Orbital Velocity of Solar System Planets

Orbital velocity refers to the speed at which an object, like a planet, moves along its orbit around another body, such as the Sun. Understanding the factors that influence this velocity helps us determine which planet moves the fastest.

Factors Affecting Orbital Velocity

The orbital velocity ($v$) of a planet is primarily determined by two factors: the mass of the central body it orbits (the Sun, denoted by $M$) and the distance between the planet and the Sun (the orbital radius, denoted by $r$). The relationship is governed by the laws of gravity and motion. For a circular orbit, the velocity can be approximated using the formula:

$$ v = \sqrt{\frac{GM}{r}} $$

Where:

• $v$ is the orbital velocity
• $G$ is the universal gravitational constant
• $M$ is the mass of the Sun
• $r$ is the orbital radius (distance from the Sun)

This formula shows that orbital velocity ($v$) is inversely proportional to the square root of the orbital radius ($r$). In simpler terms, the closer a planet is to the Sun, the smaller its $r$, and therefore, the higher its orbital velocity ($v$). Conversely, planets farther from the Sun have larger $r$ and lower orbital velocities.

Comparing Inner Planets' Orbital Velocities

Let's look at the planets mentioned in the options and their positions relative to the Sun:

*AU stands for Astronomical Unit, where 1 AU is the average distance between the Earth and the Sun.

Conclusion

Based on the order from the Sun and the relationship between distance and orbital velocity:

• Mercury is the closest planet to the Sun.
• Venus, Earth, and Mars are progressively farther away.

Therefore, Mercury has the smallest orbital radius ($r$) among these planets and consequently possesses the highest mean orbital velocity. As planets get farther from the Sun, their orbital speed decreases.