ANSWER:
(a) 4.71 x 10^8 km
(b) 9.42 x 10^8 km
STEP-BY-STEP EXPLANATION:
Given:
The average distance between the sun and the earth represents the radius of the system, therefore:
Radius (R) = 1.5 x 10^8 km
The distance traveled by the earth would be the circumference of the circle that forms while it moves, in 6 months it is half the circumference and in 1 year it would be the complete circumference, therefore:
[tex]\begin{gathered} c=2\pi R \\ \\ \text{ For 6 months:} \\ \\ c=\frac{1}{2}\cdot2\pi R=\pi R \\ \\ \text{ We replacing} \\ \\ c=3.14\cdot1.5\times10^8=4.71\cdot10^8\text{ km} \\ \\ \text{ For 1 year:} \\ \\ c=2\pi R \\ \\ \text{ We replacing:} \\ \\ c=\:2\cdot3.14\cdot1.5\times10^8\: \\ \\ c=9.42\cdot10^8\text{ km} \end{gathered}[/tex]
