Gravitational force calculator
By the law of universal gravitation, two bodies attract each other with a force proportional to the product of their masses and inversely proportional to the square of the distance between them: F = G · m₁m₂ / r². Double the distance and the force falls to a quarter.
- Acceleration of the second body
- 9.81997m/s²
Rates and thresholds
- Law of gravitation
- F = G · m₁m₂ / r²
- Gravitational constant G
- 6.67430 × 10⁻¹¹ m³·kg⁻¹·s⁻²
- Mass of the Earth
- 5.972 × 10²⁴ kg
- Mean radius of the Earth
- 6,371 km
Why doesn't the formula give exactly 9.81 for gravity?
Working it out from the Earth's mass and mean radius gives about 9.82 m/s², whereas standard gravity is defined as 9.80665 m/s². The gap is roughly 0.14 per cent and has two causes. First, the Earth rotates, and the centrifugal effect reduces the acceleration you actually measure, most of all at the equator. Second, the Earth is not a perfect sphere but flattened at the poles, so the distance to its centre varies with latitude. The figure 9.80665 is an agreed reference value rather than a measurement taken anywhere in particular.
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