Question

5 multiple choice 1 point a certain planet is 0.39 au away from the sun. what is its orbital period? (remember for this formula that the units are au for a and earth years for p. you may need to convert earth years to earth days.) 0.24 days 0.059 days 89 days 195 days previous

Explanation:

Step1: Apply Kepler's Third Law

Kepler's Third Law is given by \( P^2 = a^3 \), where \( P \) is the orbital period in Earth years and \( a \) is the semi - major axis (distance from the Sun) in AU. Given \( a = 0.39\) AU. First, we calculate \( P^2=(0.39)^3\).
\(0.39^3=0.39\times0.39\times0.39 = 0.059319\)
Then, we take the square root of \( 0.059319 \) to find \( P \). \( P=\sqrt{0.059319}\approx0.2436\) Earth years.

Step2: Convert Earth years to Earth days

We know that 1 Earth year has 365 days. So we multiply the number of Earth years by 365 to get the number of days.
\(0.2436\times365 = 0.2436\times(300 + 60+5)=0.2436\times300+0.2436\times60 + 0.2436\times5=73.08+14.616 + 1.218=89.114\approx89\) days.

Answer:

89 days (corresponding to the option "89 days")