A phase curve is an actual relationship between a rotating astronomical body and its photosphere. In the case of the Moon, the photosphere is a thin outer atmosphere made up of ice particles and dust. As the Moon orbits Earth, it revolves around the Earth at a rate of about sixty degrees per day. The amount of light received from the Sun during each phase of the Moon varies slightly from region to region due to Earth’s rotation. Kevin Heng of the University of Bern in Switzerland solves the problem posed by this classic physics question about reflected light using new mathematical modeling.

“The ability to write down mathematical solutions for phase curves of reflected light on paper means that one can use them to analyze data in seconds. Pierre Auclair-Desrotour is a more talented applied mathematician than I am, and we promise exciting results in the near future,” said Heng.

There are many previous approaches for the calculation of phase curves, including some that have existed since the 18th century, created by Johann Heinrich Lambert. While Lambert’s solution did not make the spreading of knowledge any easier, it did provide a basis for understanding what happens when light passes through a refractive medium.

Heng’s paper offers solutions for the shape of the phase curve and albedo, which are only known up to this point in computer models. By identifying the correct phase curve shape and the optimal albedo (reflectivity), Heng was able to state his findings mathematically.

Heng is collaborating with scientists from the American-led TESS space telescope to analyze currently existing phase curve data from the upcoming James Webb Space Telescope and using them to come up with new methods for analyzing future phase curve data.