21. Zodiacal light

Brian May is best known as the guitarist of the rock band Queen.[1] The band formed in 1970 with four university students: May, drummer Roger Taylor (not the drummer Roger Taylor who later played for Duran Duran), singer Farrokh “Freddie” Bulsara, and bassist Mike Grose, playing their first gig at Imperial College in London on 18 July. Freddie soon changed his surname to Mercury, and after trying a few other bass players the band settled on John Deacon.

Brian May 1972

Brian May, student, around 1972, with some equipment related to his university studies. (Reproduced from [2].)

While May continued his studies, the fledgling band recorded songs, realeasing a debut self-titled album, Queen, in 1973. It had limited success, but they followed up with two more albums in 1974: Queen II and Sheer Heart Attack. These met with much greater success, reaching numbers 5 and 2 on the UK album charts respectively. With this commercial success, Brian May decided to drop his academic ambitions, leaving his Ph.D. studies incomplete. Queen would go on to become one of the most successful bands of all time.

Lead singer Freddie Mercury died of complications from AIDS in 1991. This devastated the band and they stopped performing and recording for some time. In 1994 they released a final studio album, consisting of reworked material recorded by Mercury before he died plus some new recording to fill gaps. And since then May and Taylor have performed occasional concerts with guest singers, billed as Queen + (singer).

The down time and the wealth accumulated over a successful music career allowed Brian May to apply to resume his Ph.D. studies in 2006. He first had to catch up on 33 years of research in his area of study, then complete his experimental work and write up his thesis. He submitted it in 2007 and graduated as a Doctor of Philosophy in the field of astrophysics in 2008.

Brian May 2008

Dr Brian May, astrophysicist, in 2008. (Public domain image from Wikimedia Commons.)

May’s thesis was titled: A Survey of Radial Velocities in the Zodiacal Dust Cloud.[2] May was able to catch up and complete his thesis because the zodiacal dust cloud is a relatively neglected topic in astrophysics, and there was only a small amount of research done on it in the intervening years.

We’ve already met the zodiacal dust cloud (which is also known as the interplanetary dust cloud). It is a disc of dust particles ranging from 10 to 100 micrometres in size, concentrated in the ecliptic plane, the plane of orbit of the planets. Backscattered reflection off this disc of dust particles causes the previously discussed gegenschein phenomenon, visible as a glow in the night sky at the point directly opposite the sun (i.e. when the sun is hidden behind the Earth).

But that’s not the only visible evidence of the zodiacal dust cloud. As stated in the proof using gegenschein:

Most of the light is scattered by very small angles, emerging close to the direction of the original incoming beam of light. As the scattering angle increases, less and less light is scattered in those directions. Until you reach a point somewhere around 90°, where the scattering is a minimum, and then the intensity of scattered light starts climbing up again as the angle continues to increase. It reaches its second maximum at 180°, where light is reflected directly back towards the source.

This implies that there should be another maximum of light scattered off the zodiacal dust cloud, along lines of sight close to the sun. And indeed there is. It is called the zodiacal light. The zodiacal light was first described scientifically by Giovanni Cassini in 1685[3], though there is some evidence that the phenomenon was known centuries earlier.

Title page of Cassini's discovery

Title page of Cassini’s discovery announcement of the zodiacal light. (Reproduced from [3].)

Unlike gegenschein, which is most easily seen high overhead at midnight, the zodiacal light is best seen just after sunset or just before dawn, because it appears close to the sun. The zodiacal light is a broad, roughly triangular band of light which is broadest at the horizon, narrowing as it extends up into the sky along the ecliptic plane. The broad end of the zodiacal light points directly towards the direction of the sun below the horizon. This in itself provides evidence that the sun is in fact below the Earth’s horizon at night.

zodiacal light at Paranal

Zodiacal light seen from near the tropics, Paranal Observatory, Chile. Note the band of light is almost vertical. (Creative Commons Attribution 4.0 International image by ESO/Y.Beletsky, from Wikimedia Commons.)

The zodiacal light is most easily seen in the tropics, because, as Brian May writes: “it is here that the cone of light is inclined at a high angle to the horizon, making it still visible when the Sun is well below the horizon, and the sky is completely dark.”[2] This is because the zodiacal dust is concentrated in the plane of the ecliptic, so the reflected sunlight forms an elongated band in the sky, showing the plane of the ecliptic, and the ecliptic is at a high, almost vertical angle, when observed from the tropics.

zodiacal light at Washington

Zodiacal light observed from a mid-latitude, Washington D.C., sketched by Étienne Léopold Trouvelot in 1876. The band of light is inclined at an angle. (Public domain image from Wikimedia Commons.)

