Slide a test mass from a planet's core out into deep space and watch its weight change. Gravity climbs straight up from zero at the centre, peaks exactly at the surface, then thins out as the inverse square of distance beyond.
● Planet cross-section● Test mass at rg rises linearly inside · falls as 1/r² outside
Setup
Distance from centre r1.00 R
Surface gravity g_s9.8 m/s²
Test mass m10 kg
g = 9.80 m/s²
Local gravity at r
9.80
g (m/s²)
98.0
weight (N)
surface
region
1.00
r / R
inside g = g_s·r/Routside g = g_s·(R/r)²depth g = g_s(1−d/R)height g = g_s/(1+h/R)²
Playback
Try this: g peaks exactly at the surface (r = R). Halve r while inside and g halves; double r while outside and g drops to a quarter. Weight follows g precisely — mass never changes.