1.2 The Size of Our Cosmos

summary

Great thinkers throughout history have always been fascinated by the enormity of the world around them.

- Humans have repeatedly underestimated two things—the size of our cosmos, and our ability to comprehend its size.
- As science progressed, the scope of the universe continued to be elucidated.

More than 2,000 years ago, Eratosthenes was able to accurately calculate the circumference of the Earth.

- Eratosthenes, a Greek mathematician and astronomer, invented the discipline of geography, and later became chief librarian at the Library of Alexandria.
- By examining the overhead angle of the Sun in two different cities, he determined their angular separation on the surface of the planet.
- This allowed him to calculate the circumference of the Earth to be 39,700 km—within less than 1% error of modern measurements.

Aristarchus closely measured the size and distance of the Moon, as well as the distance of the Sun.

- He noticed that when the Earth cast a shadow on the Moon, the shadow had a curved edge. This implied that the Earth was much larger than the Moon—Aristarchus calculated Earth to be approximately 3.7 times bigger.
- Knowing the size of the Earth allowed Aristarchus to calculate that of the Moon, and by including the angle that it subtends in the sky, he worked out its distance from Earth—about 30 Earth diameters away.
- To calculate the distance of the Sun, Aristarchus contemplated right triangles between the Sun, Earth, and Moon during two moon phases, where the hypotenuse would have been the distance between the Earth and the Sun.
- Unfortunately, due to a lack of error analysis in those years, Aristarchus, Copernicus, and others had underestimated the scale of the solar system by a factor of 20.

Many years later, in the 19

^{th}century, Bessel used the method of*parallax*to accurately calculate distances of celestial bodies.- Parallax uses the orbit of the Earth to observe an apparent “shift” in position of an object against the background of other distant objects.
- When Earth is on opposite sides of the Sun during its yearly revolution, the angle we observe a celestial body at changes due to Earth’s location.
- The distance between the Sun and that distant object can then be calculated trigonometrically, having measured the parallax angles and knowing the distance between the Sun and Earth.

Astronomers continue to discover grander and grander structures that seem to go on forever.

- For instance, it wasn’t until 1925 that Hubble discovered the clustering of stars known as galaxies.
- The distances he calculated for some of these galaxies completely shattered previous expectations of the size of the universe.
- And still, the mystery of space possibly being truly infinite remains unanswered.
- The general theory of relativity suggests the possibility of a non-Euclidean, curved space (potentially meaning a finite universe), but all modern measurements point to a very “flat” universe—and so we have no evidence to suggest the universe is
*not*infinite.