Question

A planet has an average distance to the sun of 4.54 AU. In two or more complete sentences, explain how to calculate the orbital period of the planet and calculate it.

Answer 1

Using Kepler's 3rd Law of planatary motion we know that the sqare of the orbital period is proportional to the cube of the semimajor axis.
So we know the earth is 1 AU from the sun with a period of 1 year so we can set up a ratio as follows:
P^2 / r^3= 1
(P)^2 = 4^3
P = 4^(3/2) = 8 years

Answer 2

Answer:

We can use the formula for orbital time period:

T² = (4π²/GM)a³; where T is in Earth years, a is distance from sun in AU, M is the solar mass (1 for the sun), G is the gravitational constant.

In the given units, 4π²/G = 1

T² = 4.54³

T = 93.576664 Earth years = 34155.48236 Earth days