The Śaṅku Yantra

The structure of the Śaṅku Yantra is remarkably simple yet scientifically sophisticated. It consists of a circular horizontal platform at the center of which stands a vertical rod known as the śaṅku (gnomon). This rod is positioned perpendicular to the plane of the platform and serves as the principal observational element of the instrument.

Engraved on the circular platform are seven curved lines aligned along the east–west direction. These curves correspond to the zodiacal division points marked on the circumference of the platform. In essence, they indicate the Sun’s transition through the twelve zodiac signs, marking its movement from one sign to the next during the course of the year.

The position and shape of these curved lines vary according to the height of the śaṅku as well as the latitude and longitude for which the instrument is designed. Throughout the day, the shadow cast by the śaṅku falls upon the circular platform. By observing the path traced by the tip of the shadow relative to the curved lines, astronomers can determine the Sun’s declination, tropical zodiac sign, date of the year, equinoxes, altitude, the transitions of Uttarāyaṇa and Dakṣiṇāyana, and the changing seasons with remarkable accuracy.

Observation method

Observe the following components of the instrument carefully:

1. The Śaṅku Yantra is constructed on a circular horizontal platform.
2. At the exact center of the platform stands a vertical rod positioned perpendicular to the surface. This rod is known as the Śaṅku (Gnomon).
3. Seven curved lines are engraved on the circular platform, extending in the east–west direction.
4. These seven curves represent the Sun’s tropical zodiacal positions and variations in solar declination throughout the year.
5. The shadow cast by the Śaṅku falls upon the circular platform.

By observing the position of the tip of the Śaṅku’s shadow relative to these curved lines on different days of the year, one can determine various astronomical parameters, including time, the Sun’s tropical zodiac sign, solar declination, seasons, and the transitions of Uttarāyaṇa and Dakṣiṇāyana.

The above illustration shows the circular platform of the Śaṅku Yantra and the seven marked curved lines, numbered from Line 1 at the bottom to Line 7 at the top. The figure also indicates the corresponding values of solar declination and the Sun’s tropical zodiac signs.

