12. The sun

Possibly the most obvious property of our sun is that it is visible from Earth during daylight hours, but not at night. The visibility of the sun is in fact what defines “day time” and “night time”. At any given time, the half of the Earth facing the sun has daylight, while the other half is in the shadow of the Earth itself, blocking the sun from view. It’s trivial to verify that parts of the Earth are in daylight at the same time as other parts are in night, by communicating with people around the world.

The first physical property of the sun to be measured was how far away it is. In the 3rd century BC, the ancient Greek Aristarchus of Samos (who we met briefly in 2. Eratosthenes’ measurement) developed a method to measure the distance to the sun in terms of the size of the Earth, using the geometry of the relative positions of the sun and moon. Firstly, when the moon appears exactly half-illuminated from a point on Earth, it means that the angle formed by the sun-moon-Earth is 90°. If you observe the angle between the sun and the moon at this time, you can determine the distance to the sun as a multiple of the distance to the moon.

Aristarchus's method 1

Geometry of the sun, moon, and Earth when the moon appears half-illuminated.

In the figure, if you measure the angle θ, then the ratio of the distance to the sun S divided by the distance to the moon M is the reciprocal of the cosine of θ. Aristarchus then used the size of the shadow of Earth on the moon during a lunar eclipse to obtain further equations relating the distances to the sun and moon and the size of the Earth.

Aristarchus's method 2

A medieval copy of Aristarchus’s drawing of the geometry of the sun-Earth-moon system during a lunar eclipse. (Public domain image.)

By combining these results, you can calculate the distances to both the sun and the moon in terms of the radius of the Earth. Aristarchus got the wrong answer, estimating that the sun was only about 19 times further away than the moon, because of the limited precision of his naked eye angle measurements (it’s actually 390 times further away). But Eratosthenes later made more accurate measurements (which were again discussed in Eratosthenes’ measurement), most likely using the same method.

The first rigorous measurement of the absolute distance to the sun was made by Giovanni Cassini in 1672. By this time, observations of all the known celestial bodies in our solar system and some geometry had well and truly established the relative distances of all the orbits. For example, it was known that the orbital radius of Venus was 0.72 times that of Earth, while the orbit of Mars was 1.52 times that of Earth. To measure the absolute distance to the sun, Cassini used a two-step method, the first step of which was measuring the distance to the planet Mars. This is actually a lot easier to do than measuring the distance to the sun, because Mars can be seen at night, against the background of the stars.

Cassini dispatched his colleague Jean Richer to Cayenne in French Guiana, South America, and the two of them arranged to make observations of Mars from there and Paris at the same time. By measuring the angles between Mars and nearby stars, they determined the parallax angle subtended by Mars across the distance between Paris and Cayenne. Simple geometry than gave the distance to Mars in conventional distance units. Then applying this to the relative distances to Mars and the sun gave the absolute distance from the Earth to the sun.

Since 1961, we’ve had a much more direct means of measuring solar system distances. By bouncing radar beams off the moon, Venus, or Mars and measuring the time taken for the signal to return at the speed of light, we can measure the distances to these bodies to high precision (a few hundred metres, although the distances to the planets change rapidly because of orbital motions) [1].

The Earth orbits the sun at a distance of approximately 150 million kilometres. Once we know this, we can work out the size of the sun. The angular size of the sun as seen from Earth can be measured accurately, and is 0.53°. Doing the mathematics, 0.53°×(π/180°)×150 = 1.4, so the sun is about 1.4 million kilometres in diameter, some 109 times the diameter of the Earth. This is the diameter of the visible surface – the sun has a vast “atmosphere” that we cannot see in visible light. Because of its vast distance compared to the size of the Earth, the sun’s angular size does not change appreciably as seen from different parts of the Earth. The difference in angular size between the sun directly overhead and on the horizon (roughly the Earth’s radius, 6370 km, further away) is only about 6370/150000000×(180°/π) = 0.002°.

Our sun is, in fact, a star – a huge sphere composed mostly of hydrogen and helium. It produces energy from mass through well-understood processes of nuclear fusion, and conforms to the observed properties of stars of similar size. The sun appears much larger and brighter than stars, and heats the Earth a lot more than stars, because the other stars are all so much further away.

The Sun

Our sun, observed in the ultraviolet as a false colour image by NASA’s Solar Dynamics Observatory satellite. (Public domain image by NASA.)

