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Trying to understand reduced mass 
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#1
Mar1313, 08:42 PM

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I understand that the reduced mass is used to simplify a twobody problem into a one body problem, so that instead of calculating two masses rotating around a common center as in the earth and moon, you can treat the earth as stationary, and then used a "reduced" mass for the moon in the calculation.
My question is how is m1m2/m1+m2 calculated to derive the reduced mass. I'm not able to follow the arguments in my readings. Can someone give me a simple, straightforward derivation along with a conceptual "intuition" as to why this works? 


#2
Mar1413, 07:11 AM

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#3
Mar1413, 08:02 AM

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If someone simply posts a derivation, they run the risk of repeating something that you've seen already and don't understand. 


#4
Mar1513, 02:28 AM

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Trying to understand reduced mass
@DrClaude
@jtbell I'm trying to follow the derivation on the wiki page under the "Newtonian mechanics" heading. I get all the math but...why does arel = a1a2 instead of say, a2a1? Also, why is the result F12/Mred the result we are looking for? I get the derivation, I just don't understand how it works to turn the two body problem into a single body problem. So when they say at the end... I'm not catching their drift. Any help would be appreciated. 


#5
Mar1513, 03:49 AM

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The key word in that quote is "pretend." This is not rigourous. But indeed, if one of the objects is much more massive than the other, then the center of mass of the system will be located close to the middle of the massive object, and therefore you can imagine that it is as if you had an object of mass [itex]m_\mathrm{red}[/itex] orbiting in a closer orbit around the massive object.
I've just looked at the Wikipedia page, and I understand completely why you are confused. Maybe this derivation, taken from V. D. Barger and M. G. Olsson, Classical Mechanics: A Modern Perspective, 2nd ed., McGrawHill (New York), 1995, will be more helpful. 


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Mar1513, 04:07 AM

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#7
Mar1513, 06:26 AM

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#8
Mar1513, 07:45 AM

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