CLS-26

Escape speed

From a spherical mass.

Reading speed

GoverningEscape speed

Governing equation

v=\sqrt{2GM/r}

where

M: M (Mearth)
r: r (km)
v: Escape speed (km/s)

Lecture brief

Historical brief

Newtonian mechanics (1687) plus energy, angular momentum, Kepler and the ballistic parabola remain the first language of motion. Every sheet here is a closed-form orbit, throw, spin or oscillator. This sheet (CLS-26 — Escape speed) is the form associated with Escape speed. Working symbols: $M$ , $r$ $\rightarrow$ $v$ . From a spherical mass. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

v

from

M

r

in Classical mechanics via

v=\sqrt{2GM/r}

From a spherical mass. Use it when a real classical mechanics question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

M = 1.000\,\mathrm{Mearth}

r = 6371.000\,\mathrm{km}

, the governing relation

v=\sqrt{2GM/r}

yields

v = 11.186\,\mathrm{km/s}

. One governing identity, SI units, a single sweep on the sheet. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

M M1 Mearthr r6371 km

Outputs

Escape speed v11.186 km/s

Reading speed

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Narration of this film

One governing identity, SI units, a single sweep on the sheet.

From a spherical mass. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube