Here's the simplified explanation:
* The square of the orbital period of a planet is proportional to the cube of its average distance from the Sun.
This means that:
* Planets farther from the Sun take longer to orbit. This is because the farther a planet is, the larger the circumference of its orbit, and thus the longer the distance it needs to travel.
* The relationship is not linear. Doubling the distance doesn't double the orbital period. It actually increases the period by a factor of the cube root of 8 (which is about 2).
Mathematically:
* T² ∝ r³
* T = Orbital period (in years)
* r = Average distance from the Sun (in astronomical units, AU)
Example:
* Earth is about 1 AU from the Sun and takes 1 year to orbit.
* Mars is about 1.5 AU from the Sun. If we plug this into the equation:
* 1.5³ = 3.375
* T² = 3.375
* T = √3.375 ≈ 1.83 years (which is close to Mars's actual orbital period)
This law holds true for all planets in our solar system and is a fundamental principle of celestial mechanics.
