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In this activity we will build a simple cross-staff to measure angles. We will show how angular distances can be measured using this simple self-made aid in order to determine the position of a celestial object on the celestial sphere. (Please note that this activity can be followed by the activity: Chasing the Moon )
NOTE: This is the English translation of an original activity proposed by NAEC Team Croatia within the STEAM-Med co-design project developed by the OAE Center Italy (Lampedusa, Sicily, Italy from July 3 to 9, 2022). For more information about the project : read this Link
Material needed to build the cross-staff (See Image below).
Show how angular distances can be measured using one’s own body and a simple self-made aid in order to determine the position of a celestial object on the celestial sphere.
Measuring angles in astronomy is of great importance. By knowing the positions of celestial objects and their apparent movements, we can find out where we are among them, in which direction we are moving, predict eclipses, transits, occultations or even if we are in danger of colliding with one of the newly discovered asteroids. We can also find out the characteristics of other star and planetary systems or go back in time and analyze historical events. The positions of distant objects such as stars, star clusters, nebulae, galaxies, etc. are plotted in star maps where stars are represented by circles of different diameters depending on their apparent brightness (a brighter star is represented by a larger circle).¸In order to plot objects in star charts and determine their coordinates, it is necessary to define appropriate coordinate systems.
Coordinate Systems
The most frequently used celestial coordinate system is the equatorial one, whose main advantage is that it coincides with the Earth’s orientation in space. The reference plane is the celestial equator which coincides with the Earth’s, only the vernal equinox was chosen as the origin. Coordinates are right ascension and declination. The ecliptic coordinate system, in which the reference plane is the ecliptic plane measured with ecliptic longitude and latitude, is more suitable for describing motion in the solar system.
For more information:
https://en.wikipedia.org/wiki/Equatorial_coordinate_system
https://en.wikipedia.org/wiki/Ecliptic_coordinate_system
Students should be introduced to star charts and the starry sky to identify where the Moon is among the stars. Angles can be determined by the ratio of the distance and the size of the object. Using the method of similarity of triangles, it can be shown that it is possible to measure the mutual angular distances of distant objects.By simply measuring the angular distances between the Moon and nearby stars at night time without the use of instruments, it is possible to approximately determine its position on the star chart. A simple instrument such as cross-staff can be used for better accuracy, and the camera can be used to achieve even greater accuracy (comparing the position in the shot using the star chart).
Image: steps of the building procedure of the cross-staff
The cross-staff is now ready (see Image below).
Image: Cross staff measurements. (photo: A. Guštin)
Image: learning to use the cross-staff
Note: Angular distances can also be measured with a cross-staff in a plane inclined at any angle.
Look for the Big Dipper asterism in the clear night sky. Measure the distances between its stars with the cross-staff. In order to easily read the angular distance, illuminate the measuring scale with a dimmed red light. Verify if you have measured the distances correctly comparing your measurements with the calibration table below.
The big dipper.
Calibration table for angular distances between some stars in the Big Dipper asterism.
NOTE: In the southern hemisphere you should use stars in some bright constellation, Crux for example.
Evaluation of both the build-up of the physical object (cross-staff) and the knowledge acquired by the students could be considered.
To evaluate the physical object, teachers could consider the correctness, accurateness, and functioning of the cross-staff.
To evaluate the knowledge of the students , both a quiz or a guided class discussion could be used. Some of the questions that could be asked concern the angular distance of different objects both nearby and in the sky; the ability to identify specific celestial objects (e.g., Big Dipper); the understanding of sky charts.
This activity can be employed in several curricular subjects, such as: Science, Physics, Technology, and Mathematics.
For more information about the STEAM-Med co-design project : Read this Link
This activity is available in other languages: Link (to be provided soon).
In the second part of this activity, “Chasing the Moon”, students are guided in one of the practical applications of these measurement methods. Students can draw the phase and position of the Moon on a prepared celestial map and determine its coordinates in the ecliptic and/or equatorial celestial coordinate systems. Students will learn the basics of astrometry, that is, how they can determine the position of a celestial body (in this case the Moon) on the celestial sphere, and also that the Moon has a noticeable apparent motion between the stars.
