JenniferSmart1
@experimentX
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JenniferSmart1
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Let's start with Keplers laws
JenniferSmart1
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Let's see what I remember without looking at my cheat sheet
JenniferSmart1
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Something about
\[T^2=R^3\]
experimentX
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seems like I forgot Kepler laws ... let's see
JenniferSmart1
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The period of an object orbital around the sun is proportional to the radius?
JenniferSmart1
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whose radius? or perhaps some distance? The distance between that object and the sun?
JenniferSmart1
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no cheating haha
JenniferSmart1
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:P
JenniferSmart1
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draw it with me|dw:1361862577312:dw|
experimentX
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|dw:1361862616815:dw|
JenniferSmart1
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Let's see what I remember about the semi major axis.......
DLS
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\[\LARGE (\frac{T_1}{T_2})^2=(\frac{R_1}{R_2})^3\]
DLS
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\[\LARGE \frac{dA}{dT}=\frac{L}{2M}\]
JenniferSmart1
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why do we have two semi major axis?
JenniferSmart1
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what ratio is that?
experimentX
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it doesn't matter which side you take ... lol
JenniferSmart1
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|dw:1361862832161:dw|
JenniferSmart1
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|dw:1361862878591:dw|
Where is \(R_2\)
JenniferSmart1
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>:O
JenniferSmart1
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wiki didn't explain the ratio though
JenniferSmart1
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LOL I'm tired. ok I get it
JenniferSmart1
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Let's talk about escape speed
DLS
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\[\LARGE \sqrt{2gR}\]
JenniferSmart1
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|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
JenniferSmart1
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something about when the kinetic energy reaches \(\frac{GMm}{r^2}\)?
experimentX
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|dw:1361863195805:dw|
JenniferSmart1
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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
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\[\frac{-GMm}{R}+\frac{mv^2}{2}=0\]
DLS
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put the total energy=0
find V
JenniferSmart1
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Why what's the logic behind it?
WHy is the total energy zero?
DLS
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If a body's total net mec. energy=0,it will escape from the earth's gravitational field
experimentX
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find the total work done when bringing object from infinity to position 'r'
JenniferSmart1
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oh ok, so when the kinetic energy equals the potential energy?
DLS
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have u heard of binding energy
JenniferSmart1
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Let's see if I remember. When E<0 or =0
JenniferSmart1
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parabolic and hyperbolic orbits?
JenniferSmart1
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that's when they're unbound correct?
JenniferSmart1
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nope when E>0 is unbound
JenniferSmart1
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when E is less than zero is the only time when it's bound
JenniferSmart1
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So when the potential is greater than the kinetic energy the energy is bound?
JenniferSmart1
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gotta sleep =) Thanks for the discussion everyone. I look forward to hear more about bounded and unbounded Energy when I wake up. See ya :)
experimentX
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sorry ... was kinda busy not paying attention
experimentX
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this way you can do it ... for escape velocity.
|dw:1361863974972:dw|
experimentX
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You can equate those two, and hence get the result ...
experimentX
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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.