Escape Velocity

The escape velocity is the smallest launch speed that never comes back. The object escapes when $\relax K + U$ is zero or more:

$$v_{\text{esc}} = \sqrt{\frac{2GM}{R}} = \sqrt{2gR}$$

The object's own mass cancels. At the same distance, escape speed is $\sqrt{2} \approx 1.41$ times the orbit speed. Earth: $11.2\ \mathrm{km/s}$.

Same starting point: orbit speed circles, escape speed never comes back.