We've been landing people on the Moon since 1969, but how will astronauts find their way when we start exploring the lunar surface? We need a global navigation satellite system (GNSS) for the Moon, and an 800-year-old maths trick could help us.

The maths trick in question is known as the Fibonacci sphere. Here, researchers from Eötvös Loránd University in Hungary used it to better estimate the Moon's rotational ellipsoid, i.e. its slightly squashed shape as it orbits the Earth.

Contrary to what pictures of the Solar System might suggest, the Earth and Moon are not perfect spheres: the influence of gravity, rotation and tidal fluctuations mean they are more like squashed balls.

For the sake of simplicity, our GNSS technology uses a rough approximation of the Earth's squashed ball shape. If we are going to develop a Geographic Information System (GIS) for the lunar surface, we need the same estimate for the Moon's solenoid (the equivalent or true, irregular shape of the Earth's geoid).

"Because the Moon is less depressed than Earth, most lunar GIS applications use a spherical datum," geophysicist Gábor Timár and his student Kamilla Cziráki write in their paper.

"However, with the renaissance of lunar missions, it seems useful to define an ellipsoid that better fits the selenoid."

Which brings us back to the Fibonacci sphere, which uses an approach based on the Fibonacci sequence to evenly distribute points placed on a sphere. Cziráki and Timár used a computational model based on the Fibonacci sphere to map 100,000 points of the lunar surface using measurements previously taken by NASA.

This produced more accurate figures for the semi-major and semi-minor axes that define the Moon's rotational ellipsoid. The lunar poles are about half a kilometre (0.3 miles) closer to the centre of the Moon than the equator, and embedding this information in any future lunar GPS will help reduce the number of wrong turns made on the Moon.

Such detailed calculations have not been performed on the Moon since the 1960s. Moreover, when the researchers applied their technique to the Earth's rotational ellipsoid, the data matched properly, further confirming the accuracy of the approach.

The results of this study could be used to help provide better navigation systems for humans going to the Moon in the future, as well as to improve our estimates of Earth's dimensions and the navigation systems used to get around it.

"In the future, we would like to extend our research to Earth and investigate differences in the most favourable ellipsoids using different geoid models," the researchers write.

 

Source: https://www.sciencealert.com/