Ellipses contain two axes: major and minor. Half the major axis is called the semimajor axis. What is especially important about the semimajor axis of a planetary orbit?

A planetary orbit is the path that a planet follows as it revolves around a star, such as our Sun. Orbits are generally elliptical, meaning they have an oval shape instead of being perfectly circular.
One key feature of elliptical orbits is that they have two focuses, or focal points. For planetary orbits, one of these points is usually very close to the center of the star.
The major axis is the longest line you can draw within the ellipse, running through both focal points. The semimajor axis is half of this length and is critically important in understanding the orbit's dimensions.
This semimajor axis measures how far on average the planet is from the star, affecting how strong the star's gravitational pull is on the planet. Ultimately, it determines the size and shape of the orbit.

Kepler's Third Law is a fundamental principle for understanding planetary motion. It states that the square of a planet's orbital period (the time it takes the planet to make one complete orbit around the star) is proportional to the cube of the semimajor axis of its orbit.
Mathematically, this can be expressed as:
\(\frac{T^2}{a^3} = \frac{4\text{π}^2}{GM}\)
where:

• \( T \) is the orbital period
• \( a \) is the semimajor axis
• \( G \) is the gravitational constant
• \( M \) is the mass of the star

This equation shows that if you know the length of the semimajor axis, you can figure out how long it takes for the planet to complete one orbit and vice versa.
The larger the semimajor axis, the longer the orbital period, which means the planet takes more time to go around the star.

The orbital period is the time a planet takes to make one full orbit around its star. This period can vary widely depending on the size of the orbit. For instance, Earth’s orbital period around the Sun is one year.
According to Kepler's Third Law, a planet's orbital period is directly related to its semimajor axis. If a planet has a larger semimajor axis, it means it is farther from the star and thus takes a longer time for one complete orbit.
To put it simply, the orbital period can be calculated if you know the distance of the semimajor axis. This relationship is key to understanding movements within our solar system and beyond. This helps astronomers predict how planets behave and where they might be located at any given time.