Answer to Question #254215 in Astronomy | Astrophysics for Nica

Question

Mercury orbits the sun at a distance of 0.4 AU. What is mercury’s orbital period in earth

years? Keplers’s Third Law : T^2=d^3. T: orbital period in earth year. D: distance to sun

in astronomical units. 1 AU=150,000,000 or 1.5x10^8 km.

Answer 1

Indeed, apply Kepler's third law for Mercury and Earth:

$$T^2=d^3,\\\space\\ T=\sqrt{ d^3}=0.25\text{ years}.$$