# Angular Momentum in the Solar System

Data from The Nine Planets

Angular momentum is usually stated in kg m2 / sec, whereas the data is in km and days.

To change days into seconds, multiply by 24 · 60 · 60. To change km to meters, multiply by 1000. To change orbital radius into distance, multiply by 2π.

The angular momentum L of an object of mass m moving in a circle of radius r, with linear speed p is given by

L = 2π m r2 / p

Using this formula, we calculate the L column of this table from the given orbital data.

Orbital Angular Momentum
(km)
orbital period
(days)
mass
(kg)
L
Mercury 58.e6 87.973.30e239.1e38
Venus 108.e6 224.704.87e241.8e40
Earth 150.e6 365.265.97e242.7e40
Mars 228.e6 686.986.42e233.5e39
Jupiter 778.e6 4332.711.90e271.9e43
Saturn 1429.e610759.505.68e267.8e42
Uranus 2871.e630685.008.68e251.7e42
Neptune 4504.e660190.001.02e262.5e42
Pluto 5914.e690800 1.27e223.6e38
3.1e43

Moon 384e3 27.327.35e222.9e34

Io 422e3 1.778.93e226.5e35
Europa 671e3 3.554.80e224.4e35
Ganymede 1070e3 7.151.48e231.7e36
Callisto 1883e3 16.691.08e231.7e36

Angular momentum is the measure of the tendency of a rotating body to remain rotating. Angular momentum is always conserved.

The value of the angular momentum of an object swinging around in a circle is something like the mass times the speed at which the mass is moving, times the radius, squared. So when an ice-skater spins, then pulls in their arms, their rate of rotation increases, because they have reduced

The rotational angular momentum of a solid homogeneous sphere of mass m and radius r with rotational rate p is given by

L = 4π m r2 / 5 p

When applied to gaseous bodies such as the Sun or Jupiter, this will yield an overestimate, because the interiors of such gaseous bodies are denser than their outer layers.

Rotational Angular Momentum
(km)
rotational period
(days)
mass
(kg)
L
Sun 695000 24.6 1.99e301.1e42
Earth 6378 0.99 5.97e247.1e33
Jupiter 71492 0.41 1.90e276.9e38

So the rotational angular momentum of the Sun, which is 1.1e42, is less than 4% that of the total orbital angular momentum of the planets, which is 3.1e43.

Based on this calculation Jupiter’s orbital angular momentum alone accounts for over 60% of the total angular momentum of the Solar system!

The orbital angular momentum of the Moon 2.9e34 is about four times that of the rotational angular momentum of the Earth, which is 7.1e33.

However, the total orbital angular momenta of the largest moons of Jupiter is less than a hundredth the rotational angular momentum of the planet.