Encyclopedia of the Solar System 2nd ed

288 Encyclopedia of the Solar System

FIGURE 6 Orbit of Tagish

Lake meteorite with other

recovered meteorite orbits.

(Credit:AAAS Science 13

October 2000, Vol. 290.)

3.3.1 TISSERAND PARAMETER

The first clue that an asteroid-like object may be a comet in
disguise comes from its orbit. Examining orbital elements,
asteroids and comets separate out readily when plotting
orbital eccentricity versus semimajor axis (Fig. 7). Another
way to characterize an orbit is to calculate its Tisserand
parameter from the equation:

T=aJ/a+2[(a/aJ)(1−e^2 )]^1 /^2 cosi

In this equation,aandaJrefer to the semimajor axis val-
ues for the object and Jupiter. The parametersiandeare
the inclination and eccentricity of the object’s orbit. The Tis-
serand parameter is useful because it is a constant even if the
comet’s orbit is perturbed by Jupiter. Also it helps describe
whether an object is in an orbit that is strongly controlled
by Jupiter or not. Most objects that display the characteris-
tics of comets have a valueT<3, while most objects that
are asteroid-like haveT>3. The value ofT=3 is repre-
sented by the solid line in Fig. 7. Objects withT<3 are
excellent candidates for being comets in disguise – they do

not currently display any telltale coma or tail because they

are at present dormant or inactive.

3.3.2 DYNAMICAL AND PHYSICAL EVIDENCE

FOR EXTINCT COMETS

A powerful way to investigate the mystery of how many ex-

tinct comets reside in the near-Earth object population is to

explore both dynamical factors and physical measurements

to identify possible candidates. For example, numerical sim-

ulations of the orbits of short-period comets can reveal how

likely it is that gravitational interactions with Jupiter and

the other planets can send them into the near-Earth object

population. In these simulations, many thousands of hypo-

thetical comets, each with slightly different initial orbits can

be tracked for millions of years to see how they are tossed

around chaotically by the gravitational tugs and pulls of the

planets. In the same way, thousands of different starting

places for main-belt asteroid orbits can be modeled to reveal

the effectiveness of resonances for sending asteroids into

near-Earth space. Alessandro Morbidelli, William Bottke,