Unlike most other astronomical phenomena, this shows us in a single glance the position of a well-defined plane in space. From tropical regions, we can see that the plane is close to vertical with respect to the ground. At mid-latitudes, the plane of the zodiacal light is inclined closer to the ground plane. And at polar latitudes the zodiacal light is almost parallel to the ground. These observations show that at different latitudes the surface of the Earth is inclined at different angles to a visible reference plane in the sky. The Earth’s surface must be curved (in fact spherical) for this to be so.

zodiacal light from Europe

Zodiacal light observed from higher latitude, in Europe. The band of light is inclined at an even steeper angle. (Public domain image reproduced from [4].)

[I could not find a good royalty-free image of the zodiacal light from near-polar latitudes, but here is a link to copyright image on Flickr, taken from Kodiak, Alaska. Observe that the band of the zodiacal light (at left) is inclined at more than 45° from the vertical. https://www.flickr.com/photos/photonaddict/39974474754/ ]

zodiacal light at Mauna Kea

Zodiacal light seen over the Submillimetre Array at Mauna Kea Observatories. (Creative Commons Attribution 4.0 International by Steven Keys and keysphotography.com, from Wikimedia Commons.)

Furthermore, at mid-latitudes the zodiacal light is most easily observed at different times in the different hemispheres, and these times change with the date during the year. Around the March equinox, the zodiacal light is best observed from the northern hemisphere after sunset, while it is best observed from the southern hemisphere before dawn. However around the September equinox it is best observed from the northern hemisphere before dawn and from the southern hemisphere after sunset. It is less visible in both hemispheres at either of the solstices.

seasonal variation in zodiacal light from Tenerife

Seasonal variation in visibility of the zodiacal light, as observed by Brian May from Tenerife in 1971. The horizontal axis is day of the year. The central plot shows time of night on the vertical axis, showing periods of dark night sky (blank areas), twilight (horizontal hatched bands), and moonlight (vertical hatched bands). The upper plot shows the angle of inclination of the ecliptic (and hence the zodiacal light) at dawn, which is a maximum of 87° on the September equinox, and a minimum of 35° on the March equinox. The lower plot shows the angle of inclination of the ecliptic at sunset, which is a maximum of 87° on the March equinox. (Reproduced from [2].)

This change in visibility is because of the relative angles of the Earth’s surface to the plane of the dust disc. At the March equinox, northern mid-latitudes are closest to the ecliptic at local sunset, but far from the ecliptic at dawn, while southern mid-latitudes are close to the ecliptic at dawn and far from it at sunset. The situation is reversed at the September equinox. At the solstices, mid-latitudes in both hemispheres are at intermediate positions relative to the ecliptic.

seasonal variation of Earth with respect to ecliptic

Diagram of the Earth’s tilt relative to the ecliptic, showing how different latitudes are further from or closer to the ecliptic at certain times of year and day.

So the different seasonal visibility and angles of the zodiacal light are also caused by the fact that the Earth is spherical, and inclined at an angle to the ecliptic plane. This natural explanation does not carry over to a flat Earth model, and none of the observations of the zodiacal light have any simple explanation.


[1] Google search, “what is brian may famous for”, https://www.google.com/search?q=what+is+brian+may+famous+for (accessed 2019-07-23).

[2] May, B. H. A Survey of Radial Velocities in the Zodiacal Dust Cloud. Ph.D. thesis, Imperial College London, 2008. https://doi.org/10.1007%2F978-0-387-77706-1

[3] Cassini, G. D. “Découverte de la lumière celeste qui paroist dans le zodiaque” (“Discovery of the celestial light that resides in the zodiac”). De l’lmprimerie Royale, par Sebastien Mabre-Cramoisy, Paris, 1685. https://doi.org/10.3931/e-rara-7552

[4] Guillemin, A. Le Ciel Notions Élémentaires D’Astronomie Physique, Libartie Hachette et Cie, Paris, 1877. https://books.google.com/books?id=v6V89Maw_OAC

16. Lunar eclipses

Lunar eclipses occur when the Earth is positioned between the sun and the moon, so that the Earth blocks some or all of the sunlight from directly reaching the moon. Because of the relative sizes of the sun, Earth, and moon, and their distances from one another, the Earth’s shadow is large enough to completely cover the moon.

