Echoing the Somerset proverb quoted by John Ray, we can state that if we have only one celestial body, that is too few objects to study celestial dynamics. A system with two bodies, as we saw in the previous chapter, contains interesting physics. But what about a three-body system? We might conclude, considering the possible complexity of such a system, that it contains too many objects to be tractable.

Sir James Jeans Always says what he means; He is really perfectly serious About the Universe being Mysterious. E. Clerihew Bentley (1875–1956) Punch, vol. 196, issue 5100, p. 39 [1939 Jan 11]

I’m trying to relax, but it’s hard. Ryuichi Sakamoto (1952–2023) New York Times interview, 2017 Apr 22

Ships that pass in the night, and speak each other in passing, Only a signal shown and a distant voice in the darkness; So on the ocean of life we pass and speak one another, Only a look and a voice, then darkness again and a silence. Henry Wadsworth Longfellow (1807–1882)

A Frenchman who arrives in London, will find Philosophy, like every Thing else, very much chang’d there… In France, ’tis the Pressure of the Moon that causes the Tides; but in England ’tis the Sea that gravitates toward the Moon. Letters Concerning the English Nation [1733] Letter XIV: On Descartes and Sir Isaac Newton, Voltaire (1694–1778)

When night comes I stand on the steps and listen; the stars cluster in the garden and I stand, out in the darkness. Edith Södergran (1892–1923) “Stjärnorna [The Stars]” [1916] (tr. David Barrett)

The revival of the heliocentric model by Copernicus in the sixteenth century led to speculation about planets orbiting other stars. In a heliocentric model, stars must show annual parallax as the Earth moves around the Sun.

The techniques of celestial dynamics are useful within the solar system and other planetary systems. However, techniques that are useful in a system containing a few mutually gravitating objects are not as useful in a system containing a hundred thousand million objects.

The noun “dynamics” entered the English language in the eighteenth century, when natural philosophers, following the lead of Isaac Newton, began thinking of motion in terms of applied forces and the resulting accelerations. In 1788, the New Royal Encyclopaedia contained the definition, “Dynamics is the science of moving powers; more particularly of the motion of bodies that mutually act on one another.” This is still a useful definition. For the purposes of this book, we can define dynamics as the study of objects that move while interacting through mutual forces.

A gravitationally bound two-body system (if the two bodies are spheres of constant mass) shows simple periodic motion. We have seen that a three-body system, even if we install restrictions for computational simplicity, can show a rich variety of behaviors. Tadpole orbits, horseshoe orbits, and ZLK oscillations are just a sampling of what can happen.

As Russell and Vogt pointed out in the 1920s, the properties of a main sequence star depend crucially on its mass. After the main sequence, the star’s mass is also vitally important in determining its physical properties. Will helium burning begin or not? If it begins, will it begin with a flash? Will carbon burning begin or not? The answers to these questions, as we have seen, depend primarily on the star’s mass.