Copyright (c) 1996 by MA Lloyd (malloy00@io.com)

The requirement for a Hohmann transfer orbit is that the position
of one planet at departure be 180 degrees away from the position
of the other at arrival.  For concentric circular orbits the time
between launch windows is S = (Pi * Po)/(Po-Pi) where Pi and Po
are the periods (year lengths) of the inner and outer planets
respectively.  Note, the windows don't occur at the same times for
the inner and outer planets.  If you travel to the outer planet
and want to come home you will need to wait a while, Tw = S
(J-(2*Tt/Pi) where J is any integer (2 for the minimum wait), and
Tt is the Hohmann orbit transfer time equal to O.1768*Pi*(1+ao/ai)^1.5
where Pi is the inner planet period, and ao and ai are respectively
the semimajor axes of the orbits of the outer and inner planets.
For scheduled flights rather than single missions its the difference
in departure times between the inner and outer planets that matters
rather than the wait time, obviously this will be  Tt + Tw = Tt -
S(2Tt/Pi) + J * S.

There are two realistic cases where interplanetary trajectories can be
solved analytically without ignoring gravity:
One is the Hohmann transfer orbit, the minimum energy course
resulting from a short (compared to trip length) high acceleration
starting phase.  Trip time is .25 x P (1+R2/R1)^1.5, where P is the 
period of the starting orbit (1 year for a vehicle leaving Earth) and
R1 and R2 are the distances from the sun of the starting and 
ending orbits.
The other is the constant low acceleration transfer, which
goes to the limit t = 6.2832 (R1/P*a) * (1-R1/R2)^0.5, where
a is the acceleration approaching zero (valid approximation where
a << R2/P^2).  Careful, units matter here.