Escape Boundary Has Zero Specific Energy - Rotational Dynamics and Orbital Mechanics Step by Step

At the escape boundary the specific energy is exactly zero, so the kinetic term just cancels the potential well and the body reaches infinity with no speed left. The threshold is exact only for the stated speed, radius, and gravity parameter in the ideal two-body model. Real orbits add eccentricity, atmosphere/drag, perturbations, central-mass uncertainty, finite-body effects, and measurement uncertainty.

The escape boundary is where total specific energy is zero. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

The escape speed-square is checked at eight

The escape speed-square is 8 at the same radius.

v_e^{2}=8\ \mathrm{m^{2}/s^{2}}

The escape boundary has zero total specific energy

Specific kinetic energy 4 and potential negative 4 sum to 0.

4+-4=0\ \mathrm{J/kg}