Surfaces of Constant Tisserand Parameter

T

2.82

The Tisserand parameter is a constant in the frame of the restricted circular three-body problem (RC3BP) given by

T=1/a+2

a(1-

2

e

)

cos(i)

, where

a=

a

particle



a

planet

(the ratio of the semimajor axes of the body and planet),

e

is the eccentricity, and

i

is the inclination of the body's orbit with respect to the planet's orbit.

This Demonstration plots surfaces of constant Tisserand parameters

T

in the space

(x=1/a,q,i)

, where

q=periheliondistance

a

planet

. A body encountering the planet must have

0<q<1

,

x<2

(which means

a>0.5

), and

T<3

in units of the RC3BP. As the body encounters the planet, its orbital elements change but conserve

T

. The plot shows all possible orbital evolutions for the body for a given value of

T

. The boundary between asteroids and comets in the solar system occurs for

T≈3

.