Pedro Duque, the Sun and the Moon: The Ratio That Stumps Many

The Sun is 400 times larger than the Moon: Pedro Duque's math

Amidst an astronomical controversy, a statement attributed to astronaut and former minister Pedro Duque has sparked a national debate over whether 400 is a significant figure. The quote states: "The Sun is 400 times larger than the Moon, but 400 times farther away; that is why, viewed from Earth, it can completely cover it." The dispute is not just astronomical; it is also a test of how science is communicated.

Diameter, surface area, or volume: they are not the same

The starting data is undisputed. The Sun's diameter is approximately 1,392,000 kilometers, while the Moon's is 3,474. The ratio yields approximately 400.32. The average distance from the Sun to Earth is about 389.17 times that of the Moon. This proportionality allows the Moon to perfectly overlap the solar disk during a total eclipse, a precision not found elsewhere in the solar system.

The problem arises when asking what "larger" means. By diameter, 400. By projected surface area, the Sun is about 160,000 times the Moon. By volume, the figure jumps to 64 million times. Hence, some consider Duque's statement an imprecise shortcut: "larger" without specifying the measured magnitude is technically ambiguous. Others argue that the context of an eclipse requires measuring diameters, not volumes, and that those using it as a flag of ignorance are demonstrating their own.

Aristarchus knew it: eclipses as a calculation rule

The controversy has a second, historical layer. The relationship between the size and distance of the Sun and Moon was first estimated over two thousand years ago. Aristarchus of Samos deduced, from eclipses and simple geometry, that the Sun had to be much farther and larger than the Moon. His method, which today sounds like a manual rule of three, is the basis of the calculation attributed to Duque and which some currents of analysis have rescued as the true core of the matter: before accusing an astronaut, one should remember that this lesson was taught in primary school.

The former minister's defense adds an uncomfortable authority argument: he has been to space. The counterargument is also not negligible: traveling does not immunize against a poorly constructed phrase or the obligation to name the correct magnitude. At some point, science becomes semantics.

Political bias creeps into an eclipse

One does not need to read much to find the third element: ideology. In comments on the statement, political labels appear almost before the numbers. Some reduce everything to Duque's ministerial past, others reproach him for distancing himself from the official narrative, and some respond with the contrary fallacy: if the "enemy" says something, it is wrong by definition. The result is that a verifiable astronomical proportion ends up being debated as if it were a budget line.

And added to this is the anecdote many cite as a symptom of numerical illiteracy: the architecture student who claimed that 75 square centimeters are three-quarters of a square meter, with the entire class agreeing. That such a blunder circulated without correction at university explains much of the current uproar: the debate is not against the data, but against others' mathematical insecurity.

The surprising fact

While the dispute continues, it is worth remembering that the Moon, with its 3,474 kilometers of diameter, is about three times larger than the Iberian Peninsula. And that the Sun, by volume, fits into the Moon 64 million times. Duque's statement is correct if speaking of diameters, incorrect if speaking of volume, and dangerous if left without nuance. But the true measure of this episode is another: when an astronomical statement from primary school generates eleven pages of dispute, what floats in the air is not science, but the mirror of a society that no longer knows which magnitude to believe in.