Field Strength Inverse-Square Cross-Scan - Orbital Mechanics: Gravity, Circular Orbits, and Escape Step by Step

The same source parameter gives weaker field as radius-square grows. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Radius 1 gives field 16

The source parameter stays 16. Radius 1 has square 1, so the field is 16.

g=\frac{\mu}{r^{2}}=\frac{16}{1}=16

Radius 2 gives field 4

The source parameter stays 16. Radius 2 has square 4, so the field is 4.

g=\frac{\mu}{r^{2}}=\frac{16}{4}=4

Radius 4 gives field 1

The source parameter stays 16. Radius 4 has square 16, so the field is 1.

g=\frac{\mu}{r^{2}}=\frac{16}{16}=1

Field strength follows the inverse-square denominator

With the same source parameter, radius one, two, and four make radius-squares one, four, and sixteen. The field steps down as sixteen, four, and one.

\begin{array}{c|c|c|c}r&r\cdot r&\mu&g\\1&1&16&16\\2&4&16&4\\4&16&16&1\\\end{array}