Question

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 k times the mean distance from the sun as planet X, by what factor is the orbital period increased? k Superscript one-third k Superscript one-half k Superscript two-thirds k Superscript three-halves

Answer 1

Answer:

Ty = √k  * Tx

The orbital period of Y has to be be multiplied by √k .   or . k∧1/2

Step-by-step explanation:

The general equation:

T² = A³

is for the case of planet X

Tₓ² = Aₓ³

In the case of planet Y

Ty² = k * Aₓ³ .     and   Aₓ³ = Tₓ²

By substitution:

Ty² =  k *Tₓ²

Ty = √k  * Tx