Negative Specific Energy Is Bound - Orbital Mechanics: Gravity, Circular Orbits, and Escape Step by Step

Circular speed at radius four gives negative specific energy. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Circular speed-square gives two joules per kilogram

The circular speed-square 4 gives specific kinetic energy 2.

\frac{v^{2}}{2}=\frac{4}{2}=2\ \mathrm{J/kg}

Potential wins, so the specific energy is negative

Potential is negative 4 and total specific energy is negative 2.

2+-4=-2\ \mathrm{J/kg}