“Astronomy for sailors”: a web game to learn physics using the stars and a clock

If you were on a boat in the middle of the sea how could you guess your position using just the stars and a clock? This is the challenge for hundreds of students at our interactive astronomy workshop in the context of the Genoa Science Festival held in Genoa (Italy) in 2021. Visitors played on the web application Astronomy for sailors which we developed from scratch. They could estimate their latitude and longitude in a virtual environment by measuring the altitude of the Sun above the horizon at solar noon and by using a marine chronometer. By recognising the brightest circumpolar constellations, they could learn how to find the North Star. The workshop included also an interdisciplinary section regarding orientation techniques in the animal world, ancient times and modernity. In this contribution we present the workshop’s activities, highlighting their original and innovative aspects. We report on the positive feedback from students and teachers who actively played with celestial navigation during our workshop. Around 600 people have visited us and the web application Astronomy for sailors is still available online for free.


Introduction
A primary need of any science educator is to nd and explore new and e ective ways to convey interest in scienti c topics.Students often feel that this discipline has little connection to everyday experience due to the lack of practical activities available in di erent educational settings.Going back in time, however, we remember that astronomy has developed for an extremely practical need: nding the way by land and by sea.Today, the use of the advanced Global Positioning System (GPS) has made star orientation techniques relatively outdated.However, such techniques are still used by sailors as a backup to modern satellite navigation methods.In this context, learning how to navigate by the stars may be a rst step for students and the general public to experience how astronomy can be an extremely practical discipline, very useful in many everyday situation.Interesting online activities have already been developed for this purpose by combining the capabilities of free software such as Google Earth 1 and Stellarium2 [1] (see [2] and references therein).They prove the e ectiveness of virtual platforms for teaching celestial navigation and astronomy in an interactive and engaging way (see also [3]).Orientation and practical celestial navigation are the themes of the innovative workshop about astronomy that we present in this paper.It results from the collaboration between PhysicalPub3 , a cultural association dealing with scienti c dissemination on astrophysics, and a group of physicists, chemists and geologists from the University of Genoa.The workshop was presented during the nineteenth edition of the Science Festival held in Genoa (Italy) in 2021, after the COVID-19 pandemic.Due to some post-pandemic restrictions, our activity was designed to be accessible in two formats: an in-person workshop and a full online digi-lab.They were both organised with the same structure, presented in Sec. 2. At the core of the activity, there was an interactive game accessible on the web application Astronomy for sailors.The web app has been developed from scratch by the PhysicalPub association and it is described in detail in section Sec. 3. The experience at the Genoa Science Festival and the very satisfactory turnout are reported in Sec. 4, whereas Sec. 5 collects conclusions and future prospects.A complete list of the organisations and sponsors that supported this project is provided in the acknowledgements.

Structure of the workshop
The in-person workshop and the digi-lab were designed for junior college students having some basic knowledge of geography, geometry and astronomy.For in-person attendance, the workshop could welcome up to 15 visitors per session.Each session was around 45 minutes long.Four scienti c animators guided the visitors through the activities that were divided into three parts.The rst theoretical part aimed at presenting in a visual way the essential notions of astronavigation needed for the following interactive game (Sec.2.1).In the second part, visitors could play on the web application Astronomy for sailors by connecting with their own devices to a dedicated hosting platform (Sec.2.2).The third part provided an excursus on navigation and orienteering techniques in the animal world, in antiquity and with modern technologies, plus some additional time for questions and curiosities (Sec.2.3).By combining visual explanations, practical activities and moments of interactive insight, this structure has the potential to provide a complete and engaging learning experience.

