Planning interplanetary travel is about to become significantly cheaper and more efficient thanks to a breakthrough in applied mathematics. An international team of scientists has solved one of the most complex logistical conundrums in space – how to get an automated probe to fly around a long list of moving space rocks while using as little of its precious fuel as possible. The problem is a cyclopean one, because unlike Earthly addresses, celestial bodies travel in complex, ever-changing orbits.
The scientific achievement is based on the joint efforts of experts from the Department of Mathematical and Industrial Engineering at the Polytechnic Institute of Montreal, Canada, and analysts from the Faculty of Business Administration and Economics at Bielefeld University in Germany. By combining economic logistics with fundamental physics, the team has eliminated the previous limitations on deep space.
The case study itself consists of two extremely difficult levels. The first is combinatorial and seeks the ideal sequence of destinations. The second level delves deep into celestial mechanics – for each individual pair of objects, the perfect time window for launch and trajectory must be calculated, based on Lambert's equations for determining the orbital arc between two moving bodies. Since there are billions of options, standard computer calculations have so far been too time and resource-consuming.
To overcome this obstacle, the researchers have created innovative decision diagrams and a specialized graph-based algorithm. This system software nips unpromising and overly expensive routes in the bud, drastically reducing the computer calculations required. The end result is not just a list of good ideas, but mathematically proven, absolutely optimal trajectories for real space conditions.
This success opens the door to large-scale projects beyond Earth. The optimization will be used in future expeditions to capture space debris, maintain satellite constellations in near-Earth orbit, extract rare resources from meteorites, and build interplanetary supply chains. Experts emphasize that even a minimal improvement of 1% in these trajectories saves colossal amounts of money and time.
The curious thing is that the developed model can also be successfully applied on home soil – to optimize urban transport and deliveries in megacities, where traffic jams change the dynamics of travel in the same way that gravity affects ships in outer space.