1434: The Year a Chinese Fleet Sailed to Italy and Ignited the Renaissance. Gavin Menzies
360 degrees of longitude, the Chinese employed 3651⁄4 degrees. The Chinese used latitude degrees below Polaris (at 90° elevation). The Europeans used latitude above the equator (Polaris 0° elevation). The results are the same for both systems.
Diagrams showing the lines of latitude and longitude around a globe.
After establishing a common system for the earth, the Chinese next had to establish a common map of the heavens. Each navigator would have had to use the same name for the same star as well as the same star map from which longitude would have been determined.
How the Chinese Fixed the Stars’ Positions in the Sky
In the thirteenth century, the astronomer Guo Shoujing fixed the positions of key stars relative to Polaris (the Pole Star). Polaris appears on an extension of the earth’s axis, billions of miles away above the North Pole. Because of the earth’s rotation, the heavens appear to rotate around Polaris. The farther north one goes, the more of the heavens one can see.
In 1964 I was navigator of HMS Narwhal, a submarine operating under the polar ice cap. Now and then we would find clear-water “lakes,” called polynyas, where we would surface in order to fix our position by the stars. The heavens appeared like a vast globe above us. As we approached the North Pole, we seemed to be inside a bowl looking at a hemisphere of stars spreading in an arc down to the horizon all around us.
Diagram showing the positions of ships A and B on a globe.
Ship A is at 20° N 20° W, Ship B is at 0° N 20° E.
Ships A and B discovering new lands at point C will have the same
position for the new land: 10° N 0° E.
At the North Pole, the Chinese could fix the position of every star in the Northern Hemisphere relative to Polaris. The stars are so far away that to an observer on earth they never change their positions relative to one another.
The Chinese divided the sky into twenty-eight segments or mansions. Picture an orange with its skin sliced; the cuts start where the orange was fixed to its tree and continue vertically downward. They called each mansion a hsiu. They fixed the position of stars at the top of each of the twenty-eight mansions relative to the Pole Star (ABC).
Then they fixed stars in the lower part (DEF) of each segment relative to those in the upper part (ABC). Because stars never change their position relative to one another, even if the Chinese were not near the North Pole and hence could not see the stars in the lower part of each segment (because these stars were below the horizon), they always knew the stars’ positions. So they could produce star maps.
The Chinese fixed the position of stars at the top of each
of the 28 lunar mansions relative to the Pole Star.
They noted the vertical positions of each star below Polaris (none can be above Polaris) and the horizontal position of each hsiu relative to Nanjing (longitude). The Chinese called the vertical height of each star below Polaris “declination” and its position around the equator from Nanjing “right ascension.” So for the stars in the sky, the Chinese had the same system of measurement they used to determine latitude and longitude. This system was called the equatorial system—vastly simpler than the equinoctial system, used in medieval times before Guo Shoujing, which relied on the ecliptic or the horizon. After 1434, Europeans adopted the Chinese system, which remains in use today.
Next, the Chinese needed precise instruments to mea sure each star’s position. Guo Shoujing provided the tools. A sighting tube was first positioned by pointing it at Polaris at precisely the angle of the observer’s latitude—that is, if the observer was at the North Pole, the sighting tube would be at 90° elevation (see page 34). On this diagram, the instrument is aligned to Polaris at 39°49 N, the latitude of Beijing. Once positioned, the instrument was bolted down—because if the angle changed from the latitude of the observer, it became useless.
The observer then selected a star, looking at it through another tube attached to a circle marked in degrees. The movement of the tube along the circle gave the number of degrees below Polaris of the selected star (the arc y-z), which is the star’s declination.
The horizontal angle, the angle from Nanjing, was found by rotating the ring around the equatorial circle, which gave the horizontal angle of the star from Nanjing (its right ascension). The position of the star then was entered in the star tables. The Chinese entered 1,461 stars in their tables, a process that required many astronomers and hundreds of years.
Tables were printed and, along with a star map, given to each navigator. Thus all navigators possessed a common system of latitude and longitude to fix their positions on the globe, and an identical map of the heavens, which enabled them to recognize each star.
A torquetum based on the equatorial system, as used by Zheng He’s
navigators and pioneered by Guo Shoujing.
How the Star Tables Allowed Longitude to Be Calculated
For the following description, I am indebted to Professor Robert Cribbs, who has tested the method described to prove its efficacy. This method allows longitude to be determined on any clear day without waiting for a lunar eclipse and without sending messages back to the observer in Beijing. It is a much more advanced method than that described in my book 1421 (that method, kindly explained to me by Professor John Oliver and Marshall Payn, is dependent on eclipses of the moon, which do not happen all that frequently).
Professor Cribbs’s method is based on the fact that the earth not only rotates on its own axis every twenty-three hours and fifty-six minutes but also travels in an ellipse around the sun—something Guo Shoujing had worked out back in 1280. The combination of these two movements means there is a slip of four minutes each day between the time when the earth is in the same position relative to the sun (solar time, twenty-four hours) and the time when the earth is in the same position relative to the stars (sidereal time, twenty-three hours and fifty-six minutes). This slip between sidereal time and solar time amounts to one day every 1,461 days, or four years. The effect is that every midnight, twelve hours after the sun has hit its highest point in the sky, a different star will be in line with Polaris than the day before.
This is a typical star map as used by Zheng He and his navigators.
Astronomers in Nanjing observed the night sky for every day of the 1,461-day cycle and noted the star in line with Polaris at precisely midnight. They produced a table of 1,461 days, which was dispensed to navigators. The 1408 astronomical calendar covers 366 days of that cycle. A copy of a page of the 1408 astronomical tables is reproduced later in the color insert of this book.
With the tables in hand, a navigator in, say, the Indian Ocean must know only which day of the cycle it is, which he calculates by the number of sunsets that have occurred since he left Nanjing. If he left Nanjing on day 61 of the cycle and has noted eighty sunsets, then it is day 141. On the tables, he can see that Aldebaran is in line with Polaris on day 141 (to the Nanjing observer).
However, in the Indian Ocean he observes another, unrecognized star in line with Polaris. He consults his star map and confirms from the tables that it is Betelgeuse. He can now make one of two calculations: he can note the difference in right ascension between Aldebaran