Question

Two planets (X and Y) that are far apart have the same mass, but planet Y has a radius three times that of planet X. If a is the magnitude of the acceleration due to gravity on the surface of planet X, what is the magnitude of the acceleration due to gravity on the surface of planet Y?

Answer 1

The acceleration due to gravity on planet Y is one-ninth the acceleration due to gravity on planet X since planet Y has a radius three times that of planet X.

Step-by-step explanation:

The acceleration due to gravity on the surface of a planet is determined by the planet's mass (M) and radius (R) and is given by the formula g = GM/R^2, where G is the universal gravitational constant. In this question, both planets X and Y have the same mass but planet Y has a radius three times that of planet X. Therefore, by substituting the radius of Y (3R) into the formula, the acceleration due to gravity on planet Y would be g' = GM/(3R)^2 which simplifies to g'= GM/9R² = g/9, where g is the acceleration due to gravity on planet X. Thus, the acceleration due to gravity on planet Y is one-ninth that of planet X.