Area rate of change is proportional to angular momentum

The law of areas, also known as Kepler’s second law of planetary motion, states that a line the connects a planet to the attracting body (the Sun) sweeps out equal areas in the plane of the planet’s orbit in equal time intervals, and its rate of change is proportional to the planet’s angular momentum. It is equivalent to saying that the planet’s angular momentum is conserved.

1. Sivukhin D.V. (1979), Obshchiy kurs fiziki [General course of Physics], vol. 1, pp. 312—314.

time

time.

Symbol:

t

Latex:

\(t\)

Dimension:

time

area_swept

area swept by the planet.

Symbol:

A(t)

Latex:

\(A{\left(t \right)}\)

Dimension:

area

planet_angular_momentum

angular_momentum of the planet.

Symbol:

L

Latex:

\(L\)

Dimension:

length**2*mass/time

planet_mass

mass of the planet.

Symbol:

m

Latex:

\(m\)

Dimension:

mass

law

Derivative(A(t), t) = L / (2 * m)

Latex:

\[\frac{d}{d t} A{\left(t \right)} = \frac{L}{2 m}\]