Escape Speed Energy

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Minimum kinetic energy required for a mass m to escape Earth's gravity from surface (radius R) ignoring atmosphere is:

RankGuru · Accepted Answer

To escape Earth's gravity, the total mechanical energy must be at least zero at infinity ($U_{\infty} = 0, K_{\infty} \geq 0$).
1. **Potential Energy at Surface**: $U_s = -\frac{GMm}{R}$.
2. **Energy Conservation**: $K_s + U_s = E_{total} \geq 0$.
$K_s \geq -U_s$
$K_s \geq \frac{GMm}{R}$.
This corresponds to the escape velocity $v_e = \sqrt{2GM/R}$.

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Escape Speed Energy

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