You have been visiting a distant planet. Your measurements have determined that the planet's mass is twice that of earth but the free-fall acceleration at the surface is only one-fourth as large. What is the planet's radius?

Verified step by step guidance

1. Start by recalling the formula for gravitational acceleration at the surface of a planet: $g=\frac{\left(\mathrm{G}\right)\left(M\right)}{radius}$ .

Key Concepts

Gravitational Acceleration

Gravitational acceleration is the acceleration experienced by an object due to the gravitational force exerted by a massive body, such as a planet. It is denoted by 'g' and varies depending on the mass of the planet and the distance from its center. On Earth, this value is approximately 9.81 m/s², but it can be different on other celestial bodies based on their mass and radius.

Newton's Law of Universal Gravitation

Newton's Law of Universal Gravitation states that every point mass attracts every other point mass in the universe with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. This law helps us understand how gravitational forces operate between two masses and is fundamental in calculating gravitational acceleration on different planets.

Radius of a Planet

The radius of a planet is the distance from its center to its surface. It plays a crucial role in determining the gravitational force experienced at the surface. According to the relationship between mass, radius, and gravitational acceleration, if a planet's mass increases while its gravitational acceleration decreases, the radius must also change to maintain the balance dictated by gravitational laws.