To determine which planet has the fastest average orbital speed, we can rely on Kepler's third law of planetary motion. Kepler's third law states that the square of a planet's orbital period (the time it takes for a planet to complete one orbit around the sun) is proportional to the cube of the semi-major axis of its orbit (the planet's average distance from the sun).
Mathematically, this can be expressed as:
[tex]\[ T^2 \propto r^3 \][/tex]
where [tex]\( T \)[/tex] is the orbital period and [tex]\( r \)[/tex] is the average distance from the sun.
Given this, the orbital period increases as the distance from the sun increases. If a planet has a smaller average distance from the sun, it will complete its orbit more quickly and therefore have a faster orbital speed.
Let's examine the average distances from the sun for the given planets:
- Venus: 0.72 AU
- Neptune: 30.06 AU
- Jupiter: 5.20 AU
- Saturn: 9.54 AU
Among these planets, Venus has the smallest average distance from the sun, which means it will have the fastest average orbital speed according to Kepler's third law.
Therefore, the planet with the fastest average orbital speed is:
Venus
