It struck me a while ago that I have developed this extremely effective tool for solving interplanetary trajectories (OITS), so how would I be able to exploit it for alternative applications - applications which would be beyond its originally intended purpose, that of designing trajectories for chemically propelled spacecraft (and in the process assuming impulsive changes in velocity at discrete points along the way to the target)?

Then it occurred to me: why not use it for solving laser sail trajectories AFTER they have been accelerated to high speed by a GigaWatt laser beam? If we refer to the 'system model' described for example by Kevin Parkin, then we find that for GigaWatts of power from a laser, the beam would be incident on the sail for only a few minutes (~10 mins, if that). Thus compared to the flight time to the target (~ years), the acceleration can indeed be assumed to be impulsive.

To be clear we are now talking PRECURSOR missions, that is missions we might undertake before we achieve our ultimate interstellar goal: Proxima b. Destinations for these precursors might be distant objects in our Solar System, for example. With GW lasers, the initial acceleration phase can indeed be taken as an impulsive velocity increment, so something which OITS can solve quite straightforwardly. These precursor missions may happen in the late '30s to '40s, if everything goes to plan.

Actually, I have already done some work for Project Lyra on this, which can be found here as a preprint.

Essentially with a laser sail accelerated by a laser beam, it reaches a high speed very quickly (as well as in a short distance < 0.1 au) and from then onwards it travels nearly purely under the influence of gravity, for missions to objects in the Solar System, the Sun's gravity.

Thus what we can do is to take the velocity with which the laser sail is imparted by the laser and assume that it is approx. the hyperbolic excess speed of the laser sail w.r.t. Earth. Then there is no need to have a 'system model' for accelerating the lasersail (like Parkin's) - all that complexity is abstracted out of the calculations - all we need is the velocity to which the laser accelerates the laser sail.

So you can see with a modified version of OITS we can assume an impulsive firing at Earth launch, or launch using a laser on any other celestial body for that matter, and we get the resulting interplanetary trajectory of the laser sail.

Furthermore using this technique we can also derive from the sail's hyperbolic velocity w.r.t. Earth, an idea of the RA and DEC that the laser needs to fire towards, as well as the time of firing.

The results aren't 100% accurate, but they are quite sufficient for my purposes. Also we can impose constraints on the encounter velocity w.r.t. the target (to provide enough time to make observations and measurements, and sample any plumes or atmosphere if present) and this in turn imposes a constraint all the way back to the laser sail velocity imparted by the laser.

In short, there is NO NEED for me to model low thrust or high thrust light sail trajectories for this set-up.

I have already done some research, using this version of OITS, into missions to the distant dwarf planet Sedna and also Kuiper Belt dwarf planet known as Quaoar, both with laser sails launched from the Moon - refer figures.

It should be noted that these surface plots assume that there can be NO contraints on the selenographic coordinates which the laser can be pointed in to direct the laser sail to its destination.

Observe that on the Moon, where there is clearly no atmosphere, then that means there would be no 'penalty' in terms of pointing the laser significantly off vertical which there would be on Earth due to the associated problem of firing the laser through a thicker atmosphere.

Furthermore, the Moon only rotates once every ~28 days as opposed to (clearly) once every sidereal day for Earth and so there would not be any severe timing constraints placed on the laser firing duration due to the Moon's rotation, unlike there would be on Earth, due to the Earth's faster rotation.

Research is on-going.