The equation T squared = A cubed 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? 2 Superscript one-third 2 Superscript one-half 2 Superscript two-thirds 2 Superscript three-halves

If planet Y is twice the mean distance from the sun as planet X, then by a factor of is the orbital period increased and this can be determined by using the given data.

Given :

The equation T squared = A cubed shows the relationship between a planet’s orbital period, T, and the planet’s mean distance from the sun, A, in astronomical units, AU.

The following steps can be used to determine the factor from which the orbital period increased:

Step 1 - Write the relationship between a planet’s orbital period, T, and the planet’s mean distance from the sun, A, in astronomical units, AU.

Step 2 - Now, it is given that planet Y is twice the mean distance from the sun as planet X. So, the above expression becomes:

So, the correct option is D).

For more information, refer to the link given below:

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T^2 = A^3

When T =  1 then A = 1

When T = 2 then T^2 = 4 and A = cube root of 4 = 1.587401052

which also equals 2^(2/3)  

So, of the answers you posted:

A) 2 Superscript one-third

B) 2 Superscript one-half

C) 2 Superscript two-thirds

D) 2 Superscript three-halves

it seems that "C" is the answer.

(By the way T^2 = A^3 is called Kepler's Third Law.  Actually Johannes Kepler stated it as:

T^2 = R^3 where "r" means radius of orbit.)

Step-by-step explanation: