At a distance of 14,000 km from the center of Planet Z-99, the acceleration due to gravity is 32 m/s2. What is the acceleration due to gravity at a point 28,000 km from the center of this planet

A body of mass m feels a gravitational force due to the planet of

F = GmM/R ² = ma

where

• G = 6.67 × 10⁻¹¹ N•m²/kg² is the universal gravitational constant

• M is the mass of the planet

• R is the distance between the body and the planet's center

• a is the acceleration due to gravity

Solving for a gives

a = GM/R ²

Notice that 28,000 km is twice 14,000 km. The equation says that the acceleration varies inversely with the square of the distance. So if R is changed to 2R, we have a new acceleration of

GM/(2R)² = 1/4 × GM/R ² = a/4

so the acceleration of the body at 28,000 km from the planet's center would be (32 m/s²)/4 = 8 m/s².

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