The tug of war in astronomy is the ratio of planetary and solar attractions on a natural satellite

Natural satellite

A natural satellite or moon is a celestial body that orbits a planet or smaller body, which is called its primary. The two terms are used synonymously for non-artificial satellites of planets, of dwarf planets, and of minor planets....

. The term was coined by Isaac Asimov

Isaac Asimov

Isaac Asimov was an American author and professor of biochemistry at Boston University, best known for his works of science fiction and for his popular science books. Asimov was one of the most prolific writers of all time, having written or edited more than 500 books and an estimated 90,000...

 in The Magazine of Fantasy and Science Fiction in 1963.

Law of universal gravitation

According to Isaac Newton

Isaac Newton

Sir Isaac Newton PRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian, who has been "considered by many to be the greatest and most influential scientist who ever lived."...

's law of universal gravitation

In this equation

F is the force of attraction

G is the gravitational constant

Gravitational constant

The gravitational constant, denoted G, is an empirical physical constant involved in the calculation of the gravitational attraction between objects with mass. It appears in Newton's law of universal gravitation and in Einstein's theory of general relativity. It is also known as the universal...

m₁ and m₂ are the masses of two bodies

d is the distance of separation between the two bodies

The two main attraction forces on a satellite are the attraction of the sun

Sun

The Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...

 and the primary

Primary (astronomy)

A primary is the main physical body of a gravitationally-bound, multi-object system. This body contributes most of the mass of that system and will generally be located near its center of mass....

 (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

Callisto

Callisto (moon)

Callisto named after the Greek mythological figure of Callisto) is a moon of the planet Jupiter. It was discovered in 1610 by Galileo Galilei. It is the third-largest moon in the Solar System and the second largest in the Jovian system, after Ganymede. Callisto has about 99% the diameter of the...

 is a satellite of Jupiter. The parameters in the equation are

• Callisto-Jupiter distance (d_p) is 1.883 · 10⁶ km.
• Mass of Jupiter (M_p) is 1.9 · 10²⁷ kg
• Jupiter-Sun distance (ie, mean distance of Callisto from the Sun, m_s) is 778.3 · 10⁶ km.
• The solar mass (M_s) is 1.989 · 10³⁰ kg

The table of planets

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 Neptune Neptune is the eighth and farthest planet from the Sun in the Solar System. Named for the Roman god of the sea, it is the fourth-largest planet by diameter and the third largest by mass. Neptune is 17 times the mass of Earth and is slightly more massive than its near-twin Uranus, which is 15 times...	Triton Triton (moon) Triton is the largest moon of the planet Neptune, discovered on October 10, 1846, by English astronomer William Lassell. It is the only large moon in the Solar System with a retrograde orbit, which is an orbit in the opposite direction to its planet's rotation. At 2,700 km in diameter, it is...	8400
Uranus Uranus Uranus is the seventh planet from the Sun. It has the third-largest planetary radius and fourth-largest planetary mass in the Solar System. It is named after the ancient Greek deity of the sky Uranus , the father of Cronus and grandfather of Zeus...	Titania Titania (moon) Titania is the largest of the moons of Uranus and the eighth largest moon in the Solar System at a diameter of 1578 km. Discovered by William Herschel in 1787, Titania is named after the queen of the fairies in Shakespeare's A Midsummer Night's Dream...	1750
Saturn Saturn Saturn is the sixth planet from the Sun and the second largest planet in the Solar System, after Jupiter. Saturn is named after the Roman god Saturn, equated to the Greek Cronus , the Babylonian Ninurta and the Hindu Shani. Saturn's astronomical symbol represents the Roman god's sickle.Saturn,...	Titan Titan (moon) Titan , or Saturn VI, is the largest moon of Saturn, the only natural satellite known to have a dense atmosphere, and the only object other than Earth for which clear evidence of stable bodies of surface liquid has been found....	380
Jupiter Jupiter Jupiter is the fifth planet from the Sun and the largest planet within the Solar System. It is a gas giant with mass one-thousandth that of the Sun but is two and a half times the mass of all the other planets in our Solar System combined. Jupiter is classified as a gas giant along with Saturn,...	Ganymede Ganymede (moon) Ganymede is a satellite of Jupiter and the largest moon in the Solar System. It is the seventh moon and third Galilean satellite outward from Jupiter. Completing an orbit in roughly seven days, Ganymede participates in a 1:2:4 orbital resonance with the moons Europa and Io, respectively...	490
Mars Mars Mars is the fourth planet from the Sun in the Solar System. The planet is named after the Roman god of war, Mars. It is often described as the "Red Planet", as the iron oxide prevalent on its surface gives it a reddish appearance...	Phobos Phobos (moon) Phobos is the larger and closer of the two natural satellites of Mars. Both moons were discovered in 1877. With a mean radius of , Phobos is 7.24 times as massive as Deimos...	195
Earth Earth Earth is the third planet from the Sun, and the densest and fifth-largest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets...	Moon Moon The Moon is Earth's only known natural satellite,There are a number of near-Earth asteroids including 3753 Cruithne that are co-orbital with Earth: their orbits bring them close to Earth for periods of time but then alter in the long term . These are quasi-satellites and not true moons. For more...	0.46

The special case of Moon

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