Gravitation — 5 Must-Know Facts — Summary

G's dimension:

[M^{-1} L^3 T^{-2}]

— the only fundamental constant with a negative power of mass.

Depth vs altitude: g decreases linearly with depth (zero at centre) but by inverse-square with altitude — at

h = R

,

g = g/4

; at

d = R/2

,

g = g/2

.

Escape velocity independence:

v_e = \sqrt{2GM/R}

— independent of the mass and angle of projection of the escaping body.

Energy ratio:

KE : PE : E_{total} = 1 : {-2} : {-1}

for any satellite; total energy is always negative for a bound orbit.

$v_e = \sqrt{2}\,v_0$ : Escape velocity is exactly

\sqrt{2}

times the orbital velocity at the same radius — valid everywhere, not just at Earth's surface.