How did the ancient Greek calculate the circumference of the earth without the sophisticated tools & spaceships we have today?

 The ancient Greeks didn't have spaceships or advanced technology, but they were able to make reasonably accurate calculations of the Earth's circumference using simple tools and observations. One of the most famous attempts was made by the ancient Greek mathematician and astronomer Eratosthenes in the 3rd century BCE.

Eratosthenes noticed that on a particular day, the Sun was directly overhead in the city of Syene (now Aswan, Egypt), meaning that vertical objects cast no shadow. He then measured the angle of the shadow cast by a vertical stick in Alexandria, a city north of Syene, at the same time. Using this information and the distance between Syene and Alexandria, he was able to estimate the Earth's circumference.

Here's a basic outline of Eratosthenes' method:

1. **Measurement of the shadow:** Eratosthenes measured the length of a shadow cast by a vertical stick in Alexandria at noon on a specific day.

2. **Distance between cities:** He obtained the distance between Syene and Alexandria. This was done by hiring someone to pace out the distance or by using existing trade routes.

3. **Calculation:** Eratosthenes knew that the Sun's rays are essentially parallel. The angle of the shadow in Alexandria represented the difference in the Sun's angle at the two locations. Using this information and the distance between the cities, he could calculate the Earth's circumference.

Eratosthenes' estimate turned out to be remarkably accurate, coming within a few percentage points of the currently accepted value. His method was a clever application of geometry and observation, demonstrating the intellectual achievements of ancient Greek scholars in understanding the world around them without the advanced technology we have today.