Three-body problem
The problem of finding how three bodies move under their mutual gravity. Two can be solved with a formula; three in general cannot, and tiny differences can change the future completely.
With only two bodies, such as the Sun and a planet, the orbit is an ellipse and a formula gives the position at any time. With three it suddenly becomes hard. In 1890 Henri Poincaré showed that the problem has no general solution in formula form, and that a minute difference in starting position or speed can lead to entirely different motion later[1]. It was the first discovery of what would come to be called chaos.
Unsolvable does not mean hopeless. Special solutions such as the Lagrange points were found in the eighteenth century, and a computer advancing time step by step can produce an orbit to whatever precision is needed. Designing a spacecraft trajectory means working within this problem, with the gravity of Sun, Earth, Moon and others all tangled together, to find a route that uses little fuel.
Related terms
- Lagrange pointFive points where the gravity of two bodies, such as the Sun and Earth, balances the motion of orbiting around them, so a small object can hold its position.
- Halo orbitAn orbit that loops widely around a Lagrange point. It is used to keep a spacecraft stationed near the point.
- Universal gravitationThe force by which every object with mass attracts every other. Its strength is proportional to the product of the two masses and inversely proportional to the square of the distance.