical in chemistry

26. anonymous

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

27. anonymous

anyway let's get down to the central force business

28. Empty

Hahaha "Everything is empirical in chemistry"

29. Empty

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

30. anonymous

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

31. 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|

32. Astrophysics

This sort of requires you to understand lagrangian

33. Astrophysics

actually no

34. anonymous

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

35. anonymous

that equation digs up my nostalgia on universal gravitation

36. 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

37. 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?

38. Astrophysics

Yeah, pretty much

39. Astrophysics

Quit giving each other medals

40. Empty

lolwhat

41. Astrophysics

lol

42. nincompoop

try to draw a path of the log central force

43. nincompoop

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

44. Astrophysics

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

45. nincompoop

true

46. Astrophysics

The force law is attractive inverse cube

47. nincompoop

isn't it r^2 tho?

48. Astrophysics

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

49. Astrophysics

Nope

50. Astrophysics

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

51. nincompoop

looks mathematically legit

52. nincompoop

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

53. Astrophysics

How is chemistry earthly based

54. Astrophysics

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

55. nincompoop

oh that was another dude hahaha nvm

56. Astrophysics

xD

57. nincompoop