Binding Margin Speed-Square Three-Row Scan - Orbital Mechanics: Gravity, Circular Orbits, and Escape Step by Step

Three bound rows show the remaining energy margin before escape. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Speed-square 2 leaves margin 3

At radius four, potential is fixed at negative 4. Speed-square 2 gives kinetic 1, leaving binding margin 3.

\epsilon=1\mathbin{-}4=-3,\quad m=3

Speed-square 4 leaves margin 2

At radius four, potential is fixed at negative 4. Speed-square 4 gives kinetic 2, leaving binding margin 2.

\epsilon=2\mathbin{-}4=-2,\quad m=2

Speed-square 6 leaves margin 1

At radius four, potential is fixed at negative 4. Speed-square 6 gives kinetic 3, leaving binding margin 1.

\epsilon=3\mathbin{-}4=-1,\quad m=1

Three bound rows show the margin shrinking before escape

The earlier chapter crossed bound, escape, and unbound. This scan stays below escape and shows the remaining margin as speed-square rises.

\begin{array}{c|c|c|c|c}v\cdot v&K&U&\epsilon&margin\\2&1&-4&-3&3\\4&2&-4&-2&2\\6&3&-4&-1&1\\\end{array}