Question

The equation mc024-1.jpg 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 planet Y is twice the mean distance from the sun as planet X, by what factor is the orbital period increased?

mc024-2.jpg
mc024-3.jpg
mc024-4.jpg
mc024-5.jpg

Answer 1

its C StartFraction 2 StartRoot 5 EndRoot Over 5 EndFraction

Step-by-step explanation: took the unit test

Answer 2

Given that 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.
i.e.
`T= √(A^3)`

If planet Y is twice the mean distance from the sun as planet X,
i.e.
`A_Y=2A_X`,
then,

`(T_Y)/(T_X) = (√((2A_X)^3))/(√((A_X)^3)) = ((2A_X)^3)/((A_X)^3) = (8(A_X)^3)/((A_X)^3) =8`

Therefore, the orbital period increased by a factor of 2^3/2