Binding Margin Speed-Square Three-Row Scan - Rotational Dynamics and Orbital Mechanics Step by Step

Three bound rows show the remaining energy margin before escape.

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}