Abstract
In this study, a method to measure the Earth's axial tilt is attempted by using a telescope. As a principal instrument, telescopes in astronomy courses are mostly to verify the astronomical objects in sky and not to make sense of astronomical events such as seasonal changes which is explained by the Earth's axial tilt. This study outlines telescopic measurements to calculate the axial tilt at winter solstice.
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Earth's axial tilt toward ecliptic is a computable value. In a simple method, it was derived with the help of a nail's shadow on both solstice days (Işıldak 2009). In another study with homemade instruments, a method requiring observations on one of the solstice days was also offered to determine the angle (Işıldak 2016). In the current study we tried and tested this method by using a telescope on the winter solstice.
In figure 1, the directions toward the sun and Polaris are shown for equinoxial and solstitial days in a year. The blue arc represents the angle between Earth's axis of rotation and north ecliptic pole (NEP). The yellow arc represents the angle between solar direction and Polaris, and its value keeps changing during a year. One can determine its value for a specific moment by using an astronomy software. The angle between solar direction and Polaris is 90° at both equinoxes and reaches its extremum values at solstices. The angle becomes maximum (113.5°) at the winter solstice and minimum (66.5°) at the summer solstice.
Figure 1. Directions toward the Sun, north ecliptic pole (NEP) and Polaris are shown for equinoxial and solstitial points on Earth's orbit. The value of the angle (yellow) between solar and Polaris directions keeps changing during a year but is the same for every observer on the Northern Hemisphere. This angle is maximized to 113.5° on the winter solstice and minimized to 66.5° on the summer solstice. This method is only available at these days for an observer on Northern Hemisphere.
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Standard image High-resolution imageThe angle of Earth's axial tilt can be calculated with measurements on a solstice day because the vectors which are directed towards the Sun, NEP and Polaris are coplanar at such moments. Figure 2 illustrates the method used on 21 December 2015 for an observer in the Northern Hemisphere.
Figure 2. The measured angles (red and green) and computed angles (yellow and blue) for an observer (black dot) on the Northern Hemisphere. The angle of the axial tilt is between NEP and Polaris as well as ecliptic and equatorial planes.
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Standard image High-resolution imageIn this method the first step is to determine the angle (yellow arc) between the Sun and Polaris. The directions of these objects are determined and measured (red and green arcs) on 21 December at noon and midnight. Then, the angles between these objects are calculated. The difference between this angle and a 90° angle equals the value of the Earth's axial tilt (blue arc).
The existence of an almost fixed point only available for the Northern Hemisphere facilitates the calculation of this angle. The altitudes of the Sun and Polaris are not measurable simultaneously since the latter is not visible during day time. It is not a big drawback for the study because the change in the position of the Polaris with respect to an observer is a negligible amount. In fact, the Earth's rotation axis is tilted 0.75° from the Polaris star3 however this difference at most can accumulate to a 1.5° difference between midday and midnight. Therefore, the measurement for the Polaris can be conducted anytime where there is visibility of the night sky. However, it would be a reliable decision to locate and measure the directions when both the Sun and Polaris star are on the same local meridian. Then, the Polaris is measured at midnight in this study.
The telescope used in this study has an altazimuth-type mounting4. An optical tube placed on such a mounting can advance a 90° angle vertically. Before the measurements of the angle from the zenith direction to the Sun and Polaris directions, the tube must be oriented at neutral or 0° position at which it is directed toward zenith (figure 3). As a safety measure, the collector of the tube is covered with a solar filter for daytime observation. Then, the tube is declined until the sun is seen as centered on the ocular (figure 3(a)). At this point, the angle was found to be 64°. At midnight, the direction of Polaris was determined as shown in figure 3(b). Its direction was read on the telescope mount as 49°. The angle between the solar and lunar directions corresponds to the sum of the measured angles which is 113°. As described in figure 2, if one cuts down a right angle out of this obtuse angle, the resulting value which is 113° − 90° = 23° is to show the angle of the Earth' s tilt.
Figure 3. Telescope tube is at 0° position and directed toward zenith. (a) The Sun pictured through the tube. (b) Polaris pictured through the tube.
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Telescopes are nowadays available to schools for observational needs. We believe that telescopes must be utilized for measurement purposes. Telescopic measurements are opportunities for students to learn its operation actively. Also, such practices may develop awareness toward astronomy concepts in students. Telescopes must be handled in astronomy teaching to study astronomical events besides astronomical objects. Formation of seasons on Earth as an astronomical phenomenon is a miscellaneous topic in astronomy teaching and Earth's axial tilt plays a significant role in seasonal changes.
Since telescopes are common to schools, the axial tilt can be measured collectively by participation of telescope users on the hemisphere. This method can be implemented at locations with different altitudes on solstice days. Especially teachers and students at different locations who end up with similar values and can make the method prevalent.
In a previous study (Isildak 2016) the axial tilt was calculated on the summer solstice of 21 June with measurements obtained with a plastic pipe. This study repeated and verified the axial tilt by using a telescope on winter solstice. This method requires straightforward and obvious measurements and these can be carried to educational settings with various age levels. However, instructors should use caution for using a solar filter during day time observations. Children may be accompanied by their parents.