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Old Mar 19th 2013, 10:13 AM   #1
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Mass calculation

I'm having a bit of trouble with this question and was hoping to get a push in the right direction. When calculating the mass of the earth which has a greater effect; error in the length of the semi-major axis or the time period of the orbit.
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Old Mar 19th 2013, 11:13 AM   #2
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I assume this has to do with calculating the mass of the earth from orbital paramaters of the moon or satellite in orbit, right? If so, then consider that from basic orbital mechanics:

GMm/R^2 = m w^2 R, where w = rotational velocity, and the orbital period T= 2 pi/w.

Do some rearranging:

GM = 4 pi^2 R^3/T^2

Note that the powers that R and T are raised to are different. From this - would an error of, say 2% in R have a bigger or smaller effect on the calculated quantity GM than a 2% error in T?
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Old Mar 20th 2013, 03:42 AM   #3
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Thank you Chip, that makes perfect sense.
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Old Apr 1st 2013, 05:28 AM   #4
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A brief background on what the BMI is, is it is a number calculated from a person's weight and height for determining body fat and thus your ideal weight based on your height. Did you know that it wasn't even developed by a dietician, it was developed by a mathematician?
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