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http://www.skyandtelescope.com.au 27

Millions of Trojan asteroids live

in gravitational ‘sweet spots’

thatholdimportantkeystoour

Solar System’s history.

In 1765, mathematician Leonhard

Euler deduced the existence of three

‘collinear balance points’ in a three-

body system. L 1 lies between the Sun

and the planet, L 2 is just beyond the

planet in line with the Sun, and L 3 is

180 °from the planet along its orbit

(on the opposite side of the Sun). All

three haveconvex stability,such that

if an object is shifted away from the

balance point, it will likely leave the

stability region. Thus, over the age

of the Solar System, objects are not

expected to be stable at L 1 ,L 2 or L 3.

Then, in 1772, Joseph-Louis

Lagrange realised that two more

locations existed, preceding and

trailing a planet along its orbit by

60 °. Now called L 4 and L 5 ,respec-

tively, these are regions ofconcave

stability,meaning that objects per-

turbed slightly away from them will

tend to go back to the stability area.

Space observatories are some-

times parked in the Lagrangian

regions to exploit these gravitational

properties. Once there, they require

significantly less fuel to maintain

relatively stable positioning with

respect to Earth.

60 °

L 5

L 3

L 4

L 1 L 2

60 °

GRAVITY’S BALANCING ACT

S&T: LEAH TISCIONE

I

n our Solar System’s earliest days, the giant-planet

region was home to a vast number of small objects.

These bodies, similar to today’s asteroids and comet

nuclei, skipped around among the growing giants

that were themselves rustling back and forth in a

tumultuous planetary landscape. As the young planets

grew and shifted their orbits, they likely consumed

millions of these little objects and gravitationally flung

billions more out of the Solar System.

But not all of these small, primordial bodies

disappeared from the giants’ immediate

neighbourhood. One stable population remains after

4½ billion years: the Trojan asteroids.

TheTrojansmoveinanintricatedancewiththe

planets. They occupy regions roughly 60° ahead of

and behind a given planet in its orbit. Today we call

these the L 4 and L 5 Lagrangian points, respectively, in

honour of their discoverer, Joseph-Louis Lagrange (see

the box below). These are dynamical balancing points

at which the Sun’s and planet’s gravity, along with the

centrifugal force exerted on a smaller, third body due

to its orbital motion, are all in equilibrium. As a result,

objects located at L 4 or L 5 can maintain relatively stable

orbits over the age of the Solar System.

Trojans do not actually orbit right at the Lagrangian

stability points; instead, they can jossle or ‘librate’

around the point by some tens of degrees. In fact,

these objects often occupy orbits with pronounced

inclinations and eccentricities. Planetary scientists

have become very interested in the locations and

characteristics of the Trojans, as these small bodies tell

a story about the formation and evolution of the planets.

STORY BY SCOTT S. SHEPPARD

ARTWORK BY CASEY REED