Recently, DARPA challenged the research community to develop breakthrough technologies necessary to build a permanent human settlement on the moon. Among the challenges DARPA identified was handling Position, Navigation, and Timing (PNT). On Earth, this is handled easily with the Global Positioning Satellites, but an equivalent satellite constellation on the moon would be expensive for fairly small utility.

Determining your precise position on Earth was an important problem and tackled by many great minds of science and engineering. The list of scientists that worked on this reads like a who’s who of science from ancient history through the Enlightenment, including Newton, Ptolemy, Galileo, Hipparchus, Huygens, Halley, and Celsius. It wasn’t until we had accurate clocks in 1730 that the problem was solved well enough to make sea travel relatively safe. This same approach with a sextant was used until GPS became prevalent in the 1980s!

With DARPA making a request to re-address one of the world’s greatest science problems, I knew I had to write a proposal. Here’s what I sent in.

Summary

Imagine being able to navigate on the Moon using only a “smartphone” camera and an image processing application. This is the goal of our project, which proposes a new concept for lunar position, navigation, and timing (PNT). Our approach is distributed, resilient, scalable, flexible, and intuitive, and it has the potential to revolutionize lunar PNT and create new opportunities for lunar exploration and development. This document outlines our technical approach, the viability of our concept, and the work needed to bring it to fruition.

There are so many challenges posed by lunar exploration; position, navigation, and timing is no exception. The Moon does not have useful magnetic fields, making many navigation methods difficult. A network of positioning satellites would certainly suffice, but it would be a large initial and ongoing expense. Instead, we propose returning to the time-honored method of celestial navigation. Our idea is to leverage the advantages of the Moon, recent advancements in technology, and focused effort on adapting navigation algorithms to provide every astronaut, rover, and piece of equipment with an unjammable and ultra-reliable positioning system based on measuring the stars.

We propose to use a “smartphone” app that can perform the necessary calculations and display the results in real time. The app will use an astronaut’s handheld camera and accelerometer to measure the altitude of celestial bodies and compare them with a database of their positions and movements. The app will then use a modified version of the Marcq St. Hilaire method to calculate the user’s latitude and longitude on the lunar surface, as well as their orientation. This information can be transmitted for tracking or displayed on the device, just like today’s GPS on Earth. The app will have no external dependencies, working entirely offline. With this app, lunar astronauts will be able to determine their position anywhere on the Moon, at any time, with an accuracy of 10 meters or better. Only minimal investment is necessary to adapt Earth-based celestial navigation to apply to the Moon and miniaturize to a handheld device.

Technical Description

On Earth, celestial navigation was the only reliable means of maritime navigation until the availability of GPS. Using a sextant to determine position was, and remains, a skilled trade. Measurements could be taken only at sunrise, solar noon, or sunset. Cloud cover meant it was regularly impossible to use. Sextants are only marked to support calculation to 0.1 minutes of a degree, resulting in position accuracy only to 185 meters, but other error sources mean that only experts can calculate within 2000 meters.¹ We will need to do better than that on the Moon, and we can.

Life on the Moon is more difficult than on Earth in nearly all ways, but not this one. The lack of a lunar atmosphere is an advantage for celestial navigation. Without an atmosphere, celestial sightings will never be blocked by clouds. The lack of an atmosphere also prevents any error caused by atmospheric distortion. Light pollution isn’t a problem either when there is no atmosphere to scatter light back to the surface. Because the Moon’s circumference is more than three times smaller than the Earth², degrees and minutes of latitude and longitude represent three times less ground distance on the Moon. An equivalent calculation of position performed on the Moon will be possible more often, have less error, and result in a more precise location.

And how can someone take a celestial sighting on the Moon? Like on Earth, we can measure the altitude of several stars or other celestial bodies and calculate position with the Marcq St. Hilaire method. After determining the altitude of at least three celestial bodies, information can be retrieved from a newly developed calculation table, converted through some trigonometry, and plotted on a map to determine the observer’s position.

During lunar day, the light of the sun makes imaging stars more difficult. The lack of an atmosphere again provides a solution. Without Raleigh scattering, the camera can simply be moved into the shade and not have the image washed out by the sun. If the camera is also shaded from light reflecting from the lunar surface, stars can be imaged. Alternately, IR pass filters help image stars regardless of daylight. The sun also can be used to determine position, either at solar noon with the Merpass method or by taking measurements a few hours apart with the sun-run-sun method³. The sun can also be one of the three necessary celestial bodies measured with the Marcq St. Hilaire method.

On the near side of the Moon, we can determine the cardinal directions and time just by looking at the Earth. The Earth is also visible at all times on most of the near side of the Moon, even during lunar day⁴. It can be one of the three necessary celestial bodies to be measured and included with the Marcq St. Hilaire method. But consistent visibility of the Earth provides another advantage, determining the time. The Earth occludes stars at times that can be precalculated – the Terran distance as an analogue of traditional Lunar distance. Observing when this happens could be used to keep clocks in sync, as a less accurate backup to other timekeeping mechanisms. Finally, Earth’s phase and day/night terminator can be used to determine cardinal directions on the Moon’s surface by sight if the pole stars are not visible. The crescent method of navigating on Earth⁵ by the Moon can be converted to navigating on the Moon by Earth. The Moon phase method⁶ could similarly be converted to the Earth phase method.

