Adam Hibberd
I think most of you know me by now as the guy who developed the tool called 'Optimum Interplanetary Trajectory Software' (OITS) which ultimately solved the problem of how we might send a spacecraft to catch up with rapidly receding interstellar object and scientific enigma 'Oumuamua.
I decided to work on OITS - from theory through development to application - on my own and without assistance, including virtually no reference to the scientific literature on the subject.
Well more recently I've been challenging myself to develop an altogether separate software tool, this time not related to trajectories followed by rocket-propelled spacecraft, but instead those followed by Solar Sails.
Just to clarify for rockets, the spacecraft is largely only under the influence of gravity, with occasional blasts from the rockets which are in turn approximated as impulsive (instantaneous) 'DeltaVs' at certain user-defined points. For Solar Sails however, one can make no such assumption since a Solar Sail is to all intents-and-purposes a 'low thrust' propulsion option, influenced only by gravity and the continuous solar radiation pressure (SRP) from the Sun.
I shan't go into too much technical detail here which is a bit involved, but essentially the software takes the Solar Sail from a user-prescribed initial position and velocity to a final user-defined position in a user-defined time.
The more astute of you would realise that in fact there are most likely an infinite number of such paths that satisfy the intial and final constraints imposed by the user, yes that's true, so we must specify a optimization criterion. But what is it about the solution trajectory that should be minimised or alternatively maximised?
The answer to this question depends largely on the particular application one has in mind. In the end I chose to minimise the radial component of the total DeltaV applied by SRP on the sail. This is related to the equivalent optimization criterion of minimizing the overall angle the sail makes with the Sun compared to the 'edge-on' orientation.
Clearly in the case where the Solar Sail is precisely edge-on to the Sun, there is no thrust applied by SRP. Thus what we are trying to do is to create a path as close to a coast arc as possible, in other words the Sail travels as much as possible only by the influence of gravity.
I provide for you below an example solution found by my software when I ran it on a computer. The 'Displacement' is how far off the Sail gets from the user-specified final position and the 'Total DeltaV' is actually the total (absolute value of ) radial DeltaV applied by the Sun's light.