Acceleration Due to Gravity on Different Planets

What determines the free fall acceleration on a planet?

The free fall acceleration on a planet is determined by its mass and radius, according to the formula g = GM/r². How does this relationship affect the acceleration due to gravity on different planets?

Answer:

The acceleration due to gravity on a planet is determined by its mass and radius. This relationship directly impacts the free fall acceleration experienced on different planets.

Understanding the free fall acceleration on a planet involves considering the planet's mass and radius. The formula g = GM/r² illustrates how the acceleration due to gravity is influenced by these factors. When comparing two planets, such as planet Xorgon and planet Zeta, where the mass and radius of Zeta are double those of Xorgon, the acceleration due to gravity will be different.

While it may seem intuitive to assume that a larger mass would result in a greater acceleration due to gravity, the increase in the radius counteracts this effect. In the case of planet Zeta, the acceleration due to gravity is actually half of that on planet Xorgon, despite having twice the mass and radius.

This balancing act between mass and radius showcases the intricacies of gravitational forces on celestial bodies. By understanding the relationship between mass, radius, and free fall acceleration, we can calculate the acceleration due to gravity on different planets with accuracy.