Semiminor axis of elliptical orbit via orbit parameters¶

The minor semiaxis can be found as a function of the sector speed of the planet, the major semiaxis of its orbit, and the mass of body that attracts it, such as the Sun.

Notation:

\(G\) (G) is gravitational_constant.

Links:

Sivukhin, D.V. (1979). Obshchiy kurs fiziki [General course of Physics], vol. 1, p. 318, (58.5)

semiminor_axis¶: The semiminor_axis of the planet’s orbit.

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

sector_speed¶: The sector_speed of the planet, i.e. the area swept by the planet per unit time.

Symbol:: sigma
Latex:: \(\sigma\)
Dimension:: area/time

semimajor_axis¶: The semimajor_axis of the planet’s orbit.

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

attracting_mass¶: The mass of the attracting body, such as the Sun.

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

law¶

b = 2 * sigma * sqrt(a / (G * M))

Latex:: \[b = 2 \sigma \sqrt{\frac{a}{G M}}\]