Two comets are at the same distance from the Sun, but one is three times as massive. According to Newton's law, the gravitational force on the more massive comet is what?

• A. equal
• B. four times
• C. three times
• D. one third

Answer: (C)

Gravitational force from the Sun on an object at a fixed distance is proportional to the object's mass. The formula F = G M_sun m / r^2 shows that, with the Sun’s mass and the distance r held constant, F scales directly with m. If one comet has three times the mass, the gravitational force on it is three times larger. A helpful byproduct: the acceleration a = F/m = GM_sun/r^2 is the same for both comets, but the total force differs in proportion to their masses.