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:

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

Links:

1. 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:

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