Kepler's Third Law
Kepler's Third Law of Planetary Motion states that the square of a planet's orbital period (T) is proportional to the cube of its average distance from the Sun (a). Mathematically:
T² ∝ a³
Applying the Law
1. Earth's Distance and Period: Earth's average distance from the Sun is 1 Astronomical Unit (AU). Its orbital period is 1 year.
2. Hypothetical Planet: Our hypothetical planet is twice as far from the Sun, so its distance (a) is 2 AU.
3. Calculating the Period:
* Let the period of the hypothetical planet be T'.
* We can set up a proportion: T²/a³ = T'²/a'³
* Plugging in the values: 1²/1³ = T'²/2³
* Solving for T': T'² = 8
* T' = √8 = 2√2 years (approximately 2.83 years)
Conclusion
A hypothetical planet twice as far from the Sun as Earth would have an orbital period of approximately 2.83 years.
