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]}

## Contents

## Law of universal gravitation

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 between the two bodies

The two main attraction forces on a satellite are the attraction of the Sun and the satellite's primary (the planet the satellite orbits). Therefore, the two forces are

where the subscripts *p* and *s* represent the primary and the sun respectively, and *m* is the mass of the satellite.

The ratio of the two is

## Example

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, d
_{s}) is 778.3 · 10^{6}km. - The solar mass (M
_{s}) is 1.989 · 10^{30}kg

## The table of planets

Asimov lists tug-of-war ratio for 32 satellites (then known in 1963) of the 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

Unlike other satellites of the solar system, the 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

- ^
^{a}^{b}Asimov, Isaac (1976).*Asimov on Astronomy*. Coronet Books. pp. 125–139. ISBN 0-340-20015-4. **^**Arny, Thomas.*Explorations*. Mc Graw Hill. pp. 543–545. ISBN 0-07-561112-0.