To talk about eclipses, we need to define some terms. The sun is a large, extended source of light, not a point source, so the shadows that objects cast in sunlight have two components: the umbra, where light from the sun is totally blocked, and the penumbra, where light from the sun is partially blocked.

Umbra and penumbra

Diagram showing the umbra and penumbra cast by the Earth. Not to scale. Public domain image from Wikimedia Commons.

When the moon passes entirely inside the Earth’s umbra, that is a total lunar eclipse. Although no sunlight reaches the moon directly, the moon is not completely dark, because some sunlight refracts (bends) through the Earth’s atmosphere and reaches the moon. This light is red for the same reason that sunsets on Earth tend to be red: the atmosphere scatters blue light more easily than red, so red light penetrates large distances of air more easily. This is why during a total lunar eclipse the moon is a reddish colour. Although a totally eclipsed moon looks bright enough to our eyes, it’s actually very dark compared to a normal full moon. Our eyes are very good at compensating for the different light levels without us being aware of it.

Total lunar eclipse

Total lunar eclipse of 28 August 2007 (photographed by me). 1 second exposure at ISO 800 and aperture f/2.8.

The amount of refracted light reaching the moon depends on the cleanliness of the Earth’s atmosphere. If there have been recent major volcanic eruptions, then significantly less light passes through to reach the moon. The brightness of the moon during a total lunar eclipse can be measured using the Danjon scale, ranging from 0 for very dark eclipses, to 4 for the brightest ones. After the eruption of Mount Pinatubo in the Philippines in 1991, the next few lunar eclipses were extremely dark, with the eclipse of December 1992 rating a 0 on the Danjon scale.

When the moon is only partly inside the Earth’s umbra, that is a partial lunar eclipse. A partial phase occurs on either side of a total lunar eclipse, as the moon passes through the Earth’s shadow, and it can also occur as the maximal phase of an eclipse if the moon’s orbit isn’t aligned to carry it fully within the umbra. During a partial eclipse phase, you can see the edge of the Earth’s umbral shadow on the moon.

Partial lunar eclipse phase

Partial phase of the same lunar eclipse of 28 August 2007. 1/60 second exposure at ISO 100 and f/8, which is 1/3840 the exposure of the totality photo above. If this photo was 3840 times as bright, the dark part at the bottom would look as bright as the totality photo (and the bright part would be completely washed out).

Lunar eclipses can only occur at the full moon – those times when the sun and moon are on opposite sides of the Earth. The moon orbits the Earth roughly once every 29.5 days and so full moons occur every 29.5 days. However, lunar eclipses occur only two to five times per year, because the moon’s orbit is tilted by 5.1° relative to the plane of the Earth’s orbit around the sun. This means that sometimes when the moon is full it is above or below the Earth’s shadow, rather than inside it.

Okay, so what can lunar eclipses tell us about the shape of the Earth? A lunar eclipse is a unique opportunity to see the shape of the Earth via its shadow. A shadow is the same shape as a cross-section of the object casting the shadow. Let’s have another look at the shape of Earth’s shadow on the moon, in a series of photos taken during a lunar eclipse:

Lunar eclipse montage

Montage of photos taken over 83 minutes during the lunar eclipse of 28 August 2007. Again, the bottom row of photos have 3840 times the exposure of the top row, so the eclipsed moon is nearly 4000 times dimmer than the full moon.

As you can see, the edge of the Earth’s shadow is curved. The fact that the moon’s surface is curved doesn’t affect this, because we are looking from the same direction as the Earth, so we see the same cross-section of the moon. (Your own shadow looks the shape of a person to you, even if it falls on an irregular surface where it looks distorted to someone else.) So from this observation we can conclude that the edge of the Earth is rounded.

Many shapes can cause a rounded shadow. However, if you observe multiple lunar eclipses, you will see that the Earth’s shadow is always round, and what’s more, it always has the same radius of curvature. And different lunar eclipses occur at any given location on Earth with the moon at different points in the sky, including sometimes when the moon is not in the sky (because the location is facing away from the moon). This means that different lunar eclipses occur when different parts of the Earth are facing the moon, which means that different parts of the Earth’s edge are casting the shadow edge on the moon. So from these observation, we can see that the shape of the shadow does not depend on the orientation of the Earth to the moon.

There is only one solid shape for which the shape of its shadow doesn’t depend on the object’s orientation. A sphere. So observations of lunar eclipses show that the Earth is a globe.

