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,

Question

2 months ago

12

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?

Mathematics

1 answer:

PIT_PIT [12.4K] · Answer 1 · 2026-03-07T05:41:39+03:00

Let's denote the orbital period of planet X as T and its average distance from the sun as A. For planet Y, let its orbital period be T_1, implying that if planet Y's mean distance from the sun is twice that of planet X:

$Z^2=(2A)^3\\ Z^2=8A^3\implies\\ Z^2=8T^2 \implies\\ Z=2\sqrt{2}T$

This indicates that the orbital period for planet Y increases by a factor of $2\sqrt{2}$