Surfaces of Constant Tisserand Parameter
Surfaces of Constant Tisserand Parameter
The Tisserand parameter is a constant in the frame of the restricted circular three-body problem (RC3BP) given by , where (the ratio of the semimajor axes of the body and planet), is the eccentricity, and is the inclination of the body's orbit with respect to the planet's orbit.
T=1/a+2
a(1-)
cos(i)2
e
a=
a
particle
a
planet
e
i
This Demonstration plots surfaces of constant Tisserand parameters in the space , where . A body encountering the planet must have , (which means ), and in units of the RC3BP. As the body encounters the planet, its orbital elements change but conserve . The plot shows all possible orbital evolutions for the body for a given value of . The boundary between asteroids and comets in the solar system occurs for .
T
(x=1/a,q,i)
q=periheliondistance
a
planet
0<q<1
x<2
a>0.5
T<3
T
T
T≈3