[To continue: I got interrupted and sent the incomplete message.
Sorry.]
.... The pericenter of the ellipse is the point on the ellipse
closest to the foci of the ellipse.
(This is supposed .......p.......
to be an ellipse) . .
. 1 2 a
. .
.......p.......
If 1,2 are the foci, then 'p' are the pericenters, and 'a' is
the apocenter if the sun is at '1'.
The Hollman transfer orbit is the lowest energy method of
getting to an orbit. It assumes that the fuel burn is short
compared to the travel time. If you have a constant acceleration
engine (ion-drive, or something), the transfer orbit will be much
more gradual, resulting in a spiral that moves out toward the
other orbit. The travel time is not necessarily longer for a
spiral transfer orbit, since greater speeds are possible.
Most of the time in the Hollman orbit is coasting.