Acceleration formula for satellites

• A. a = GM/r^2
• B. a = G M r
• C. a =GM/r
• D. a = G / (M r^2)

Answer: (A)

Gravitational acceleration follows the inverse-square law. The gravitational force on a satellite of mass m is F = GMm/r^2, where M is the planet’s mass and r is the distance to its center. Acceleration is force per unit mass, so a = F/m = GM/r^2. This is the acceleration toward the planet and it gets smaller as the distance grows, proportional to 1/r^2.

In circular motion, that same acceleration provides the centripetal requirement a = v^2/r, linking orbital speed to radius via v^2 = GM/r. The parameter GM (often written μ) encapsulates the planet’s gravitational influence.

The other options don’t match the way gravity scales with distance: GM r grows with distance instead of shrinking; GM/r is a potential-related quantity (not acceleration) with different dimensions; G/(M r^2) has incorrect units and dependence.