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Let's start with Keplers laws

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

Something about
\[T^2=R^3\]

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.......

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

\[\LARGE \frac{dA}{dT}=\frac{L}{2M}\]

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

\[\LARGE \sqrt{2gR}\]

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

|dw:1361863195805:dw|

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

put the total energy=0
find V

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

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?

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?

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 ...