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[tex]4\pi^{2}/G = 1yr^{2} M_{Sun}/AU^{3} [/tex]

and that therefore Kepler's 3rd Law reduces to

[tex]P^{2}=a^{3}/(m_{1}+m_{2})[/tex]

if the period P is expressed in years, the semimajor axis a is expressed in AU, and the sum of the masses is expressed in solar masses.

[tex]G = 6.672*10^{-11}Nm^{2}/kg^{2}[/tex]

[tex]N = kg m/s^{2}[/tex]

[tex]1 year = 3.15581*10^{7}seconds[/tex]

[tex]1 AU = 1.49598*10^{11}meters[/tex]

[tex]1 Solar mass = 1.9891*10^{30}kg[/tex]

[tex]\frac{4\pi^{2}}{6.672*10^{-11} \frac{N m^{2}}{kg^{2}}}=\frac {3.15581*10^{7}s^{2}*1.9891*10^{30}kg}{1.49598*10^{11}m^{3}}[/tex]

Substitute [tex]kg m/s^{2} for N[/tex]

[tex]\frac{4\pi^{2}}{6.672*10^{-11} \frac{kg\frac{m}{s^{2}} m^{2}}{kg^{2}}}=\frac {3.15581*10^{7}s^{2}*1.9891*10^{30}kg}{1.49598*10^{11}m^{3}}[/tex]

in the left side of the equation, cancel kg's and combine m's

[tex]\frac{4\pi^{2}}{6.672*10^{-11} \frac{\frac{m^{3}}{s^{2}}}{kg}}=\frac {3.15581*10^{7}s^{2}*1.9891*10^{30}kg}{1.49598*10^{11}m^{3}}[/tex]

re-write the equation

[tex]{4\pi^{2} * 1.49598*10^{11}m^{3} = 6.672*10^{-11} \frac{\frac{m^{3}}{s^{2}}}{kg} * 3.15581*10^{7}s^{2}*1.9891*10^{30}kg [/tex]

The m^3 on the right cancels with the m^3 on the left

the s^2's in the left side of the equation cancel with each other since one is in the denomanator of a fraction, and the other one isn't.

The kg's in the left side of the equation cancel with each other since one is in the denomanator of a fraction, and the other one isn't.

[tex]{4\pi^{2} * 1.49598*10^{11} = 6.672*10^{-11} * 3.15581*10^{7}*1.9891*10^{30} [/tex]

and when I compute this I get:

[tex]591702901743.965 = 4.1881622988912*10^{27}[/tex]

and that's just not right!! Where did I go wrong?

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# Homework Help: Formula relationship

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