![]() Unfortunately, with these tiny angles, we can only measure stellar parallax for stars closer than about 300 light years. To measure this, we needed very precise instruments, indeed. Bright Sirius, a very close star at 8.6 light years, only shows a parallax of a mere 0.38 arcseconds, that is, 38 percent of 1/3600th of a degree. An excellent argument, but incorrect due to the great distances to the stars. Aristotle argued against the heliocentric model of the Solar System because he did not see the star positions changing through the year due to parallax. As Earth orbits the Sun, we see stars from opposite sides of our orbit. Parallax is also used to measure the distances to stars. The method was excellent, but the accuracy was limited by their instruments. Our current measurement is 93 million miles on average. Both measurements resulted in the Earth-Sun distance being about 87 million miles. Flamsteed observed the position of Mars just after sunset one evening and before sunrise the next morning (at opposition, a planet rises at sunset and sets at sunrise), so that Earth’s orbital motion changed his viewing position (Earth’s average orbital speed is 66,000 mph). Cassini’s colleague, Jean Richer, traveled to Cayenne Island, off the coast of French Guiana to observe the opposition while Cassini remained in Paris. Opposition is when a planet is opposite the Sun in the sky. The advent of the telescope allowed for more accurate measurements of angles so Giovanni Cassini and John Flamsteed both measured the distance to Mars using parallax during its opposition in 1672. Using careful observations and other geometry, the relative distances to the planets were known and used in the heliocentric model of the solar system presented by Copernicus so that once one distance was known accurately, the others were easily calculated. Thanks to the Apollo and other lunar missions, we have reflective cubes (corner cubes) on the Moon that reflect laser beams used to monitor its distance now. We now know it to be 60.3 Earth radii away on average, so this method was very accurate. His measurements gave a distance was between 62 and 73 Earth radii (the uncertainty is because the distance units he used are not precisely known). As shown in the diagram, this gave the distance to the moon as the distance from Alexandria to Syene divided by 1/10th of a degree in radians. The eclipse was total in Syene, but in Alexandria it was only 80% of totality. The Greek astronomer Hipparchus measured the distance to the Moon in units of Earth’s radius (Aristotle argued the Earth was round based on the shape of the shadow it cast on the Moon during eclipses) during a total eclipse of the Sun. In fact, there’s a simple trigonometric relationship between the angular shift in position (degrees of arc against the background), the separation of the eyes and the distance to the pencil. Most of us also realized that the distance the pencil appeared to move was smaller when it was held farther away from our eyes. Most of us discovered parallax as bored children holding a pencil in front of our face, looking with one eye then the other and noticing that the pencil appeared to move. The first tool used to measure cosmic distances was parallax, the apparent change in position of an object due to the change in position of the observer.
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