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:

1. \(G\) (G) is gravitational_constant.

Links:

1. 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:

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