If we want to reach for the stars, we have to start in our own backyard.
By looking at the sky alone, we can see the apparent, angular sizes of the Sun and Moon.
The Moon and Sun are both approximately half a degree in angular size, as viewed from Earth, with slight variations due to the elliptical nature of Earth’s and the Moon’s orbits. The Moon varies by more between apogee and perigee than the Sun does between aphelion and perihelion, indicating the Moon’s orbit around Earth is more elliptical than the Earth’s orbit around the Sun. (EHSAN ROSTAMIZADEH OF ASTROBIN)
But when the Sun, Earth, and Moon all align to produce a total eclipse, it teach us how far astronomical distances truly are.
When passing through a large amount of atmosphere, the bluer wavelengths of light are mostly scattered away, while the red light can make it through and land on the lunar surface during a total eclipse, which is why the Moon is visible, but red and dim, during a total lunar eclipse. (NASA)
During a lunar eclipse, the Earth’s shadow falls on the Moon; showing that the Earth is almost perfectly round.
By looking at the curvature of the Earth’s shadow that falls on the Moon, we can reconstruct the relative size of the Moon versus the Earth’s shadow-cone, allowing us to geometrically reconstruct the Earth-Moon distance. (FRED ESPENAK / MRECLIPSE.COM)
Local measurements of Earth’s curvature, combined with roundness, determine Earth is a sphere with a radius of ~6,400 km.
During the partial phases of a lunar eclipse, the shadow of Earth can be seen on the surface of the Moon, indicating quite clearly that it casts a roughly circular shape. With a knowledge of Earth’s size, we can use these measurements to determine the sizes of the Moon and Sun, and therefore their distances as well. (E. SIEGEL; ECLIPSE SEQUENCES BY WIKIMEDIA COMMONS USERS ZAERETH AND JAVIER SÁNCHEZ)
Geometry teaches us what the angular size of Earth’s shadow is relative to the Moon.
By digitally stitching together a series of images during the July 27th, 2018 lunar eclipse, Tom Harradine was able to demonstrate the relative size of Earth’s shadow on the Moon to the size of the apogee Moon itself. The Earth’s shadow appears 260% the size of the Moon.(TOM HARRADINE, VIA FACEBOOK, WITH PERMISSION)
recent, apogee lunar eclipse of July 27th gave a shadow-size of 260% the Moon’s apparent diameter. The Earth-Moon distances as shown, to scale, relative to the sizes of the Earth and Moon. This is what it looks like to have the Moon be approximately 60 Earth radii away: the first ‘astronomical’ distance ever determined, more than 2000 years ago. (NICKSHANKS OF WIKIMEDIA COMMONS)
This corresponds to an Earth-Moon distance that’s around 64 times the radius of Earth: 400,000 km at apogee.
Even modern missions that orbit nearly spatially aligned with the Earth and Sun need to be aware of the length of Earth’s shadow-cone, determined with surprising accuracy via eclipse measurements since well before the development of the telescope. (ESA)
It also teaches us the distance of Earth’s shadow-cone: 220 Earth radii: 1,400,000 km.
The average Sun-Earth distance is approximately 400 times the average Earth-Moon distance, allowing us to determine a distance measurement to the Sun. Note that using the apogee Moon distance will skew the results to be slightly too distant to the Sun. (NATIONAL AIR AND SPACE MUSEUM, SMITHSONIAN INSTITUTION)
From these figures and observations, we can derive the Earth-Sun distance as well, now known to be 23,000 Earth radii: 150,000,000 km.
The parallax method, employed since telescopes became good enough in the 1800s, involves noting the apparent change in position of a nearby star relative to the more distant, background ones.(ESA/ATG MEDIALAB)
The Earth-Sun distance can then be used in conjunction with parallax or relative brightness measurements.
The brightness distance relationship, and how the flux from a light falls off as one over the distance squared. If we learn how intrinsically bright a star is relative to the Sun, we can know its distance just by measuring its apparent brightness. (E. SIEGEL / BEYOND THE GALAXY)
Solely from measuring the Earth, Moon, and Sun, humans can determine how far away the stars are.
The distances between the Sun and many of the nearest stars shown here are accurate, but require us to calibrate with the Earth-Sun distance. We can learn that from eclipses alone. (ANDREW Z. COLVIN / WIKIMEDIA COMMONS) Mostly Mute Monday tells the astronomical story of an object, class, event or phenomenon in visuals, images, and no more than 200 words. Talk less; smile more. Ethan Siegel is the author of Beyond the Galaxy and Treknology. You can pre-order his third book, currently in development: the Encyclopaedia Cosmologica.