Data from The Nine Planets

Angular momentum is usually stated in kg m^{2} / 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

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

Body | orbital radius (km) | orbital period (days) | mass (kg) | L |
---|---|---|---|---|

Mercury | 58.e6 | 87.97 | 3.30e23 | 9.1e38 |

Venus | 108.e6 | 224.70 | 4.87e24 | 1.8e40 |

Earth | 150.e6 | 365.26 | 5.97e24 | 2.7e40 |

Mars | 228.e6 | 686.98 | 6.42e23 | 3.5e39 |

Jupiter | 778.e6 | 4332.71 | 1.90e27 | 1.9e43 |

Saturn | 1429.e6 | 10759.50 | 5.68e26 | 7.8e42 |

Uranus | 2871.e6 | 30685.00 | 8.68e25 | 1.7e42 |

Neptune | 4504.e6 | 60190.00 | 1.02e26 | 2.5e42 |

Pluto | 5914.e6 | 90800 | 1.27e22 | 3.6e38 |

3.1e43 | ||||

Moon | 384e3 | 27.32 | 7.35e22 | 2.9e34 |

Io | 422e3 | 1.77 | 8.93e22 | 6.5e35 |

Europa | 671e3 | 3.55 | 4.80e22 | 4.4e35 |

Ganymede | 1070e3 | 7.15 | 1.48e23 | 1.7e36 |

Callisto | 1883e3 | 16.69 | 1.08e23 | 1.7e36 |

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

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.

Body | radius (km) | rotational period (days) | mass (kg) | L |
---|---|---|---|---|

Sun | 695000 | 24.6 | 1.99e30 | 1.1e42 |

Earth | 6378 | 0.99 | 5.97e24 | 7.1e33 |

Jupiter | 71492 | 0.41 | 1.90e27 | 6.9e38 |

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.

© 2001 Stevan White. All rights reserved.