Central Fields

Central Field Uses Mu over Radius Square

A central gravitational field falls off as g = mu / r^2, where mu = G * M bundles the source mass and the gravitational constant. The inverse square comes from geometry: field lines spread over the surface of a growing sphere. The exact value holds only for the stated mu and radius with a point or spherically symmetric source; real bodies have oblateness, perturbations from other masses, and radius and ephemeris uncertainty.

A central field is computed from a source parameter and radius. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

The radius square is part of the source ledger

At radius 4, the checked radius-square is 16.

r2=42=16r^{2}=4^{2}=16
Inverse-square field sourceThe source, radius vector, body, and field labels are checked.mu=16 m^3/s^2radius=4 mradiusSquared=16 m^2field=1 m/s^2

The field is mu divided by radius square

The source parameter 16 divided by radius-square 16 gives field 1.

g=μr2=1616=1 m/s2g=\frac{\mu}{r^{2}}=\frac{16}{16}=1\ \mathrm{m/s^{2}}
Checked inward fieldThe field arrow points inward toward the source.mu=16 m^3/s^2radius=4 mradiusSquared=16 m^2field=1 m/s^2