Like all normal stars, the sun radiates energy uniformly in all directions. This is expected from the models of its structure, and can be inferred from the uniformity of illumination across its visible disc. The fact that the sun’s polar regions are just as bright as the equatorial edges implies that the radiation we see in the ecliptic plane (the plane of Earth’s orbit) is reproduced in all directions out of the plane as well.

NASA’s Ulysses solar observation spacecraft was launched in 1990 and used a gravity slingshot assist from Jupiter to put it into a solar orbit inclined at about 80° to the ecliptic plane. This allowed it to directly observe the sun’s polar regions.

Ulysses' orbit

Polar orbit of Ulysses around the sun, giving it views of both the sun’s north and south poles. (Public Domain image by NASA.)

Now, I tried to find scientific papers using data from Ulysses to confirm that the sun indeed radiates electromagnetic energy (visible light, ultraviolet, etc.) uniformly in all directions. However, it seems that no researchers were willing to dedicate space in a paper to discussing whether the sun radiates in all directions or not. It’s a bit like looking for a research paper that provides data on whether apples fall to the ground or not. What I did find are papers that use data from Ulyssessolar wind particle flux detectors to measure if the energy emitted by the sun as high energy particles varies with direction.

Solar proton flux versus latitude

Proton flux density observed by Ulysses at various heliographic (sun-centred) latitudes. -90 is directly south of the sun, 0 would be in the ecliptic plane. The track shows Ulysses’ orbit, changing in distance and latitude as it passes under the sun’s south polar regions. Figure reproduced from [2].

Solar wind energy flux versus latitude

Various solar wind plasma component energy fluxes observed by Ulysses at various heliographic latitudes. Figure reproduced from [3].

As these figures show, the energy emitted by the sun as solar wind particles is pretty constant in all directions, from equatorial to polar. Interestingly, there is a variation in the solar wind energy flux with latitude: the solar wind is slower and less energetic close to the plane of the ecliptic than at higher latitudes. The solar wind, unlike the electromagnetic radiation from the sun, is affected by the structure of the interplanetary medium. The denser interplanetary medium in the plane of the ecliptic slows the wind. The amount of slowing provides important constraints on the physics of how the solar wind particles are accelerated in the first place.

Anyway, given there are papers on the variation of solar wind with direction, you can bet your bottom dollar that there would be hundreds of papers about the variation of electromagnetic radiation with direction, if it had been observed, because it goes completely counter to our understanding of how the sun works. The fact that the sun radiates uniformly in all directions is such a straightforward consequence of our knowledge of physics that it’s not even worth writing a paper confirming it.

Now, in our spherical Earth model, all of the above observations are both consistent and easily explicable. In a Flat Earth model, however, these observations are less easily explained.

Why is the sun visible in the sky from part of the Earth (during daylight hours), while in other parts of the Earth at the same time it is not visible (and is night time)?

The most frequently proposed solution for this is that the sun moves in a circular path above the disc of the Flat Earth, shining downwards with a sort of spotlight effect, so that it only illuminates part of the disc. Although there is a straight line view from areas of night towards the position of the sun in the sky, the sun does not shine in that direction.

Given that we know the sun radiates uniformly in all directions, we know this cannot be so. Furthermore, if the sun were a directional spotlight, how would such a thing even come to be? Directional light sources do occur in nature. They are produced by synchrotron radiation from a rapidly rotating object: for example, a pulsar. But pulsars rotate and sweep their directional beams through space on a timescale of approximately one second. If our sun were producing synchrotron radiation, its spotlight beam would be oscillating many times per minute – something which is not observed.

Even furthermore, if the sun is directional and always above the plane of the Flat Earth, it should be visible in the night sky, as an obscuration passing in front of the stars. This prediction of the Flat Earth model is not seen – it is easy to show that no object the size of the sun obscures any stars at night.

And yet furthermore, if the sun is directional, there are substantial difficulties in having it illuminate the moon. Some Flat Earth models acknowledge this and posit that the moon is self-luminous, and changes in phase are caused by the moon itself, not reflection of sunlight. This can easily be observed not to be the case, since (a) there are dark shadows on the moon caused by the light coming from the location of the sun in space, and (b) the moon darkens dramatically during lunar eclipses, when it is not illuminated by the sun.

