# Columbus could have used a wrong estimate of earth's diameter

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In the tradition of the measurement of Eratosthenes (see Eratosthenes Measurement of the Circumference of the Earth), it is said the Columbus had the wrong number when planning his voyage []. Apparently, Posidonius estimated the Earth circumference to 180.000 stades instead of 250.000.

Now, assuming the Earth circumference is 40000km, and 250000 stades are the proper measurement, we get that 180.000 stades would give a circumference of 28000km. The distance from Madrid to Beijing is 9217km, which means that traveling the other way around would require 21000km (roughly). This is much more than the distance from Madrid to Mexico: 9000km.

With the proper measurement (250000 stades), the distance Madrid/Beijing through the ocean would have been 31000km.

## At constant latitude

At constant latitude, the distance Madrid/Beijing is 16000km through the ocean, and 9000km through land. Assuming the scaling factor of

$$180/250$$
for the earth circumference, and keeping the land-distance fixed at 9000km, one gets a total circumference at constant latitude of
$$25000km*180/250 = 18000km$$
. This means that the distance from Madrid to Beijing would have been 9000km through the ocean, which happens to be, by change, the distance from Madrid to Mexico.

• check how accurate was the measurement of the distance Europe/China in the XV century. #TODO