Understanding the Concepts
* Kepler's Third Law: This law states that the square of the orbital period (T) of a planet (or probe) is proportional to the cube of the semi-major axis (a) of its orbit. Mathematically: T² ∝ a³
* Semi-major Axis: The semi-major axis is the average distance between the object and the Sun. For an elliptical orbit, it's half the length of the major axis.
Calculations
1. Calculate the semi-major axis (a):
* a = (0.5 AU + 5.5 AU) / 2 = 3 AU
2. Use Kepler's Third Law:
* T² ∝ a³
* To make this an equation, we need a constant of proportionality. For objects orbiting the Sun, this constant is 1 year²/AU³.
* Therefore: T² = a³
* T = √(a³) = √(3 AU)³ ≈ 5.196 years
Answer: The orbital period of the space probe would be approximately 5.196 years.
