Kepler's Third Law
Kepler's Third Law states that the square of the orbital period (P) of a planet is proportional to the cube of the semi-major axis (a) of its orbit. Mathematically:
P² = a³
Where:
* P is the orbital period in years
* a is the semi-major axis in astronomical units (AU)
Calculation
1. Plug in the distance: We know the object is 65 AU from the Sun. Assuming a circular orbit (which is a simplification), this is our semi-major axis (a = 65 AU).
2. Solve for P:
* P² = (65 AU)³
* P² = 274,625
* P = √274,625 ≈ 524 years
Approximate Orbital Period
Therefore, an object orbiting the Sun at a distance of 65 AU would have an approximate orbital period of around 524 years.
