Acceleration Due to Gravity Formula (g)

The formula to calculate the acceleration due to gravity on the surface of any celestial body is:

g = (G × M) / R²

Where:

• g = Acceleration due to gravity (m/s²)
• G = Universal Gravitational Constant (6.674 × 10⁻¹¹ N·m²/kg²)
• M = Mass of the planet or body (kg)
• R = Radius of the planet or body (m)

Crucial Point: Notice that the formula does NOT contain the mass of the falling object (m). This mathematically proves Galileo's famous discovery: all objects, regardless of their mass, fall at the same rate in a vacuum.

Let's plug in Earth's values:

• M (Mass of Earth) ≈ 5.972 × 10²⁴ kg
• R (Radius of Earth) ≈ 6.371 × 10⁶ m

g = (6.674×10⁻¹¹ × 5.972×10²⁴) / (6.371×10⁶)² g ≈ 9.8 m/s²

(Note: 'g' is slightly higher at the poles and slightly lower at the equator because the Earth is not a perfect sphere; it bulges at the equator, making R larger there).

1. With Altitude (Height): 'g' decreases as you go higher above the Earth's surface.
2. With Depth: 'g' decreases as you go deep into a mine, becoming zero at the Earth's core.
3. On the Moon: The Moon has less mass and a smaller radius. Its 'g' is about 1.62 m/s² (roughly 1/6th of Earth's gravity).