Could You Escape?

The escape velocity is the minimum speed an object needs to break free from a body's gravitational pull without further propulsion:

$$v_{\text{escape}} = \sqrt{\frac{2\,G\,M}{R}}$$

where $G = 6.674 \times 10^{-11}$ m$^3$ kg$^{-1}$ s$^{-2}$ is the gravitational constant, $M$ is the planet's mass, and $R$ is its radius.

Human jump: an average jump launches you at $v_0 \approx 3.1$ m/s. On a small asteroid like Bennu ($v_{\text{esc}} \approx 0.2$ m/s), a gentle hop sends you drifting into space forever.

Rocket launch: a rocket must first pass the liftoff check — its thrust-to-weight ratio on the planet must exceed 1:

$$\text{TWR} = \frac{F_{\text{thrust}}}{m_{\text{rocket}} \, g_{\text{surface}}} > 1$$

If it lifts off, it must then spend enough $\Delta v$ (total velocity budget from the Tsiolkovsky equation) to reach escape velocity. On super-Earths with $g \gtrsim 2\,g_\oplus$, even the Saturn V cannot lift off — and nothing we've built can escape Jupiter.

Entering orbit: you don't always need to escape — sometimes staying is the goal. The minimum orbital velocity for a circular orbit at the surface is:

$$v_{\text{orbit}} = \sqrt{\frac{G\,M}{R}} = \frac{v_{\text{escape}}}{\sqrt{2}}$$

That's about 71% of escape velocity. The orbital period at this altitude is $T = 2\pi R / v_{\text{orbit}}$ — for Earth that's roughly 85 minutes, similar to the ISS. On smaller bodies, orbital velocity can be walking speed: you could theoretically jog into orbit around a small asteroid.