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Starts With A Bang

This Is How You Can Prove The Earth Is Round This Equinox

Two-hemisphere global composites of Moderate Resolution Imaging Spectroradiometer (MODIS) data, taken in 2001 and 2002. The twice-a-year equinox is the one time of year where measuring the Sun’s rays properly can allow you to determine your latitude without any other corrections, and if two or more people at the same longitude do this simultaneously, they can even calculate the circumference of the Earth. (NASA)

And if you have a friend at the same longitude, you can even measure its circumference.

This year’s equinox, on March 19/20 of 2020 (longitude-dependent), is Earth’s earliest in 124 years.

Even though the Earth always rotates on its axis, which is tilted at 23.5 degrees, the equinoxes are special for having that axial tilt be perpendicular to the Sun-Earth plane, rather than at an angle, which occurs on all other days of the year. Similarly, the solstices are what occurs at the midpoints between the equinoxes: when the Earth’s axis is maximally tilted with respect to the Earth’s orbital plane around the Sun. Our orbit’s elliptical nature is extremely important. (LARRY MCNISH / RASC CALGARY CENTRE)

At the moment of equinox, the Sun’s rays will strike the Earth perfectly perpendicular to its axis.

The equinoxes mark the exact moments when the Earth’s axis, as it revolves around the Sun in its orbit, is tipped perfectly perpendicular to the Sun’s rays. This only occurs twice a year: during the March and September equinoxes. (WIKIMEDIA COMMONS USER BLUESHADE)

It’s also the perfect time to do an experiment that reveals the curvature of the Earth.

The Earth always receives sunlight on 50% of its surface, but days and nights are only of equal length everywhere on our world during the equinox, when our rotational axis is tipped perpendicular to the orbital plane. (NASA / MESSENGER MISSION)

Wherever you are on Earth, find a perfectly vertical object and measure its height.

As the Sun moves throughout the sky, there will be an instant where a shadow cast by a perfectly vertical object reaches its minimum. If you can measure the angle cast by the shadow at that time, you’ll get an angle that corresponds perfectly to your latitude, but only if you perform this measurement on the day of the equinox. (BORA SHIN)

When the Sun reaches its highest point in the sky on the equinox, measure the length of that object’s shadow.

If you construct an apparatus with a perfectly vertical stick, you can use the moment at which the shadow is shortest to identify the angle at which the Sun (or Moon) must be at the zenith. For the Sun on the equinox, we can calculate our latitude; for the Moon, as long as we know our latitude, we can devise a way to calculate the Moon’s orbital tilt. (LARRY SESSIONS / COMMUNITY COLLEGE OF AURORA)

With a little math, you should be able to calculate the angle that the Sun makes with your vertical object.

If you measure the height (H) of your vertical object, along with the length (L) of the smallest shadow cast by that object with the Sun at its highest, you can take the inverse tangent of the ratio (L/H) to find an angle. On the equinox, that angle corresponds to your latitude. (ULRICH H. KURZWEG / UNIVERSITY OF FLORIDA)

On the equinox — and only on the equinox — that angle will be exactly equal to your latitude.

On the equinox, all of the Sun’s rays will strike the Earth at an angle that’s perpendicular to our axial tilt. This means that, at the Sun’s highest point in the sky, the shadows cast by a perfectly vertical object will create an angle that equals your latitude at all location on the planet’s surface. (NASA ILLUSTRATION BY ROBERT SIMMON)

Someone who experiences the Sun’s highest point at the same exact moment will have an identical longitude.

There is one particular latitude, coincident with Earth’s equator, where perfectly vertical objects will cast a shadow of 0 degrees on the equinox. To anyone located between the Tropic of Cancer and the Tropic of Capricorn, there will be at least one day out of the year where perfectly vertical objects cast no shadows as well, such as ‘Lahaina Noon’ as illustrated here in Hawaii. (DANIEL RAMIREZ / FLICKR)

The measured difference in angle will tell you your latitude difference, demonstrating the Earth’s curvature.

If the Earth were perfectly flat, then the Sun’s rays would cast identical shadows at the same time on all days everywhere on Earth (top), no matter where you were located. But if the Earth’s surface were curved (bottom), shadows at different locations would cast different shadows on the same day, depending on the angle that the Sun’s rays struck the object in question. By measuring the difference in shadow angle between two points on Earth’s surface, it became possible to measure the size of the Earth for the first time. (E. SIEGEL / BEYOND THE GALAXY)

If you measure (or know) the angular and physical distance between both observers, a 360° extrapolation reveals the Earth’s circumference.

If you know the arc-length between two points on Earth’s surface (by measuring the distance) as well as the difference in angle in degrees that the Sun’s rays make at identical longitudes at the same time, you can use the fact that there are 360 degrees in a circle to calculate the Earth’s circumference. (LARRY PHILLIPS; MODIFICATIONS BY E. SIEGEL)

This experiment was first performed ~2300 years ago: by Eratosthenes in Egypt.

More than two millennia ago, Eratosthenes realized that two different locations, Alexandria and Syene, had different length shadows cast on the same day of the year at the Sun’s highest point. By estimating the distance between the two cities (using travel-by-camel as a proxy), he made the first known calculation of the Earth’s circumference. (PIXABAY USER CLOUDBIRD)

This first proved Earth’s roundness, centuries before the space age, Biruni, or even Columbus.

The first photogram (1946) of the Earth’s curvature, as seen from a human-launched rocket. Although the space age enabled direct photography of the Earth’s curvature from space, methods stretching back more than two millennia have revealed not only the Earth’s shape, but its size as well. (U.S. MILITARY, WHITE SANDS NAVAL BASE, NEW MEXICO)

Mostly Mute Monday tells an astronomical story in images, visuals, 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.


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