In addition to the directional spotlight effect, typical Flat Earth models state that the distance to the sun is significantly less than 150 million kilometres. Flat Earth proponent Wilbur Glenn Voliva used geometry to calculate that the sun must be approximately 3000 miles above the surface of the Earth to reproduce the zenith angles of the sun seen in the sky from the equator and latitudes 45° north and south.

Voliva's distance to the sun calculation

Wilbur Glenn Voliva’s calculation that the sun is 3000 miles above the Flat Earth. Reproduced from Modern Mechanics, October 1931, p. 73.

Aside from the fact that Voliva’s distance does not give the correct zenith angles for any other latitudes, it also implies that the sun is only about 32 miles in diameter, given the angular size seen when it is overhead, and that the angular size of the sun should vary significantly, becoming only 0.53°/sqrt(2) = 0.37° when at a zenith angle of 45°. If the sun is this small, there are no known mechanisms than can supply the energy output it produces. And the prediction that the sun would change in angular size is easily disproved by observation.

The simplest and most consistent way of explaining the physical properties of our sun is in a model in which the Earth is a globe.

References:

[1] Muhleman, D. O., Holdridge, D. B., Block, N. “The astronomical unit determined by radar reflections from Venus”. The Astrophysical Journal, 67, p. 191-203, 1962. https://doi.org/10.1086/108693

[2] Barnes, A., Gazis, P. R., Phillips, J. L. “Constraints on solar wind acceleration mechanisms from Ulysses plasma observations: The first polar pass”. Geophysical Research Letters, 22, p. 3309-3311, 1995. https://doi.org/10.1029/95GL03532

[3] Phillips, J. L., Bame, S. J., Barnes, A., Barraclough, B. L., Feldman, W. C., Goldstein, B. E., Gosling, J. T., Hoogeveen, G. W., McComas, D. J., Neugebauer, M., Suess, S. T. “Ulysses solar wind plasma observations from pole to pole”. Geophysical Research Letters, 22, p. 3301-3304, 1995. https://doi.org/10.1029/95GL03094

7. Supernova 1987A

Stars produce energy from nuclear fusion reactions in their cores, where the light elements making up the bulk of the star are compressed and heated by gravity until they fuse into heavier elements. There is a limit to this, however, because once iron is produced in the core no more energy can be extracted from it. Fusing iron requires an input of energy. As iron accumulates, the layers near the core collapse inwards, because not enough energy is being produced to hold them up. At a certain point, the collapse speeds up suddenly and catastrophically, the whole core of the star collapsing in a few seconds. This releases an enormous amount of gravitational energy, fusing heavier elements and initiating nuclear reactions in the outer parts of the star, which blow off in a vast explosion. The star has turned into a supernova, one of the most energetic phenomena in the universe. A supernova can, briefly, shine brighter than the entire galaxy of 100 billion (1011) stars containing it.

Historically, supernovae were detected visually, when a “new star” suddenly appeared in the night sky, shining brightly for a few weeks before fading away from sight. We have reliable records of visible supernovae appearing in the years 1006, 1054, 1181, 1572, and 1604, as well as unconfirmed but probable events occurring in 185 and 393. These supernovae all occurred within our own Milky Way Galaxy, so were close enough to be visible to the naked eye. Since 1604, there have been no supernovae detected in our Galaxy – which is a bit of a shame because the telescope was invented around 1608, just too late to observe the most recent one.

Astronomers have used telescopes to observe supernovae in other galaxies since the late 19th century. Almost none of these are visible to the naked eye. But in 1987 a supernova occurred in the Large Magellanic Cloud, a dwarf galaxy satellite of our own, making it the nearest supernova ever observed in the telescopic era. It reached magnitude 3, making it as bright as a middling star in our sky. It was first seen by independent observers in Chile and New Zealand on 24 February 1987.

The Large Magellanic Cloud is visible from the southern hemisphere of Earth, and in the north up to a latitude around 21°N. It is never visible from any point further north. And so supernova 1987A (the first supernova detected in 1987) was never visible from any point further north than 21°N.

Supernova 1987A

Supernova 1987A and the Large Magellanic Cloud. SN 1987A is the bright star just right of the centre of the image. (Photo: Creative Commons Attribution 4.0 International by the European Southern Observatory.)