		Near side	Far side
Lunar Day	Celestial bodies to measure	Earth, sun, stars	Sun, stars
Lunar Day	Special requirements	Camera must be shaded or have an IR pass filter	Camera must be shaded or have an IR pass filter
Lunar Night	Celestial bodies to measure	Earth, stars	Stars
Lunar Night	Special requirements	Camera must have a level to determine the horizon	Camera must have a level to determine the horizon

Viability

We don’t think that lunar astronauts will want to spend much of their time regularly taking measurements of the altitude of stars. Our culture has moved on to expect very accurate PNT, instantly, with a handheld smartphone. Although not as dramatically as personal computing, progress has continued in celestial navigation technology. The U.S. military has automated the process and miniaturized it to fit into the B-2 Sprit bomber and other vehicles.⁷ In just the last few years, Honeywell demonstrated a celestial navigation system on Earth with 30 meter accuracy.⁸

We believe that an off-the-shelf camera will be able to quickly determine its position on the Moon’s surface to 10-meter accuracy or better, due to the lack of atmosphere and smaller circumference of the Moon. Further, we imagine integrating lunar celestial navigation into the existing cameras and processors that will be used in a lunar colony. Astronauts will need a personal computer for their work, and they will expect that it has integrated technology like their smartphone on earth.

The camera module of Samsung’s latest smartphone, the Galaxy S24 Ultra, has a 200 Megapixel sensor and a dedicated astrophotography mode that takes clear images of stars already.⁹ We expect that smartphone camera technology will continue to improve over the next several years. Although during lunar day the camera may need to be shaded, holding up a smartphone analogue and turning it to a few parts of the sky will only take a few seconds. This will provide all the information necessary for software to stitch the images together, identify stars, and then determine position. The CosmoGator project among others is applying this same sighting mechanism to handheld devices for soldiers and sailors on Earth.¹⁰ This process could be further simplified to only require a single image taken of the lunar sky by adding to the device an IR pass filter to block glare and fisheye lens to capture a wider field of view.

A major reason the U. S. military has continued to invest in projects like the automatic celestial navigation systems in the B-2 or CosmoGator is that GPS is not always reliable. GPS is susceptible to centralized failure and signal jamming, but celestial navigation avoids these problems. When the celestial tables and navigation algorithms are updated for the Moon, any device with a functioning camera and preloaded tables can determine its location on the Moon. There is no signal to get blocked nor centralized device that can fail.

Work needed

Performing these calculations and adapting the existing celestial navigation software is the bulk of the required work. The equivalent of a radiation-shielded smartphone is all the hardware that is necessary. We can partially determine the viability of lunar celestial navigation now with existing images taken from previous missions to the Moon’s surface, which have well-documented locations. We will need to take photos of the sky from the Moon’s surface during the Artemis missions in order to verify calculations related to the position of stars. This testing is necessary both to verify the visibility of stars and the accuracy possible without an atmosphere.

If those images are taken, we can complete the testing and develop the software quickly at very low cost. The final test can be performed by taking sightings during a future moonwalk. As any cameras being sent to the Moon can be used with this method, there should be no incremental hardware cost into the future.

Conclusion

Many methods of PNT rely on a magnetic field to support a compass or bouncing radio signals off an atmosphere. Previous missions to the Moon have relied on line-of-sight stations and inertial navigation, requiring special equipment on both the sender and receiver. A constellation of lunar satellites would be extremely expensive.

Adapting celestial navigation to the Moon will be by far the cheapest approach to lunar navigation, relying on cameras that are also used for other mission purposes. It also will rival the accuracy of a combination of inertial navigation and line-of-sight beacon stations; only a satellite constellation is likely to be more accurate. Like a satellite constellation, lunar celestial navigation can apply to the entire lunar surface. But unlike an equivalent to GPS, viewing the stars cannot be blocked nor suffer a centralized failure.

If this project succeeds, lunar astronauts will have a handheld navigation app that actually works better in many ways than navigation on Earth.

Bibliography

1. https://casualnavigation.com/how-accurate-is-celestial-navigation-compared-to-gps/ ↩︎
2. https://nssdc.gsfc.nasa.gov/planetary/factsheet/moonfact.html ↩︎
3. https://casualnavigation.com/6-methods-for-celestial-navigation/ ↩︎
4. Makowiecki, Piotr (1985). Pomyśl zanim odpowiesz. Warszawa: Państwowe Wydawnictwo “Wiedza Powszechna”. ISBN 83-214-0419-7. ↩︎
5. https://www.naturalnavigator.com/find-your-way-using/moon/ ↩︎
6. https://www.naturalnavigator.com/news/2018/12/moon-phase-navigation/ ↩︎
7. https://www.popularmechanics.com/military/research/a36078957/celestial-navigation/ ↩︎
8. https://aerospace.honeywell.com/us/en/products-and-services/product/hardware-and-systems/sensors/alternative-navigation-systems ↩︎
9. https://www.tomsguide.com/phones/samsung-phones/forget-moon-shots-i-used-the-samsung-galaxy-s24-ultra-to-try-photographing-galaxies ↩︎
10. https://athenanavy.wordpress.com/2014/02/06/project-pulse-cosmogator/ ↩︎