← All parts of this equation

Equation 131 · Part 2 · The Bend an Elevator Cannot Fake

Symbol M_oplus

GM⊕/R⊕3≈1.541×10−6 s−2GM_\oplus/R_\oplus^3 \approx 1.541\times10^{-6}\,\mathrm{s^{-2}}
M⊕M_\oplus

What this part means

MoM_oplus is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Its job in the formula

MoM_oplus is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

The passage around this formula

For Earth modelled as a point mass, Φ(r)\Phi(r) = -GM/r gives a radial second derivative of magnitude 2GM/R3R^3 and, since Φ\Phi is harmonic in vacuum, transverse second derivatives of magnitude GM/R3R^3 with the opposite sign — a trace-free tensor in the exact ratio 2:{-1}:{-1} . With the standard gravitational parameter GM⊕M_\oplus = 3.986×\times10^{14}\,m3 s−2\mathrm{m^3\,s^{-2}} and mean radius R⊕R_\oplus = 6.371×\times10^{6}\,m\mathrm m , this gives GM⊕M_\oplus/R⊕3R_\oplus^3 ≈\approx 1.541×\times10^{-6}\,s−2\mathrm{s^{-2}} and a radial magnitude of 3.08×\times10^{-6}\,s−2\mathrm{s^{-2}} , matching the standard geodetic free-air gravity gradient of about 3.086×\times10^{-6}\,s−2\mathrm{s^{-2}} , or 0.3086 milligal per metre,…

Read this part in the article →

Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

Open the illustrated subscripts: which member of a family? guide →

See this notation across published equations →

Sources cited in the surrounding passage

These citations provide research context; check each source for the exact claim it supports.