Pigeon head-bobbing → motion parallax → astronomical parallax → distances to nearby stars → calibration of Cepheid variable stars → distances to nearby galaxies → compare galaxy distance with spectral redshift → Hubble–Lemaître law → Hubble constant.
Today, let’s talk parallax.
As a young inchoate, nascent proto-WLBOTTer (approximately aged 5), I was sitting underneath my mom’s sewing table, and noticed that I could hold my hand out, close one eye, then the other, and see different things in the distance – some obscured when one eye open, but visible when the other eye was open. I naturally drew the conclusion that I had X-ray vision.
Little did I know that life was preparing me for a blott about parallax.
I also remember riding in the car and looking out the window. The nearby rows of crops would blur by, but the far end of the rows moved slowly. Distant hills moved even slower, and the newly risen full moon seemed to not move at all, as if it were following us.
So what is Parallax?
Parallax is a displacement or difference in the apparent position of an object viewed along two different lines of sight and is measured by the angle or half-angle of inclination between those two lines. Due to foreshortening, nearby objects show a larger parallax than farther objects, so parallax can be used to determine distances.
Old cartoons are a great way to observe the parallax effect. The Word Press Ninja has a good example:
From Gemini:
The system Disney developed was called the Multiplane Camera, invented by director and animator William Garity in 1937 specifically to solve the lack of parallax in traditional 2D animation.
The machine stood over twelve feet tall. Technicians arranged hand-painted animation cels and backgrounds on multiple horizontal sheets of plate glass suspended below a vertically mounted camera. Each layer of glass could slide independently and be lit separately, allowing foreground elements (like tree trunks) to move across the frame much faster than background elements (like distant mountains or the moon) as the camera zoomed or panned.
Disney first tested this setup on the 1937 Silly Symphony short The Old Mill before deploying it extensively on feature films like Snow White and the Seven Dwarfs, Pinocchio, and Bambi.
What Is Parallax? By Tereza Pultarova, Jim Lucas / Published January 11, 2022
Parallax is the observed displacement of an object caused by the change of the observer’s point of view. In astronomy, it is an irreplaceable tool for calculating distances of far away stars. […] It works like this: hold out your hand, close your right eye, and place your extended thumb over a distant object. Now, switch eyes, so that your left is closed and your right is open. Your thumb will appear to shift slightly against the background. By measuring this small change and knowing the distance between your eyes, you can calculate the distance to your thumb. That’s trigonometry.
When it comes to measuring distances to other stars, there are no two eyes that could do the trick. Instead, the orbit of Earth around the sun provides the baseline for these calculations.
Every six months, the planet changes its position with respect to the surrounding universe by 186 million miles (300 million kilometers). Since we are making this motion together with Earth, we can (theoretically) observe its effect as tiny circles that stars perform in the sky every year. Due to the vast distances to even the nearest stars, these circles are barely noticeable so detecting and measuring them is extremely difficult. […] The first known astronomical measurement using parallax didn’t involve a star but the moon. The ancient Greek astronomer Hipparchus reportedly used observations of a solar eclipse from two different locations to calculate the distance of Earth’s celestial companion.
Ancient Greeks used parallax for measurements An astronomer must measure the moon’s angular distance from a background object on a given night. At the same moment, another astronomer at a distant location must measure the same angular distance. Plug the information into a trigonometric formula and voila — instant distance.
More than two millennia ago, the Greek astronomer Hipparchus did just that.
As his background object, he chose the sun during a solar eclipse, probably the eclipse of 190 BCE. It was briefly total in the region of Greece called the Hellespont, a narrow strait we moderns call the Dardanelles.
However, at the exact moment some distance away in Alexandria, the eclipse covered only four-fifths of the sun. From that set of observations, Hipparchus drew a simple triangle and determined that the moon’s distance was at least 35.5 times the diameter of the Earth.
He later refined the minimum distance to 30.5 Earth diameters using a similar geometric technique.
Unfortunately, Hipparchus could not determine Earth’s diameter, but we can.
The Earth is, on average, 7.917.5 miles wide. If he had accurately determined Earth’s diameter, Hipparchus would have calculated the lunar distance as 241,284 miles away.
Modern radar technology has determined that the moon is 238,855 miles away on average. That’s 30.17 times Earth’s diameter, remarkable precision given the ancient Greeks’ technological level.
The Delaware Gazette by Tom Burns, the former director of the Perkins Observatory in Delaware.
Tom Burns teaches both introductory and upper-level writing courses, including Writing for the Workplace.
He combines diverse but complementary careers as a teacher, columnist, and astronomer. As an expository writing teacher for the past 21 years, he has taught a wide array of writing courses and given seminars on writing for businesses, schools, and other organizations.
As an astronomer, he is Director of Ohio Wesleyan’s Perkins Observatory and teaches astronomy classes in the OWU Department of Physics and Astronomy.
Combining these careers, he writes a weekly column on astronomy for The Delaware Gazette and regularly does both public relations and grant writing on behalf of Perkins Observatory and the endowment campaign to save this unique and historical facility.
Not only did Hipparchus figure out the method of determining the relative size of the moon, but he predicted a solar eclipse. How did he do that? According to Elder G2,
Hipparchus cracked this challenge using three key steps:
1. Orbital Cycles and Eclipse Limits (The Babylonian Data): Hipparchus synthesized centuries of Babylonian records to define precise lunar months—including the synodic month (new moon to new moon) and the draconic month (the time it takes the Moon to return to an orbital node where its tilted path crosses the ecliptic). A solar eclipse can only occur when a New Moon happens precisely at or near one of these nodes.
2. Inventing Trigonometry (Chords): To turn flat cycles into spherical reality, Hipparchus compiled the world’s first known table of chords (the precursor to modern sines). This gave him the tools to compute spherical triangles on the celestial sphere, tracking the exact angular speeds and positions of the Sun and Moon rather than assuming uniform, simple circles.
3. Calculating Topocentric Parallax: This was his true masterstroke. The Moon is close enough to Earth that two observers separated by a few hundred miles see it projected against completely different parts of the sky. Hipparchus realized that an eclipse predicted for the center of the Earth (geocentric) must be adjusted for an observer standing on the curved surface of the Earth (topocentric). By accounting for the Moon’s angular size (about 0.5°) and its parallax angle, he could calculate whether the Moon’s disk would actually align with the Sun from a specific geographic latitude.
Hipparchus turned this geometry right around in 129 BCE during a real solar eclipse. Noticing that the eclipse was 100% total at the Hellespont (the Dardanelles strait) but only 80% covered in Alexandria, he used the angular difference (0.1°, or 20% of the Sun’s diameter) and the known geographic distance between the two cities as a baseline.
Hipparchus
Hipparchus (ππαρχος) c. 190 – c. 120 BC, was a Greek astronomer, geographer, and mathematician. He is considered the founder of trigonometry, but is most famous for his incidental discovery of the precession of the equinoxes. Hipparchus was born in Nicaea, Bithynia, and probably died on the island of Rhodes, Greece. He is known to have been a working astronomer between 162 and 127 BC.
Hipparchus is considered the greatest ancient astronomical observer and, by some, the greatest overall astronomer of antiquity.
