Radial kinetic energy plus potential energy is constant

The total energy of the planet is composed of its radial kinetic energy and potential energy. Note that the sign of the total energy determines the type of the planet’s orbit:

1. If \(E < 0\), the orbit is elliptical.

2. If \(E = 0\), the orbit is parabolical.

3. If \(E > 0\), the orbit is hyperbolical.

Links:

1. Physics LibreTexts.

planetary_mass

The mass of the planet.

Symbol:

m

Latex:

\(m\)

Dimension:

mass

radial_speed

The projection of the velocity vector in the radial direction. See speed.

Symbol:

v_r

Latex:

\(v_{r}\)

Dimension:

velocity

potential_energy

The potential energy of the planet. See potential_energy.

Symbol:

U

Latex:

\(U\)

Dimension:

energy

total_mechanical_energy

Total mechanical_energy of the planet, assumed to be constant.

Symbol:

E

Latex:

\(E\)

Dimension:

energy

law

m * v_r^2 / 2 + U = E

Latex:

\[\frac{m v_{r}^{2}}{2} + U = E\]