Speed-square moves specific energy through bound, escape, and unbound rows. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
Total specific energy -2
At radius four, potential stays negative four. Speed-square 4 gives kinetic 2 and total -2.
2−4=−2
Total specific energy 0
At radius four, potential stays negative four. Speed-square 8 gives kinetic 4 and total 0.
4−4=0
Total specific energy 1
At radius four, potential stays negative four. Speed-square 10 gives kinetic 5 and total 1.
5−4=1
Specific-energy sign separates bound, escape, and unbound
Kinetic energy rises with speed-square while the potential term stays fixed. Negative, zero, and positive totals mark the three statuses.