If a planet had a semi-major axis length of 2.3 AU as it orbits the Sun, what would be its period in years?
a. 1.74 years
b. 2.3 years
c. 3.49 years
d. 12.2 years
Using Kepler's third law, the period of an orbiting planet can be calculated using the formula:
period^2 = semi-major axis^3
Plugging in the values given:
period^2 = (2.3 AU)^3
Simplifying:
period^2 = 12.167 AU^3
Taking the square root:
period = √12.167 AU^3
Calculating the square root:
period ≈ 3.49 years
The correct answer is c. 3.49 years.