Physics
medo12341
2016-04-12 00:41:12
Saturn has an orbital period of 29.46 years. In two or more complete sentences, explain how to calculate the average distance from Saturn to the sun and then calculate it.
ANSWERS
Carol11
2016-04-12 02:02:34

[latex]Given:\T=29.46yapprox 9.29cdot 10^8s\M_Sapprox2.0cdot 10^{30}kg\G=6.67cdot 10^{-11} frac{m^3}{kgcdot s^2} \\Find:\R=?\\Solution:\\F_g= Gfrac{mM_s}{R^2} \\F_c= frac{mv^2}{R} \\F_g=F_c\\Gfrac{mM_s}{R^2}=frac{mv^2}{R} Rightarrow Gfrac{M_s}{R^2}=frac{v^2}{R}\\v=omega r\\Gfrac{M_s}{R^2}= frac{omega^2R^2}{R}Rightarrow Gfrac{M_s}{R^2}=omega^2R \\omega= frac{2 pi }{T} \\Gfrac{M_s}{R^3}= frac{4 pi ^2}{T^2} [/latex] [latex]GM_ST^2=4 pi ^2R^3Rightarrow R= sqrt[3]{ frac{GM_ST^2}{4 pi ^2} }\\\R= sqrt[3]{ frac{6.67cdot 10^{-11} frac{m^3}{kgcdot s^2}cdot2.0cdot 10^{30}kg( 9.29cdot 10^8s)^2}{4cdot 3.14^2} } approx 1.42cdot 10^{12}m[/latex]

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