Astronavigation in a nutshell
The rst part of the workshop covered in an intuitive way a broad range of topics relevant to celestial navigation, with minimum mathematical formalism.These topics were introduced by using schematic drawings on slides and the virtual 3D planetarium Stellarium [1].
In the beginning, the notions of geographic position and terrestrial coordinates, in terms of latitude ( ) and longitude ( ), are introduced showing a nautical chart.Terrestrial coordinates can be generalised to celestial coordinates afterwards: latitude and longitude on the globe correspond to right ascension (r) and declination ( ) on the celestial sphere.Basic concepts about the Earth's motion are also introduced, focusing on their relation with the apparent motion of the celestial objects in the sky.By using Stellarium software it is possible, in particular, to easily explain how the apparent motion of the Sun as seen by an observer on Earth carries information about the observer's latitude.This information can be derived by measuring the altitude of the Sun above the horizon (h Sun ) at a precise moment of the day called solar noon.At solar noon the Sun reaches the highest altitude above the horizon.With where Sun is the Sun's declination, i.e. the angular distance of the Sun from the celestial Equator.This value can be retrieved from the so-called nautical almanacs, scheduling the coordinates of several celestial objects for each whole hour of the year4 .At Solstices and Equinoxes, in particular, Sun assumes the values reported in Tab. 1.The maximum and minimum values of Sun (±23 4 ) derive from the inclination of the Earth's rotation axis with respect to the ecliptic, i.e. the imaginary plane de ned by the Earth's path around the Sun.The Sun's elevation h Sun at solar noon in Eq. 1 can be directly measured by the observer using a sextant.This instrument allows determining the angle of a celestial object above the horizon thanks to a system of two mirrors, a movable arm, and a graduate angular scale.This measurement is called noon sight.With a noon sight, the observer can estimate its latitude but also its longitude.The longitude estimation takes into account that the Earth rotates around its axis at an angular velocity of about Earth = 15 h.For this reason, the same astronomical event, such as the Sun's culmination at solar noon, will be observed with a certain time delay between two locations far apart on the globe.By convention, the Greenwich Meridian is taken as a reference for these time measurements.The time di erence t between the observer's local time (e.g. at the solar noon) and the reference Greenwich Mean Time (GMT) carries information about the observer's longitude.In this case, the formula is simple, and it adopts the following sign convention: if t is positive (negative) the observer is East (West) of Greenwich.The reference GMT can be read on a marine chronometer which is an accurate timepiece able to remain una ected by the changing conditions met by ships at sea 5 .In summary, the nautical almanacs, the sextant, and the marine chronometer are three fundamental tools for celestial navigation.They were exhibited at the Genoa Science Festival and could be discovered by visitors during the rst part of the workshop (see Fig. 1).
At night, latitude and longitude can be estimated by looking at the stars.A particularly important star in the Northern hemisphere is the North Star or Polaris.Being (almost) above the North Pole, it represents a reference for navigation.Its height above the horizon can be measured with the sextant, and this value corresponds to the observer's latitude.To identify the North Star it is useful to recognise four bright circumpolar constellations: the Ursa Major (with its seven brightest stars called Big Dipper), the Ursa Minor (or Little Dipper), Cassiopeia, and Cepheus.These constellations were shown to visitors using Stellarium.

The interactive game
The second part of the workshop aims to reinforce and apply the notions learned during the introduction through an interactive game.This activity consists of a set of three challenges in which visitors have to: i) estimate their unknown location on the globe with a noon sight, ii) identify the circumpolar constellations and the North Star, iii) complete a 5-question quiz.These challenges allow the players to go head-to-head trying to get the highest score.Everyone can access the interactive game through the web application Astronomy for sailors which is described in detail in Sec. 3. It is interesting to mention that the last challenge of the game guides the visitor towards the third part of the workshop.The very last quiz's question anticipates, indeed, one of the topics covered in the nal poster session, in order to stimulate imagination and curiosity.

More about orientation
The last part of the workshop covers the themes of navigation in the natural world, among the ancient mariners and in our times.Three posters provide examples and curiosities on these subjects, touching also on more advanced topics for high school and university students.
The animals' orientation ability and the di erent types of navigational skills exploited in nature are the themes of the rst poster.It focuses, in particular, on the robin's magnetic sense, being one of the most sophisticated orientation methods known.It involves the quantum entanglement of electron spins in the bird's eyes and it is an interesting example of how quantum physics can play a key role in bioscience [5][6].A second poster concerned navigation methods adopted by ancient mariners.The techniques developed by the Phoenicians and the Vickings constituted, in particular, a valuable example of navigation by the stars and the Sun.The interdisciplinary perspective of this nal poster session makes the workshop more stimulating and richer.The animators covered the more advanced topics in an attractive and accessible way.During the explanations, the audience was encouraged to interact, leaving time for questions and curiosities.

The web application Astronomy for sailors
The most innovative and peculiar aspect of the workshop is the web app Astronomy for sailors, entirely developed and maintained by the cultural association PhysicalPub.Its cover image is shown in Fig. 2.
Web applications o er exible accessibility to virtual resources that can be used also for educational purposes.If necessary, these resources can provide a viable alternative to reallife experiences.This has become particularly important during and after the COVID-19 pandemic.The e ectiveness of virtual experiences was already tested in other educational activities promoted by PhysicalPub [12].For the web app's infrastructure, a modern architecture has been adopted to ensure simple development and maintenance, as described in Sec.3.1.The details about the interactive game accessible through the web app are reported in Sec.3.2.