Variation in the Śaṅku’s Shadow Throughout the Year

• 22 June – 22 July: During this period, the tip of the shadow of the Śaṅku (gnomon) gradually shifts from Line 1 toward Line 2. On 22 June, it lies on Line 1, and by 22 July, it reaches Line 2. The region between these two lines represents the tropical zodiac sign Cancer (Karka). During this interval, the Sun’s declination decreases from approximately 23.5° N to 20.2° N.
• 23 July – 22 August: During this period, the tip of the shadow of the Śaṅku gradually shifts from Line 2 toward Line 3. On 23 July, it lies on Line 2, and by 22 August, it reaches Line 3. The region between these lines represents the tropical zodiac sign Leo (Siṁha). During this interval, the Sun’s declination decreases from approximately 20.2° N to 11.5° N.
• 23 August – 22 September: During this period, the tip of the shadow of the Śaṅku gradually shifts from Line 3 toward Line 4. On 23 August, it lies on Line 3, and by 22 September, it reaches Line 4. The region between these lines represents the tropical zodiac sign Virgo (Kanyā). During this interval, the Sun’s declination decreases from approximately 11.5° N to 0°.
• 23 September – 22 October: During this period, the tip of the shadow of the Śaṅku gradually shifts from Line 4 toward Line 5. On 23 September, it lies on Line 4, and by 22 October, it reaches Line 5. The region between these lines represents the tropical zodiac sign Libra (Tulā). During this interval, the Sun’s declination changes from 0° to approximately 11.5° S, marking the southward motion of the Sun during Dakṣiṇāyana.
• 23 October – 21 November: During this period, the tip of the shadow of the Śaṅku gradually shifts from Line 5 toward Line 6. On 23 October, it lies on Line 5, and by 21 November, it reaches Line 6. The region between these lines represents the tropical zodiac sign Scorpio (Vṛścika). During this interval, the Sun’s declination increases from approximately 11.5° S to 20.2° S.
• 22 November – 21 December: During this period, the tip of the shadow of the Śaṅku gradually shifts from Line 6 toward Line 7. On 22 November, it lies on Line 6, and by 21 December, it reaches Line 7. The region between these lines represents the tropical zodiac sign Sagittarius (Dhanu). During this interval, the Sun’s declination increases from approximately 20.2° S to 23.5° S.
• 22 December – 20 January: During this period, the tip of the shadow of the Śaṅku gradually shifts from Line 7 toward Line 6. On 22 December, it lies on Line 7, and by 20 January, it reaches Line 6. The region between these lines represents the tropical zodiac sign Capricorn (Makara). During this interval, the Sun’s declination decreases from approximately 23.5° S to 20.2° S.
• 21 January – 19 February: During this period, the tip of the shadow of the Śaṅku gradually shifts from Line 6 toward Line 5. On 21 January, it lies on Line 6, and by 19 February, it reaches Line 5. The region between these lines represents the tropical zodiac sign Aquarius (Kumbha). During this interval, the Sun’s declination decreases from approximately 20.2° S to 11.5° S.
• 20 February – 20 March: During this period, the tip of the shadow of the Śaṅku gradually shifts from Line 5 toward Line 4. On 20 February, it lies on Line 5, and by 20 March, it reaches Line 4. The region between these lines represents the tropical zodiac sign Pisces (Mīna). During this interval, the Sun’s declination decreases from approximately 11.5° S to 0°.
• 21 March – 20 April: During this period, the tip of the shadow of the Śaṅku gradually shifts from Line 4 toward Line 3. On 21 March, it lies on Line 4, and by 20 April, it reaches Line 3. The region between these lines represents the tropical zodiac sign Aries (Meṣa). During this interval, the Sun’s declination increases from 0° to approximately 11.5° N as it moves northward during Uttarāyaṇa.
• 21 April – 21 May: During this period, the tip of the shadow of the Śaṅku gradually shifts from Line 3 toward Line 2. On 21 April, it lies on Line 3, and by 21 May, it reaches Line 2. The region between these lines represents the tropical zodiac sign Taurus (Vṛṣabha). During this interval, the Sun’s declination increases from approximately 11.5° N to 20.2° N.
• 22 May – 22 June: During this period, the tip of the shadow of the Śaṅku gradually shifts from Line 2 toward Line 1. On 22 May, it lies on Line 2, and by 22 June, it reaches Line 1. The region between these lines represents the tropical zodiac sign Gemini (Mithuna). During this interval, the Sun’s declination increases from approximately 20.2° N to 23.5° N, completing the annual cycle.

Note:

• 22 June (Summer Solstice): Sun in Cancer (Karka); longest day and shortest night.
• 22 September (Autumnal Equinox): Sun in Libra (Tulā); day and night are nearly equal.
• 21 March (Vernal Equinox): Sun in Aries (Meṣa); day and night are nearly equal.
• 22 December (Winter Solstice): Sun in Capricorn (Makara); shortest day and longest night.

This tool allows you to generate a calibrated template of the Śaṅku Yantra for your location by plotting the required curved lines on the instrument’s base. Follow the steps below:

1. Enter the Latitude and Longitude of your location.
2. Click the Reset button.
3. Click the Trace button and wait until the calibration tool completes the plotting of all seven curves.
4. Click the Trace button one more time if simulation stoped after tracing 6 curves.
5. Once the plotting process is complete, click the Print button to download the calibrated template.
6. Print the downloaded template at a suitable size according to your requirements.
7. Mark the required reference points and labels on the printout as shown in the figure below.

8. Carefully attach the printed template to the base platform of the Śaṅku Yantra.
9. Install the Śaṅku (Gnomon) vertically at the exact center of the circular base. The height of the gnomon should be maintained according to the following relation:
   
   Gnomon Height = 0.425 × Radius of the Generated Circle
10. Once assembled, the calibrated Śaṅku Yantra can be used to perform various astronomical observations and calculations specific to your location.