Addendum: A common rebuttal by Flat Earthers is that lunar eclipses are not caused by the Earth’s shadow, but by some other mechanism entirely – usually another celestial object getting between the sun and moon and blocking the light. But any such object is apparently the same colour as the sky, making it mysteriously otherwise completely undetectable, and does not have the simple elegance of explanation (and the supporting evidence from numerous other observations) of the moon moving around the Earth and entering its shadow.

6. Gegenschein

If you shine a light into a suspension of fine particles, the particles will scatter the light. This is easy enough to show with a little bit of flour stirred into a glass of water, or with a dilute solution of milk in water, in which case the particles are small globules of fat. You can see a beam of light passing through such a medium because of the scattering, which is known as the Tyndall effect.

We can model the interaction of light with the scattering particles using Mie scattering theory, named after German physicist Gustav Mie. This is essentially a set of solutions of Maxwell’s equations for the propagation of electromagnetic radiation (in this case, light) in the presence of the scattering objects. If you solve these equations for diffuse particles a bit bigger than the wavelength of light, you can derive the angular distribution of the scattered light. The scattering is far from uniform in all directions. Rather, it has two distinct lobes. Most of the light is scattered by very small angles, emerging close to the direction of the original incoming beam of light. As the scattering angle increases, less and less light is scattered in those directions. Until you reach a point somewhere around 90°, where the scattering is a minimum, and then the intensity of scattered light starts climbing up again as the angle continues to increase. It reaches its second maximum at 180°, where light is reflected directly back towards the source.

This bright spot of reflected light back towards the source is called backscatter. It can be seen when shining light into smoke or fog. It’s the reason why some cars have special fog lights, angled down to illuminate the road, rather than shine straight into the fog and reflect back into the driver’s eyes. Backscatter is also the reason for the bright spot you might have noticed on clouds around the shadow of a plane that you’re flying in (at the centre of the related optical phenomenon of glories).

Another place where there is a collection of smoke-sized particles is in interplanetary space. In the plane of the planets’ orbits around the sun, there is a considerable amount of left over material of sizes around 10 to 100 micrometres, constantly being replenished by asteroid collisions and outgassing from comets. This material is called the interplanetary dust cloud, or the zodiacal dust cloud, because it is densest in the ecliptic—the plane of the planets—which runs through the zodiac constellations. This dust has been sampled directly by several deep space probes: Pioneers 10 and 11, Ulysses, Galileo, Cassini, and New Horizons.

The brightest source of light in the solar system is the sun. As it shines through this interplanetary dust cloud, some of the light is scattered. Most of the scattered light is deflected only by small angles, in accordance with Mie theory. But some is backscattered, and in the backscatter direction there is a peak in brightness of the scattered light directly back towards the sun. S. S. Hong published a paper in 1985, with calculations of the scattering angles of light by the interplanetary dust cloud [1]. Here’s the pertinent plot from the paper:

Scattering intensity v. angle for interplanetary dust

Scattering intensity versus scattering angle for interplanetary dust. Figure reproduced from [1].

The different curves correspond to different choices of a power law to model the size distribution of the dust particles. In each case you can see that most of the scattering occurs at small angles, there is a minimum of scattering intensity around 90°, and the scattering increases again to a second maximum at 180°, the backscattering angle.

As an aside, this backscattering also occurs in interstellar dust, and here’s a figure from a paper by B. T. Draine showing scattering intensity versus angle for the measured dust distributions of the Small Magellanic Cloud, Large Magellanic Cloud, and Milky Way galaxy, plotted for several wavelengths of light [2]. The wavelengths are shown in Angstroms, and in these units visible light occurs between 4000 and 7000 Å (lower being ultraviolet and higher infrared). In these cases the models show minima in scattering around 130°, with the backscattering again being maximal at 180°.

Scattering intensity v. angle for interstellar dust

Scattering intensity versus scattering angle for interstellar dust. Figure reproduced from [2].

We’re not concerned with interstellar dust here, but it shows the general principle that there is a peak in scattered light directly back towards the light source, from fog, smoke, and space dust.

We are concerned with backscatter from the interplanetary dust cloud. Given that this phenomenon occurs, it implies that if we could look into space in the direction exactly opposite the direction of the sun, then we should see backscatter from the interplanetary dust.

If the Earth is spherical, then night time corresponds to the sun being behind the planet. You should see, in the night sky, the point exactly opposite the direction of the sun. You should be able to see, in that direction, the backscattered light of the sun from the interplanetary dust cloud.

