Second escape velocity¶

The second cosmic velocity is the lowest velocity that must be given to an object starting from the surface of a celestial body, the mass of which is negligible compared to the mass of a celestial body, in order to overcome the gravitational attraction of this celestial body and leave a closed orbit around it.

Notation:

\(G\) (G) is gravitational_constant.

Links:

Physics LibreTexts. Conservation of Energy, Escape velocity (13.4.10).

speed¶: Second escape speed.

Symbol:: v
Latex:: \(v\)
Dimension:: velocity

planet_mass¶: Planetary mass.

Symbol:: m
Latex:: \(m\)
Dimension:: mass

planet_radius¶: Planetary radius.

Symbol:: r
Latex:: \(r\)
Dimension:: length

height¶: Elevation (see height) of the body above the planet’s surface.

Symbol:: h
Latex:: \(h\)
Dimension:: length

law¶

v = sqrt(2 * G * m / (r + h))

Latex:: \[v = \sqrt{\frac{2 G m}{r + h}}\]