When Kevin Heng thought about how light reflected from a planet or moon, he derived novel solutions to a problem that had been around for a long time. The phase curve of the moon, as observed from Earth, shows us its varying phases. Based on where the moon is located in its orbit (its perigee and apogee), the size of its orbit, and the angle between its two sides, the moon appears in different colors. The transit of the moon over the face of the Earth occurs during different phases because the moon is rotating at different speeds along its orbit. The angular size difference between the Sun and Moon is 40 percent wider at perigee than at apogee and 90 percent wider at max range
Astronomers have struggled for decades to understand why the phases of the moon occur as they do. Phase curves are best explained as a mathematical progression of an infinite series. Ultimately, an observer could measure the length of the shortest path between two points on Earth. As the years passed, new instruments and techniques were developed to further improve our understanding of the phases of the moon.
“I was fortunate that this rich body of work had already been done by these great scientists. Hapke had discovered a simpler way to write down the classic solution of Chandrasekhar, who famously solved the radiative transfer equation for isotropic scattering. Sobolev had realized that one could study the problem in at least two mathematical coordinate systems,” Heng declared.
The new formulae contain mathematical terms that were previously too complex to quantify using simple equations. Their use may create a greater understanding of planetary atmospheres, for instance. Researchers believe that the discovery of the new formulae may change the way future textbooks are written.