Now let’s imagine the Earth is flat. The sun shines on some part of the Earth at all times, so therefore it must be above the plane of the Earth at all times. (How some parts of that plane are in the dark of night is a question for another time. Some Flat Earth models propose a sort of cosmic lampshade for the sun, which makes it more like a spotlight.) At any rate, it should never be possible to look into the sky in the exact opposite direction to the sun. So there should be no point in the night sky with a peak of backscattered sunlight.

Now that we’ve made the predictions from our models, what do we actually see? It turns out that the backscattered sunlight is a visible phenomenon, and it can be seen exactly where predicted by the spherical Earth model. It’s a faint glow in the night sky, centred on the point in the exact opposite direction to the sun. The earliest recorded description of it comes from 1730, by the French astronomer Esprit Pézenas. The German explorer Alexander von Humboldt wrote about it around 1800 on a trip to South America, and gave it the name Gegenschein (German for “counter-shine”).

Unfortunately, in our modern industrial society light pollution is so bad that it’s almost impossible to see the gegenschein anywhere near where people live. You need to go somewhere remote and far away from any settlements, where it is truly dark at night. If you do that, you can see something like this:


Gegenschein, as seen from the Very Large Telescope site, Cerro Paranal, Chile. (Photo: Creative Commons Attribution 4.0 International by the European Southern Observatory.)

The gegenschein is the glow in the sky just above the centre of the image. Heck, it’s so beautiful, here’s another one:


Gegenschein, as seen from the Very Large Telescope site, Cerro Paranal, Chile. (Photo: Creative Commons Attribution 4.0 International by the European Southern Observatory.)

This is a fisheye image, with the band of the Milky Way and the horizon wrapped around the edge of the circle. Here the gegenschein is the broad glow centred around a third of the way from the centre, at the 1 o’clock angle.

The visibility of the gegenschein shows that, in places where it is night time, the sun is actually behind the Earth. On a flat Earth, the sun can never be behind the Earth, so the gegenschein would never be visible. And so the optical effect of backscatter provides evidence that the Earth is a globe.


[1] Hong, S. S. “Henyey-Greenstein representation of the mean volume scattering phase function for zodiacal dust”. Astronomy and Astrophysics, 146, p. 67-75, 1985. http://adsabs.harvard.edu/abs/1985A%26A…146…67H

[2] Draine, B. T. “Scattering by Interstellar Dust Grains. I. Optical and Ultraviolet”. The Astrophysical Journal, 598, p. 1017-1025, 2003. https://doi.org/10.1086/379118

1. The Blue Marble

The most straightforward way to check the shape of the Earth is to look at it. There’s one small problem, though. To see the shape of the Earth as a whole, you need to be far enough away from it. For most of human history, this has not been possible. It was only with the advent of the space age that our technology has allowed us to send a human being, or a camera, more than a few kilometres from the surface.

The earliest photo of the whole Earth from space was taken by NASA’s ATS-3 weather and communications satellite in 1967. The photo was taken from geostationary orbit, some 34,000 kilometres above the surface of the Earth, and shows most of the western hemisphere, with South America most prominent. And you can see quite clearly that the Earth is round. It looks spherical, for the other landmasses that we know are there are hidden around the other side, and there is foreshortening of the features near the edges which matches our experience with spherical objects.

ATS-3 image of Earth

Photo of Earth taken by NASA’s ATS-3 satellite in 1967. (Public domain image by NASA.)

A more famous image of Earth taken from space is the Blue Marble image, captured by the Apollo 17 astronauts on their way to the Moon in 1972. This photo was taken from a distance of about 45,000 kilometres.

Blue Marble image of Earth

The Blue Marble photo of Earth taken by Apollo 17 astronauts in 1972. (Public domain image by NASA.)

This image is clearer and it’s arguably easier to see the spherical shape of the planet. Both these photos were taken with the full hemisphere lit by the sun.

The Apollo 13 astronauts, in their ill-fated flight, captured a different view, with part of the Earth in darkness because the sun was not behind them.

Apollo 13 image of Earth

The Earth photographed by Apollo 13 astronauts in 1970. (Public domain image by NASA.)

Here it is even easier to get a feeling for the round, spherical shape of Earth, because our experience with the way light falls on round objects helps our minds make sense of the curved shadow.

Well, that’s pretty definitive. But what else do we have?