Space debris: the orientation of a Falcon 9 stage deduced solely from its light curve in 15 seconds

Using automatic differentiation, a general method fits a photometric model to the observations and estimates the attitude of an object in orbit without the need for a dedicated model for each target.

The increase in launches is increasing the population of debris in orbit, which threatens active satellites and future missions. Knowing the orientation and rotation of these objects helps to monitor them and anticipate their behaviour, but current methods are often based on target-specific, faceted models that are not very generalizable.

A gradient descent on the reflected light

Hui Li and his co-authors propose a more generic approach based on light curves, i.e. the evolution of the brightness of an object observed from the ground. They define an error function between the measured curve and a theoretical curve dependent on attitude parameters, then exploit automatic differentiation to calculate the gradients and quickly converge towards the correct orientation.

Applied to a Falcon 9 rocket body, the method estimates the parameters in about 15 seconds with a root mean square error of the order of a thousandth. Validated on a third-party database, it shows, according to the authors, a good ability to generalize to other objects.