Question

Use the formula below to calculate the time it takes this planet to orbit around our Sun P²=a³. The planet is 297,600,000 miles from the sun. If we convert that to Astronomical Units (AU) we get (a) Converted: a=3.4 AUs a= 3.4 AU. Solve for P if P²=a³. Use the formula and data above, how long is one period (p) for the planet? Or, said differently, one year (p) on this planet is equal to how many Earth Years?

Answer 1

The orbital period (P) for the planet at 3.4 AU from the Sun is approximately 6.27 Earth years, as calculated using Kepler's Third Law (P² = a³).

Step-by-step explanation:

The student is asking to calculate the orbital period, or year, of a planet that is 3.4 Astronomical Units (AU) away from the Sun. We are using Kepler's Third Law, which is expressed as P² = a³, where P is the orbital period in Earth years and a is the mean distance from the Sun in AU. Since the distance to the planet is given as 3.4 AU, we can solve for P by taking the square root of the cube of the semimajor axis, a. In other words, P = √(a³).

Calculating this gives us P = √(3.4³) = √(39.304) ≈ 6.27 years. Therefore, one year on this planet, at 3.4 AU away from the Sun, is approximately 6.27 Earth years.