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Let's start with Keplers laws
Let's see what I remember without looking at my cheat sheet
Something about \[T^2=R^3\]

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seems like I forgot Kepler laws ... let's see
The period of an object orbital around the sun is proportional to the radius?
whose radius? or perhaps some distance? The distance between that object and the sun?
http://en.wikipedia.org/wiki/Kepler's_laws_of_planetary_motion ellipse ... semi major axis.
no cheating haha
:P
draw it with me|dw:1361862577312:dw|
|dw:1361862616815:dw|
Let's see what I remember about the semi major axis.......
  • DLS
\[\LARGE (\frac{T_1}{T_2})^2=(\frac{R_1}{R_2})^3\]
  • DLS
\[\LARGE \frac{dA}{dT}=\frac{L}{2M}\]
why do we have two semi major axis?
what ratio is that?
it doesn't matter which side you take ... lol
|dw:1361862832161:dw|
|dw:1361862878591:dw| Where is \(R_2\)
http://en.wikipedia.org/wiki/Semi-major_axis
>:O
wiki didn't explain the ratio though
LOL I'm tired. ok I get it
Let's talk about escape speed
  • DLS
\[\LARGE \sqrt{2gR}\]
|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
something about when the kinetic energy reaches \(\frac{GMm}{r^2}\)?
|dw:1361863195805:dw|
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?
  • DLS
\[\frac{-GMm}{R}+\frac{mv^2}{2}=0\]
  • DLS
put the total energy=0 find V
Why what's the logic behind it? WHy is the total energy zero?
  • DLS
If a body's total net mec. energy=0,it will escape from the earth's gravitational field
find the total work done when bringing object from infinity to position 'r'
oh ok, so when the kinetic energy equals the potential energy?
  • DLS
have u heard of binding energy
Let's see if I remember. When E<0 or =0
parabolic and hyperbolic orbits?
that's when they're unbound correct?
nope when E>0 is unbound
when E is less than zero is the only time when it's bound
So when the potential is greater than the kinetic energy the energy is bound?
gotta sleep =) Thanks for the discussion everyone. I look forward to hear more about bounded and unbounded Energy when I wake up. See ya :)
sorry ... was kinda busy not paying attention
this way you can do it ... for escape velocity. |dw:1361863974972:dw|
You can equate those two, and hence get the result ...
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.

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