1. Understand Kepler's Third Law
Kepler's Third Law of Planetary Motion states that the square of the orbital period (T) is proportional to the cube of the semi-major axis (a) of the orbit:
T² ∝ a³
2. Calculate the Semi-Major Axis
* The semi-major axis is the average distance between the probe and the Sun.
* It's calculated as the average of the perihelion (r_p) and aphelion (r_a):
a = (r_p + r_a) / 2
In your case:
* r_p = 0.5 AU
* r_a = 5.5 AU
* a = (0.5 + 5.5) / 2 = 3 AU
3. Use the Constant of Proportionality
For objects orbiting the Sun, the constant of proportionality in Kepler's Third Law is:
* k = 1 year²/AU³
4. Solve for the Orbital Period
Now we can rewrite Kepler's Third Law to solve for the orbital period (T):
T² = k * a³
Substitute the values we found:
T² = (1 year²/AU³) * (3 AU)³
T² = 27 years²
T = √27 years²
T ≈ 5.2 years
Therefore, the orbital period of the space probe would be approximately 5.2 years.
