pull down to refresh
U
\frac{GMm}{R}
v_{esc}
\sqrt{\frac{2GM}{r}}
\begin{align} K_0 &= \frac{1}{2}m(2v_{esc})^2 = \frac{1}{2} m 4v_{esc}^2 \\ &= 2 m v_{esc}^2 = 2m \frac{2GM}{r} \\ &= 4 U \end{align}
K_0 - U
3U
\begin{align} 3U &= 3 \frac{GMm}{r} = \frac{3}{2} \frac{2GM}{r} \\ &= \frac{3}{2} v_{esc}^2 = \frac{1}{2} \left(\sqrt{3}v_{esc}\right)^2 \end{align}
\sqrt{3}v_{esc}
U=\frac{GMm}{R}v_{esc}=\sqrt{\frac{2GM}{r}}K_0 - U=3U\sqrt{3}v_{esc}