Trojan Asteroids of Jupiter
When bodies orbit in 1:1 resonance they may become synchronised
such that the smaller bodies get trapped at positions +60 or -60
degrees round the orbit of major body (See Lagrange Points below).
This behaviour was first observed relative to Jupiter when 588
Achilles was discovered in 1906. Since then it has become tradition
for such bodies to be named after heroes of the Trojan war and this
type of orbit is called a Trojan orbit.
In this integration we are using rotating coordinates to hold
Jupiter constantly in the same direction relative to the Sun. The two
Asteroids are seen to hold their positions roughly +60 and - 60
degrees from Jupiter. Use the tilt
control to see that their orbits are quite inclined to that of
Jupiter.
Tilt back to get circular orbits and
click the Orbit control. Now you can see the trails of the two
Asteroids relative to Jupiter. These kinds of orbits are sometimes
called 'tadpole' orbits.
Lagrange Points
The French
mathematician Joseph Louis Lagrange was the first to note the theoretical
possibility of co-orbital bodies
- where two or more bodies have the same orbital period. In 1772
Lagrange described five special orbital positions known as
Lagrange Points.
 At Lagrange Points, the
gravitational attractions of two bodies, (e.g. the Sun and a planet, or a
planet and one of its satellites), combine to provide just the right forces
to maintain a third object in orbit with the same period as it's 'parent'. The
points are shown as L1 - L 5 in the diagram.
Lagrange points L1, L2 and L3 are unstable, objects
here will tend to wander away under the perturbing influence of other
planets.
Objects at L4 and L5 are quite stable, and can
remain at or near their Lagrange point indefinitely.
At that time no examples of such bodies were known but in 1906 Max Wolf
discovered an asteroid, later named 588 Achilles, at Jupiter’s leading
Lagrange point. Since then many more have been discovered leading or
following Jupiter. By convention asteroids at Jupiter's Lagrange points are
named after participants in the Trojan War, and the name ‘Trojan’ is often
used to refer to any object orbiting at a Lagrange point. |
