Question

The average distance between the sun and the earth is R=1.5 x 10^8 km. Calculate the distance traveled and the displacement of the planet after exactly : (a) 6 months, (b) 1 year.

Answer 1

(a) 4.71 x 10^8 km

(b) 9.42 x 10^8 km

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:

`\begin{gathered} c=2\pi R \\ \\ \text{ For 6 months:} \\ \\ c=(1)/(2)\cdot2\pi R=\pi R \\ \\ \text{ We replacing} \\ \\ c=3.14\cdot1.5*10^8=4.71\cdot10^8\text{ km} \\ \\ \text{ For 1 year:} \\ \\ c=2\pi R \\ \\ \text{ We replacing:} \\ \\ c=\:2\cdot3.14\cdot1.5*10^8\: \\ \\ c=9.42\cdot10^8\text{ km} \end{gathered}`