Estimate the length of venusian year using the fact that the earth is 1.49*10'8km and venus is 1.08*10'8km from the sun on average.
To estimate the length of the Venusian year using the given information, we can make use of Kepler's Third Law of Planetary Motion. This law states that the square of the orbital period of a planet is proportional to the cube of its average distance from the sun.
Let's denote the length of the Venusian year as T_v, and the average distance of Venus from the sun as D_v. Similarly, we denote the length of the Earth's year as T_e and the average distance of Earth from the sun as D_e.
According to Kepler's Third Law, we have the following relationship:
(T_v^2) / (T_e^2) = (D_v^3) / (D_e^3)
Substituting the given values, we get:
(T_v^2) / (1 year)^2 = (1.08 * 10^8 km)^3 / (1.49 * 10^8 km)^3
Simplifying the equation, we get:
(T_v^2) / (1 year)^2 = (1.08^3) / (1.49^3) * (10^8)^3 / (10^8)^3
(T_v^2) / (1 year)^2 = 0.658 * 10^8 / 2.2 * 10^8
(T_v^2) / (1 year)^2 = 0.299
Taking the square root of both sides to solve for T_v, we obtain:
T_v / (1 year) = √(0.299)
T_v = √(0.299) * 1 year
Calculating the value, we find:
T_v ≈ 0.547 years
Therefore, the estimated length of the Venusian year is approximately 0.547 years.