The **tug of war** in astronomy is the ratio of planetary and solar attractions on a natural satellite. The term was coined by Isaac Asimov in *The Magazine of Fantasy and Science Fiction* in 1963.^{[1]}

## Law of universal gravitation Edit

According to Isaac Newton's law of universal gravitation

In this equation

**F**is the force of attraction**G**is the gravitational constant**m**and_{1}**m**are the masses of two bodies_{2}**d**is the distance of separation between the two bodies

The two main attraction forces on a satellite are the attraction of the sun and the primary (the planet around which the satellite revolves) Thus the two forces are

where the subscripts p and s represent the primary and the sun respectively.

The ratio of the two is

## Example Edit

Callisto is a satellite of Jupiter. The parameters in the equation are ^{[2]}

- Callisto-Jupiter distance (d
_{p}) is 1.883 · 10^{6}km. - Mass of Jupiter (M
_{p}) is 1.9 · 10^{27}kg - Jupiter-Sun distance (i.e., mean distance of Callisto from the Sun, m
_{s}) is 778.3 · 10^{6}km. - The solar mass (M
_{s}) is 1.989 · 10^{30}kg

## The table of planets Edit

Asimov lists tug of war ratio for 32 satellites (then known in 1963) of Solar system. The list below shows one example from each planet.

Primary | Satellite | Tug of War ratio |
---|---|---|

Neptune | Triton | 8400 |

Uranus | Titania | 1750 |

Saturn | Titan | 380 |

Jupiter | Ganymede | 490 |

Mars | Phobos | 195 |

Earth | Moon | 0.46 |

## The special case of the Moon Edit

Unlike other satellites of the solar system solar attraction on the Moon is more than that of its primary. According to Asimov, the Moon is a planet moving around the Sun in careful step with the Earth.^{[1]}

## References Edit

- ↑
^{1.0}^{1.1}Isaac Asimov:*Asimov on Astronomy*Coronet Books,1976, ISBN 0-340-20015-4 pp125-139 - ↑ Thomas Arny:
*Explorations*, Mc Graw Hill, ISBN 0-07-561112-0 pp.543-545