🛰️ Gravitational Field: Why g Falls as 1/r²
Gravitational field strength is a_g = GM/r², where r is measured from the centre of the planet, not its surface. Because r is squared, doubling your distance from the centre cuts the field to a quarter, not a half — at r = 2R the field is 1/4 of its surface value, at 3R it is 1/9, and at 4R it is 1/16. The field depends only on the planet's mass M and the distance r; the orbiting object's own mass never enters the equation.
Drag the satellite below to any altitude and watch it happen.
Gravitational Field: Why Field Strength Falls as 1/r²
Distance is measured from the centre, not the surface. In g = GM/r2, the distance is r = R + h. Lift the satellite one planet radius (h = R) and r doubles, so g falls to a quarter of its surface value, not a half. At 2R, 3R and 4R it is gs/4, gs/9 and gs/16, the dots on the graph. Drag the satellite, or type h.
The field belongs to the planet, not to the satellite. g is the force on each kilogram, Fg/m, in N/kg, and GM/r2 has no m in it. Change the satellite’s mass and its weight Fg = mg changes, but g does not. Released, anything there falls with a = g: at GPS height, a field of 0.564 N/kg gives 0.564 m/s2. On the ISS, 420 km up, g is still 8.64 N/kg; astronauts float because they and the station fall together.
A straight line proves the inverse square. Plot g against 1/r2 and the curve becomes a straight line through the origin, g = GM × (1/r2), of slope GM. Raise M and the line gets steeper. Change R and only the surface end of the line moves: outside the planet, g depends on M and r alone.
Switch the graph between a_g vs r and a_g vs 1/r². The second view straightens thecurve into a straight line through the origin whose gradient is GM — that is how you confirm an inverse-square law from data rather than assuming it. Use the orbit presets to test it against real spacecraft. At the ISS altitude of 420 km the field is still 88% of surface gravity. Astronauts float because they are in free fall — the station and everyone inside accelerate together, so nothing pushes up on them — not because gravity has vanished. At geostationary altitude (35786 km) the field is down to 2.3% of its surface value.
Change OBJECT MASS m and watch the weight F_g change while a_g stays fixed. That isthe whole point of a field: it belongs to the planet, not to the object sitting in it
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