From: 3blue1brown
While it was initially believed that the Sun revolved around the Earth, the ancient Greeks made significant strides in attempting to measure cosmic distances and even proposed a heliocentric model of the solar system [00:11:16].
Estimating the Sun’s Distance and Size
Determining the distance to the Sun was challenging [00:11:15]. The fact that the Moon and the Sun appear to be almost exactly the same size during a solar eclipse is a coincidence [00:11:30]. This visual similarity means that the ratio between the Moon’s radius and its distance from Earth is approximately the same as the ratio between the Sun’s radius and its distance from Earth [00:11:53]. Since the Greeks already knew the Moon’s ratio, they could estimate the Sun’s size if they could find its distance, or vice versa [00:12:09].
Using Moon Phases for Distance
To find the distance to the Sun, observers could use the phases of the Moon [00:12:50]. The Sun illuminates half of the Moon, and our perspective from Earth creates the observable phases [00:13:00]. The Moon’s phases also provide evidence that the Moon is round; if it were flat, we would not see phases but only a dim or lit Moon [00:13:14].
A crucial point for estimation is determining when a half Moon occurs [00:13:32]. A half Moon is observed when the Earth and the Sun form a right angle at the Moon [00:13:45]. The timing of a half Moon, relative to the midpoint between a new Moon and a full Moon, is directly related to the Sun’s distance [00:14:19]. A smaller angle between these points indicates a greater distance to the Sun [00:14:41]. Specifically, the distance to the Sun is the distance to the Moon divided by the sine of that measured angle [00:14:49].
Limitations and Inaccuracies
Ancient Greek astronomy encountered technological limitations at this point [00:14:56]. Aristarchus estimated that half Moons occurred 6 hours before the midpoint between new and full Moons [00:15:05]. However, this estimate was significantly incorrect; the actual discrepancy is only half an hour [00:15:16]. The inaccuracies stemmed from a lack of precise instruments like clocks that worked in the dark or telescopes [00:15:27]. While the mathematical method was sound, the technology available prevented accurate measurements [00:15:31].
Aristarchus’s calculation led him to believe the Sun was about 20 times further away than the Moon [00:15:38], when the true distance is closer to 370 times the Moon’s distance [00:15:46]. Consequently, he thought the Sun was 7 times larger than the Earth [00:15:49], while it is actually 109 times larger [00:15:53].
Aristarchus and the Heliocentric Model
Despite the measurement errors, Aristarchus made a profoundly important conceptual leap [00:15:55]. Given his (albeit inaccurate) estimate that the Sun was 7 times larger than the Earth, he concluded that it made more sense for the Earth to orbit the Sun rather than the other way around [00:16:08]. This marked the first proposal of the heliocentric model [00:16:23]. Copernicus later acknowledged Aristarchus’s prior proposition in his famous book [00:16:28].
Dismissal by Contemporaries: The Parallax Problem
Aristarchus’s contemporaries, however, dismissed his theory, for what they considered “good mathematical reasons” [00:16:32]. Their primary objection centered on the concept of parallax [00:16:49].
Parallax is the apparent shift in the relative position of objects due to a change in the observer’s viewing position [00:17:10]. If the Earth were orbiting the Sun, it would undergo significant movement through space over a year [00:17:37]. This movement should cause observable shifts in the patterns of constellations, with nearby stars appearing to move more than background stars [00:17:48].
Because the Greeks did not observe any such changes in the shape of constellations between seasons, they reasoned that the Earth could not be moving around the Sun [00:17:57]. The only way Aristarchus’s model could be true without observable parallax was if the stars were vastly further away than they believed—thousands and thousands of times bigger [00:18:03]. This seemed too improbable, leading to the dismissal of his theory [00:18:11].
The universe is, in fact, not just thousands of times larger than what the Greeks theorized, but actually billions and trillions of times larger [00:18:22]. This highlights how having correct mathematical reasoning or hypotheses can still lead away from the truth if technological limitations prevent accurate data collection or if the scale of reality is far beyond current imagination [00:18:13].
Later, Kepler would build upon the work of Copernicus, who had already established that planets revolve around the Sun in circular orbits and determined their orbital periods based on centuries of Babylonian observational data [00:18:52]. However, even Copernicus’s model, assuming circular orbits, did not perfectly fit the precise observational data collected by Tycho Brahe [00:21:05]. Kepler’s subsequent insights into elliptical orbits would become a moment of “pure genius” in understanding the solar system’s structure [00:00:02] [00:00:09] [00:01:56] [00:26:55].