Around a spherically symmetric source, the field strength depends only on radius, so every point at the same r feels the same pull. Direction points inward, but the magnitude is shared across the whole shell. This is the ideal central-field result; real sources are oblate and lumpy, and other bodies break the symmetry, while the radius itself is measured with ephemeris uncertainty.

Field magnitude depends on radius while direction points inward. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Equal radii give equal field magnitudes

Both bodies sit at radius 4, so both checked field magnitudes are 1.

gright=1gtop=1g_{\mathrm{right}}=1\quad g_{\mathrm{top}}=1
Same radius, different angleEach field vector points toward the same source.right fieldtop fieldsame radius

Direction changes while magnitude stays radius-bound

The right body and top body use different inward arrows, but the value 1 is unchanged.

∣g∣=1616=1|g|=\frac{16}{16}=1
Field direction is inwardThe checked radius fixes magnitude; the vector geometry fixes direction.right fieldtop fieldsame radius