The infrastructure
The web application Astronomy for sailors is based on a REpresentational State Transfer (REST) client-server architecture.The backend engine is written in JavaScript using the runtime environment NodeJS whereas a Structured Query Language (SQL) database is adopted for data management.The frontend is written in ELM language and transpiled to HyperText Markup Language (HTML) and JavaScript.Cascading Style Sheets (CSS) is used to style and layout the web pages.Astronomical calculations (e.g. the Sun's trajectory as seen from di erent locations on Earth) are performed with a Python script importing the Astropy6 package [11].The outputs are processed using Blender7 for video rendering, with the Eevee engine.Blender allows to create beautiful virtual environments providing an immersive experience similar to a video game.The whole application is hosted on a Virtual Private Server (VPS) and it is accessible via a Uniform Resource Locator (URL) using the standard web browsers of any internet-connected personal device.Its usage is completely free and does not require any account.

The three-challenge game
For connecting to Astronomy for sailors, visitors can resolve its URL8 through a Quick Response (QR) code using their own devices (smartphones, laptops or tablets).They can insert a nickname and choose either to play alone or to join a multi-player session.Each game session is associated with a token and multi-player sessions share the same one.The interactive game consists of three challenges in which players can earn points.The goal is to score as high as possible.
In the rst challenge, the player has to estimate its unknown location on the globe with a noon sight, as explained during the rst part of the workshop (see Sec. 2.1).By choosing a number from 1 to 18, the player is blindly associated with one of the locations available (18 ports in the Northern hemisphere).A sailing boat appears on the screen and the player sees the Sun rising in the East, culminating and then setting in the West.To estimate its unknown latitude and longitude, the player has to stop the Sun at the solar noon, hence when it is supposed to be at its maximum altitude above the horizon.At the stop, a grid appears on the screen together with the date and time (GMT) of the virtual noon sight, as shown in Fig. 3. Using the grid, the player can measure the elevation of the Sun and derive its latitude using Eq. 1.In the calculation, the Sun's declination Sun must be taken into account.Looking at the date, the player will always recognise the Summer or the Winter Solstice at which Sun is known and reported in Tab. 1.To derive its longitude with Eq. 2, the player has to calculate the time delay between its local noon and the time (GMT) displayed on the screen.The estimated latitude and longitude can be entered into two appropriate windows.Finally, a world map appears showing the estimated and the true locations, as shown in Fig. 4. The closer the estimated location is to the true one, the higher the player's score.The estimation is clearly a ected by large uncertainties which   In the second challenge, the player has to identify the most important circumpolar constellations and the North Star.A night view of the Northern sky appears on the screen.The player can click on the four circumpolar constellations Ursa Minor, Ursa Major, Cepheus, and Cassiopeia, and look at their shapes.Each shape must be associated with the right name considering multiple choices in a sub-window, as shown in Fig. 5.A correct answer is rewarded with a point and a penalty is given for being wrong.
The last challenge consists of a 5-question quiz mainly on the topics covered in the rst part of the workshop (Sec.2.1).The rst 4 questions are randomly selected from a pool of 30.The last question, instead, is on a topic not introduced yet, but discussed in the following third part of the workshop (Sec.2.3).This question is randomly selected from a pool of 3 and the random choice determines the topic of the following poster session.
At the end of the three challenges, the nal player's score is shown.In multi-player sessions, all the players appear on the same nal rank and the winner is drawn.

The experience at the Genoa Science Festival
The experience at the Genoa Science Festival was very positive and rewarding.The wide variety of topics and the didactic experience of educators made it possible to adjust the level to both young students and adults.The visits could be reserved in advance on the Genoa Science Festival online platform, and organisers took care of creating homogeneous groups of visitors in terms of age and scienti c background.
The in-person workshop was accessible during the full two weeks of the Genoa Science Festival from October 21 st to November 1 st , 2021.It was installed in a dedicated area (around 40 m 2 ) at the University Library of Genoa (see Fig. 6 left).The setup included a screen for slide projection, some nautical instruments, and three posters (59.4 cm × 84.1 cm each).In Fig. 6 right, a scienti c animator was showing one of the posters to some students.The workshop was visited by around 300 people in-person and the highest turnout was recorded on public holidays.
The digi-lab was online in the morning on November 3 rd , 4 th and 5 th .The activities were accessible through a web conference and students could virtually interact with the scienti c animators.This experience was very e ective in reaching far-away students that were not able to join the workshop in Genoa.Several remote sessions were carried out by two scienti c animators and were attended by about 350 students from 9 di erent schools all over Italy.Overall, the feedback from visitors was excellent, both regarding the quality of the pedagogical explanations and the originality of the interactive game.After every session, we collected the visitors' questions, opinions, and comments on the activities and the game's results.Several students reported that they were inspired by this activity and revealed their interest in delving deeper into the topics covered, approaching the sky with a more curious and scienti c approach.Moreover, teachers often asked us to use our application in class, considered it a valuable educational resource to introduce or consolidate topics related to coordinates and astronomy during their lessons.Lastly, suggestions have been collected to improve some technical aspects of the web app.They will be useful to upgrade the current version of Astronomy for sailors for future educational initiatives.
After the Genoa Science Festival, the PhysicalPub association rewarded the player who obtained the highest score.The prize up for grabs was a one-day sailing course at Lake Como, in Italy, o ered by the sponsor forSailing9 .Several gadgets were o ered also during the workshop notably, a paper-sextant to assemble provided by Reinventore e-shop10 .

