Understanding Kepler's Third Law
Kepler's Third Law of Planetary Motion states that the square of an object's orbital period (P) is proportional to the cube of its average distance from the Sun (a). Mathematically:
P² = a³
Units
* P: Orbital period in Earth years
* a: Average distance from the Sun in Astronomical Units (AU)
Calculation
1. Given: a = 3 AU
2. Plug into Kepler's Third Law: P² = (3 AU)³ = 27
3. Solve for P: P = √27 ≈ 5.2 years
Therefore, the best estimate of the orbital period for a typical asteroid at 3 AU from the Sun is approximately 5.2 years.
