Acceleration due to Gravity Calculator

The calculation is based on Sir Isaac Newton's Law of Universal Gravitation combined with Newton's Second Law of Motion. The formula used is g = (G * M) / r^2, where 'g' represents the acceleration due to gravity, 'G' is the universal gravitational constant (approximately 6.67430 x 10^-11 m^3 kg^-1 s^-2), 'M' is the mass of the object in kilograms, and 'r' is the radius from the center of mass to the point of measurement in meters. This inverse-square relationship means that doubling the radius of a planet reduces its surface gravity by a factor of four.

Let us calculate the acceleration due to gravity for an imaginary planet with a mass (M) of 4.0 x 10^24 kg and a radius (r) of 3.5 x 10^6 meters. First, square the radius: (3.5 x 10^6)^2 = 1.225 x 10^13 m^2. Next, multiply the universal gravitational constant by the mass: (6.674 x 10^-11) * (4.0 x 10^24) = 2.6696 x 10^14. Finally, divide the result by the squared radius: (2.6696 x 10^14) / (1.225 x 10^13) = 21.8 m/s^2. Thus, the surface gravity of this planet is roughly 2.18 times that of Earth.

Always ensure your inputs are converted to standard SI units before calculating: kilograms for mass and meters for radius. If a problem provides a planet's diameter instead of its radius, remember to divide the diameter by two first. Pay close attention to scientific notation exponents to avoid order-of-magnitude errors that can completely invalidate your final result.