Sky and Telescope - June 2016 - 17

Scott S. Sheppard

JUPITER'S MINIONS Millions of small
bodies - known as Trojan asteroids -
have shared Jupiter's orbit since the dawn
of the solar system.

Artwork by Casey Reed

In 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
ejected billions more from the solar system.
But not all of these small, primordial bodies disappeared from the giants' immediate neighborhood. One
stable population remains after 4½ billion years: the
Trojan asteroids.
The Trojans move in an intricate dance with the
planets. They occupy regions roughly 60° ahead of and
behind a given planet in its orbit. Today we call these
the L 4 and L5 Lagrangian points, respectively, in honor
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 L5 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 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.

Gravity's Balancing Act
In 1765, mathematician Leonhard
Euler deduced the existence of three
collinear balance points in a threebody system. L1 lies between the Sun
and the planet, L 2 is just beyond the
planet in line with the Sun, and L3 is
180°° from the planet along its orbit
(on the opposite side of the Sun). All
three have convex 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 L1, L 2, or L 3.
Then, in 1772, Joseph-Louis

L4

Lagrange realized that two more
locations existed, preceding and
trailing a planet along its orbit by
60°. Now called L4 and L5, respectively, these are regions of concave
stability, meaning that objects perturbed slightly away from them will
tend to go back to the stability area.
Space observatories are sometimes 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°
L3

L1

60°

L2

L5
S&T: LEAH TISCIONE

Sk yandTelescope.com June 2016

17


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Sky and Telescope - June 2016

Table of Contents for the Digital Edition of Sky and Telescope - June 2016

Contents
Sky and Telescope - June 2016 - Cover1
Sky and Telescope - June 2016 - Cover2
Sky and Telescope - June 2016 - 1
Sky and Telescope - June 2016 - Contents
Sky and Telescope - June 2016 - 3
Sky and Telescope - June 2016 - A
Sky and Telescope - June 2016 - B
Sky and Telescope - June 2016 - 4
Sky and Telescope - June 2016 - 5
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Sky and Telescope - June 2016 - Cover3
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