The equation mc025-1.jpg shows the relationship between a planet’s orbital perio

Mathematics
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The equation shows the relationship between a planet’s orbital period, T, and the planet’s mean distance from the sun, A, in astronomical units, AU. If the orbital period of planet Y is twice the orbital period of planet X, by what factor is the mean distance increased?

Jul 22nd, 2015

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can u post mc025.jpg  or the equation

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Jul 22nd, 2015

The equation T^2=A^3 shows the relationship between a planet’s orbital period, T, and the planet’s mean distance from the sun, A, in astronomical units, AU. If the orbital period of planet Y is twice the orbital period of planet X, by what factor is the mean distance increased?

Jul 22nd, 2015

T^2=A^3

T1^2=A1^3                                         for planet X

T2^2=A2^3                                         for planet Y

 T2=2T1                                             given

therefore,

4T1^2=A2^3

T1^2=(A2^3)/4

but 

T1^2=A1^3

therefore,

A1^3=A2^3/4

A2=cuberoot of 4(A1)



mean distance is increased by cuberoot of 4.

Jul 22nd, 2015

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