Equations · equation

Escape Velocity

Celestial Mechanics · 1687

Equation: v_esc = √(2GM/r)
Field: Celestial Mechanics
Named After: Isaac Newton
Symbols: v_esc minimum speed to leave forever, ignoring drag · G gravitational constant · M mass of the body · r starting distance from its centre
Year: 1687

Significance

The vis-viva equation with the orbit opened to infinity — 11.2 km/s from Earth's surface, 2.4 from the Moon, 620 from the Sun. Set v_esc equal to the speed of light and Schwarzschild's radius appears two centuries early: John Michell imagined 'dark stars' this way in 1783.

Timeline

Andromeda Arrives

Celestial Objects

Sun

Theories

Newtonian Mechanics

Related

Schwarzschild Radius Critical Density Tsiolkovsky Rocket Equation

Constants

Solar mass Newtonian constant of gravitation

Requires

Gravitational Potential Energy Conservation of Mechanical Energy

Referenced by

constant

Newtonian constant of gravitation Solar mass

equation

Conservation of Mechanical Energy Critical Density Gravitational Potential Energy Schwarzschild Radius Tsiolkovsky Rocket Equation

event

Andromeda Arrives

theory

Newtonian Mechanics

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From the Equations database in Notion, last edited 2026-08-18. This page is the row, rendered by the build; nothing on it is written by hand.