Question

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 planet y is twice the mean distance from the sun as planet x, by what factor is the orbital period increased?

Answer 1

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Explanation:

Answer 2

Since the relationship between a planet's orbital period and the planet's mean distance from the sun are already given, to simplify and understand the factors by which these two factors affect each other, let us assign simple values to each.

Given: t^2 = a^3

let:
2 = mean distance from the sun of planet x
4 = mean distance from the sun of planet y

For planet X:

t^2 = 2^3
t = sqrt(8) = 2.828

For planet Y:

t^2 = 4^3
t = sqrt(64) = 8

Factor of increase = 8/2.828 = 2.828

Therefore, the orbital period has increased by a factor of 2.828.