Conclusion and prospects
In this contribution we have presented an educational workshop regarding orientation and celestial navigation that we had developed to engage students (at the junior college level) and the general public with astronomy.In particular, we focused on the innovative web application Astronomy for sailors which is the core of our workshop and provides a fun and interactive way of learning the basics of celestial navigation.We illustrated the technical solutions adopted for the web application's infrastructure, demonstrating how it is possible to set up a web platform from scratch in a relatively simple and way.We went through the structure of our workshop, articulated in three parts, including the last interdisciplinary session dedicated to naturalistic, historical and technological aspects, with an additional moment of confrontation for collecting questions and feedback.In future, we plan to couple the oral discussion with The workshop was presented in-person during the nineteenth edition of the Science Festival held in Genoa (Italy) in 2021, after the COVID-19 pandemic.To increase access to the workshop even in the post-pandemic period, also a full online digi-lab version was o ered.The total turnout was around 600 people.
At present, the web application Astronomy for sailors is still available online for free and it is currently adopted for seminars by the cultural association PhysicalPub.These educational activities may also be proposed in sailing centres and in the local divisions of the Italian Naval League (LNI).The interface, currently in Italian and in English will be available in Spanish and French soon.

Figure 1 :
Figure 1: Nautical instruments exhibited at the Genoa Science Festival: a marine chronometer, a sextant, a nautical almanac and some celestial charts.(Credit: G.Verna) Phoenicians became masters of the southwestern Mediterranean during the 1st millennium BCE being able to estimate the north-south position by looking at the North Star which the later Greeks called the Phoenician Star[7].Vikings colonised much of northern Europe, Iceland and Greenland around 1000 CE and crossed the Atlantic Ocean 500 years before Columbus landed in America.They could probably navigate by means of sky polarization in cloudy weather using a Sun compass and sunstone crystals[8].The sunstone crystals were possibly the Iceland spar, a transparent variety of calcite (CaCO 3 ) displaying an optical property called birefringence.This property permits to guess the position of the Sun when the sky is overcast[9].The geology department of the University of Genova provided some pieces of Icelandic spar that visitors could handle to directly observe the birefringence property.Coming to modern times, the functioning of satellite-based navigation systems was described in a third poster.Satellite navigation provides geo-spatial positioning using satellites and atomic clocks.The attention is focused on the accurate timing (up to a few nanoseconds) provided by atomic clocks which monitor the resonant frequency of atoms[10].The technologies employed in satellite navigation are a practical application of quantum physics, special and general relativity which are very captivating topics even for a non-specialist audience.

Figure 2 :
Figure 2: Cover image of the web application Astronomy for sailors (in Italian Astronaviganti literally means Astronavigators ).(Credit: C.Righi)

Figure 3 :
Figure 3: Virtual noon sight during the rst challenge in the Astronomy for sailors web app.The screen shows the session token (top left), the player's nickname (top right), the animation frozen at the (supposed) Sun's culmination (left), and two elds for entering the estimated latitude and longitude (right).

Figure 4 :
Figure 4: World map showing the position estimated by the player and its true location at the end of the rst challenge in the Astronomy for sailors web app.

Figure 5 :
Figure 5: The constellation identi cation game (image adapted from the web app Astronomy for sailors).

Figure 6 :
Figure 6: The workshop at the Genoa Science Festival 2021.Left: area reserved for the workshop (around 40 m 2 ) at the University Library of Genoa.Right: a scienti c animator showing one of the posters.(Credit: G.Verna) . It will allow us to quantitatively evaluate the didactic e cacy of the activities and the appreciation from the public.

Table 1 :
Sun's declination Sun at Solstices and Equinoxes.