## anonymous 3 years ago @experimentX

1. anonymous

2. anonymous

Let's see what I remember without looking at my cheat sheet

3. anonymous

Something about $T^2=R^3$

4. experimentX

seems like I forgot Kepler laws ... let's see

5. anonymous

The period of an object orbital around the sun is proportional to the radius?

6. anonymous

whose radius? or perhaps some distance? The distance between that object and the sun?

7. experimentX

http://en.wikipedia.org/wiki/Kepler's_laws_of_planetary_motion ellipse ... semi major axis.

8. anonymous

no cheating haha

9. anonymous

:P

10. anonymous

draw it with me|dw:1361862577312:dw|

11. experimentX

|dw:1361862616815:dw|

12. anonymous

Let's see what I remember about the semi major axis.......

13. DLS

$\LARGE (\frac{T_1}{T_2})^2=(\frac{R_1}{R_2})^3$

14. DLS

$\LARGE \frac{dA}{dT}=\frac{L}{2M}$

15. anonymous

why do we have two semi major axis?

16. anonymous

what ratio is that?

17. experimentX

it doesn't matter which side you take ... lol

18. anonymous

|dw:1361862832161:dw|

19. anonymous

|dw:1361862878591:dw| Where is $$R_2$$

20. experimentX
21. anonymous

>:O

22. anonymous

wiki didn't explain the ratio though

23. anonymous

LOL I'm tired. ok I get it

24. anonymous

25. DLS

$\LARGE \sqrt{2gR}$

26. anonymous

|dw:1361863110279:dw| sweetheart, I have all the formulas staring at me from my notebook. I'm trying to have a discussion about those wonderful formulas

27. anonymous

something about when the kinetic energy reaches $$\frac{GMm}{r^2}$$?

28. experimentX

|dw:1361863195805:dw|

29. anonymous

THanks! When do we know we have reached escape speed? $U_f+K_f=U_i+K_i$ Let's derive escape speed. we don't have a final kinetic energy when we've reached escape speed correct?

30. DLS

$\frac{-GMm}{R}+\frac{mv^2}{2}=0$

31. DLS

put the total energy=0 find V

32. anonymous

Why what's the logic behind it? WHy is the total energy zero?

33. DLS

If a body's total net mec. energy=0,it will escape from the earth's gravitational field

34. experimentX

find the total work done when bringing object from infinity to position 'r'

35. anonymous

oh ok, so when the kinetic energy equals the potential energy?

36. DLS

have u heard of binding energy

37. anonymous

Let's see if I remember. When E<0 or =0

38. anonymous

parabolic and hyperbolic orbits?

39. anonymous

that's when they're unbound correct?

40. anonymous

nope when E>0 is unbound

41. anonymous

when E is less than zero is the only time when it's bound

42. anonymous

So when the potential is greater than the kinetic energy the energy is bound?

43. anonymous

gotta sleep =) Thanks for the discussion everyone. I look forward to hear more about bounded and unbounded Energy when I wake up. See ya :)

44. experimentX

sorry ... was kinda busy not paying attention

45. experimentX

this way you can do it ... for escape velocity. |dw:1361863974972:dw|

46. experimentX

You can equate those two, and hence get the result ...

47. experimentX

I think ... if the velocity is less than esc velocity, the orbit will be elliptical or circular at escape velocity, the orbit is parabolic, and beyond that .... it's hyperbolic.