Final answer:
To determine the orbital period of Sedna with its semi-major axis of 500 AU, Kepler's Third Law is used, which entails cubing the semi-major axis to find a relationship with the square of the orbital period. By extrapolation from known orbits, Sedna's period is estimated to be significantly greater than 350,000 years.
Step-by-step explanation:
To calculate the orbital period of Sedna, which has a semi-major axis of 500 AU, we use Kepler's Third Law. This law states that the square of the period (P) of an object's orbit is proportional to the cube of the semi-major axis (a) of its orbit. The formula can be expressed as P² ≈ a³ for objects in the solar system when P is measured in Earth years and a in Astronomical Units (AU).
First, we calculate the cube of the semi-major axis: a³ = 500³. To simplify, we know that the Earth has a semi-major axis of 1 AU and an orbital period of 1 year. This gives us a reference point where 1³ = 1² to compare with Sedna's orbit. When we cube 500, we do not need an exact number, simply an understanding that the period will be related by the cube root of this value.
The cube of 500 is a very large number, which suggests that the period of Sedna will be much longer than Earth's. To estimate this period without precise calculations, we look at available data that indicates an object with a semi-major axis of around 50 AU has an orbital period of about 353.6 years (rounded to 350 years for simplicity). As this is a rough estimation based on available data points, we can assert that since 500 AU is 10 times more than 50 AU, Sedna's period would be roughly 1000 times the period of an object at 50 AU because the period increases with the cube of the semi-major axis. This results in an estimated period well over 350,000 years for Sedna.