Navigating the Stars

Chronicles of Computation — The Early Mechanisms

As we continue to go through the history of computation, we find ourselves under the starlit skies of ancient Greece where the astrolabe, an intricate device used for observing the heavens, was born. The astrolabe was a marvel of ancient engineering that allowed its users to solve complex problems related to time and the position of celestial bodies.

Photo by Johannes Plenio on Unsplash

The astrolabe was primarily invented by the ancient Greeks around 225 BCE, with Apollonius of Perga often credited for its creation, based on the theories and findings of Hipparchus. The device was a complex assembly of discs and pointers, capable of modeling the motion of the Sun, Moon, and stars. By aligning the device with a celestial body and reading the scales, users could determine the time of day or night, the time of sunrise and sunset, the length of the day, and the location of celestial objects in the sky.

The astrolabe was not just a tool for astronomers and navigators; it was also a symbol of the profound connection between the ancient Greeks and the cosmos. The Greeks believed that the universe was a harmonious and ordered system, and the astrolabe, with its intricate design and precise measurements, was a reflection of this cosmic order.

The astrolabe’s influence was not confined to Greece. During the Islamic Golden Age, the device was refined and widely used in navigation, astronomy, and even astrology. Islamic scholars made significant contributions to the development of the astrolabe, adding new features and scales, and creating a variety of types and designs. The astrolabe became an essential tool for Islamic astronomers, who used it to determine the times for prayer and the direction of Mecca.

Let’s create a simple example that demonstrates the concept of measuring the altitude of a celestial body, which is one of the functions of an astrolabe.

In this example, we’ll calculate the altitude of the sun at noon on the summer solstice, given the latitude of the observer. This is a simplified model, but it gives a basic idea of how an astrolabe can be used to measure celestial altitudes.

Here’s the Python code:

import math

TILT_OF_THE_EARTH_AXIS = 23.44 # Degrees

NEW_YORK_CITY_LATITUDE = 40.71 # Degrees

def get_sun_altitude(latitude):
    # Convert latitude from degrees to radians
    latitude_rad = math.radians(latitude)

    # Calculate the sun's declination
    # at the summer solstice
    declination = math.radians(TILT_OF_THE_EARTH_AXIS)

    # Calculate the altitude of the sun
    # at noon on the summer solstice
    altitude_rad = (math.pi / 2
                    - abs(latitude_rad - declination))

    # Convert altitude from radians to degrees
    altitude_deg = math.degrees(altitude_rad)

    return altitude_deg

# Get the altitude of the sun at noon
# on the summer solstice in New York City
altitude = get_sun_altitude(NEW_YORK_CITY_LATITUDE)

print("Altitude of the sun at noon "
      f"on the summer solstice: {altitude} degrees")

In this code, we first convert the observer’s latitude from degrees to radians. We then calculate the sun’s declination at the summer solstice, which is equal to the tilt of the Earth’s axis (23.44 degrees). The altitude of the sun at noon on the summer solstice is then calculated as 90 degrees minus the absolute difference between the observer’s latitude and the sun’s declination. Finally, we convert the altitude from radians back to degrees to get the final result.

Save the previous file as astrolabe.py and run it using Python. Here’s the output:

Altitude of the sun at noon on the summer solstice: 72.73 degrees

The astrolabe, with its intricate design, allowed the ancient Greeks and Islamic scholars to make precise astronomical observations and predictions. It was a critical tool for navigation, timekeeping, and even religious observances.

This story is part of the Chronicles of Computation book. The next section is Roman Counting Boards.