Orbital speed from semimajor axis and planet mass

The orbital speed of a body is the speed at which it rotates around the barycenter of the system, usually around a more massive body. It can be calculated from the mass of the planet and the orbit configuration parameters.

Notation:

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

Conditions:

1. The distance to the barycenter \(r\) must not exceed the length \(a\) of the semi-major axis of the orbit.

Links:

1. Wikipedia.

orbital_speed

Orbital speed of the satellite.

Symbol:

v

Latex:

\(v\)

Dimension:

velocity

distance

euclidean_distance at which the speed is calculated.

Symbol:

d

Latex:

\(d\)

Dimension:

length

semimajor_axis

semimajor_axis of the satellite’s orbit.

Symbol:

a

Latex:

\(a\)

Dimension:

length

planet_mass

mass of the planet.

Symbol:

m

Latex:

\(m\)

Dimension:

mass

law

v = sqrt(G * m * (2 / d - 1 / a))

Latex:

\[v = \sqrt{G m \left(\frac{2}{d} - \frac{1}{a}\right)}\]