How this calculator works
The falling test mass cancels from Newton's force law, leaving a field determined by source mass and centre distance. Altitude mode adds height to the surface radius. Its comparison table uses multiples of that reference radius, so it works for a hypothetical sphere as well as a planet. Other modes treat the entered or solved centre distance as the table's reference surface. The model assumes a spherically symmetric source and an exterior observation point. Rotation, latitude, terrain, tides and relativity are excluded. Solving G from measurements is an algebra exercise; real experiments must account for geometry and uncertainty.
Formula
g = GM/r²; M = gr²/G; r = sqrt(GM/g); G = gr²/M. At altitude h above radius R: g(h) = GM/(R+h)² and g(h)/g(0) = [R/(R+h)]².
Worked example
For an illustrative source with GM = 400 m³/s², a centre distance of 10 m gives 4 m/s². At 10 m above that 10 m surface radius, distance doubles to 20 m and gravity falls to 1 m/s².
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Frequently asked questions
Is radius measured from the surface?
The ordinary mode needs distance from the centre. In altitude mode, enter surface radius and height above the surface separately.
Why is surface gravity different from 9.80665 m/s²?
Standard gravity is a conventional reference. This spherical model uses your mass and radius and omits rotation and local variations.
Can I use the whole planet mass below its surface?
No. Inside an ideal sphere, only enclosed mass contributes to the radial field. A density profile is needed for the interior.