Find the acceleration due to Earth's gravity at the distance of the Moon's orbit, 3.84 x 10^8 m from Earth's center, using g = GM/r^2 with Earth's mass 5.98 x 10^24 kg.

1. The acceleration due to gravity at distance r from Earth's center is g = GM/r^2. 2. Substituting G = 6.67 x 10^-11 N*m^2/kg^2, M = 5.98 x 10^24 kg, and r = 3.84 x 10^8 m gives g = (6.67 x 10^-11)(5.98 x 10^24) / (3.84 x 10^8)^2. 3. The numerator is about 3.99 x 10^14, and the denominator, r squared, is about 1.47 x 10^17. 4. Dividing gives g = 2.70 x 10^-3 m/s^2, far smaller than the 9.80 m/s^2 felt at Earth's surface because the Moon is so much farther from Earth's center. 5. 2.70 x 10^3 m/s^2 and 2.70 x 10^-6 m/s^2 each misplace the decimal point by several orders of magnitude relative to the correctly computed value. _Source: OpenStax College Physics (CC BY 4.0), Ch 6 "Uniform Circular Motion and Gravitation", section 6.5 Newton's Universal Law of Gravitation_