When a supernova explosion occurs, the collapsing star emits vast quantities of matter and radiation into the surrounding space. Visible light is just one part of the radiation. SN 1987A also emitted gamma rays, x-rays, and ultraviolet light, the latter two of which were detected by space-based telescopes. And it also blasted particles into interstellar space: heavy element nuclei, neutrons, electrons, and other subatomic particles. One of the types of particles produced was neutrinos. Neutrinos have such a small mass that so far we’ve been unable to perform any experiment that can distinguish their mass from zero. And this means that they move at close to the speed of light – so close that we’ve never made any observation that shows them to move any slower.

At the moment of collapse, SN 1987A emitted a huge burst of neutrinos. These travelled through intergalactic space and some of the neutrinos made it to Earth, where some of them were detected. This neutrino burst was detected almost simultaneously at three different neutrino observatories in different parts of the world:

While a total of 24 neutrinos might not sound like a lot, this is significantly higher than the background detection rate of neutrinos from other sources such as our sun and general cosmic rays from random directions in space. And all 24 of these neutrinos were detected within a single 13-second time window – if corrected for the differences in light travel time from SN 1987A to each observatory caused by their locations on the spherical Earth.

You might notice that all three of the detectors listed are in the northern hemisphere. In fact, the southernmost of them is Kamioka, at 36° 20′ 24″ N. This means that the Large Magellanic Cloud, and SN 1987A in particular, are not visible in the sky at any of these detector locations. This fact by itself provides fairly convincing evidence to most people that the Earth cannot be flat, but Flat Earth enthusiasts propose various solutions for the limited visibility of celestial objects from different parts of the Earth. In Flat Earth theory, all visible stars and galaxies are above the plane of the Earth, and obscured from some parts by distance or intervening objects. This obviously requires SN 1987A to be above the plane of the Flat Earth.

In fact, at this point it might seem that the spherical Earth has a problem: If SN 1987A is not visible from the locations of the neutrino detectors, then how did they detect neutrinos from it? The answer is that neutrinos are extremely elusive particles – they barely interact with matter at all. Neutrinos are known to pass right through the Earth with ease. So although the spherical Earth blocked the light from SN 1987A from reaching the neutrino observatories, it did not stop the neutrinos. The neutrinos passed through the Earth to reach the observatories.

Astronomers estimate SN 1987A released around 1058 neutrinos. The blast was 168,000 light years away, so at the distance of Earth, the number of neutrinos passing through the Earth would be approximately 3×1020 neutrinos per square metre. The Kamiokande-II detector is a cylinder of water 16 metres high and 15.6 metres in diameter, so nearly 1023 SN 1987A neutrinos would have passed through it, leading to just 11 detections. This matches the expected detection rate for neutrinos very well.

Additionally, the Kamioka and Irvine-Michigan-Brookhaven detectors are directional – they can determine the direction from which observed neutrinos arrive. They arrived coming up from underground, not down from the sky. The observed directions at both detectors correspond to the position of the Large Magellanic Cloud and SN1987A on the far side of the spherical Earth [1][2].

Kamiokande-II results

Distribution of SN 1987A neutrino detections at Kamiokande-II in energy of produced electrons and angle relative to the direction of the Large Magellanic Cloud (LMC). Detected electrons are produced by two different processes, the first is rapid and highly aligned with neutrino direction, while the second is a slower secondary particle generation process and randomises direction uniformly. Neutrinos 1 and 2 (the earliest in the burst) are aligned directly with the LMC, and the remainder are distributed uniformly. This is statistically consistent with the burst having originated from the LMC. Figure reproduced from [1].

In a flat Earth model, SN 1987A would have to be simultaneously above the plane of the Earth (to be visible from the southern hemisphere) and below it (for the neutrino burst to be visible coming up from under the plane of the Earth). This is self-contradictory. However the observations of SN 1987A are all consistent with the Earth being a globe.

References:

[1] Hirata, K.; Kajita, T.; Koshiba, M.; Nakahata, M.; Oyama, Y.; Sato, N.; Suzuki, A.; Takita, M.; Totsuka, Y.; Kifune, T.; Suda, T.; Takahashi, K.; Tanimori, T.; Miyano, K.; Yamada, M.; Beier, E. W.; Feldscher, L. R.; Kim, S. B.; Mann, A. K.; Newcomer, F. M.; Van, R.; Zhang, W.; Cortez, B. G. “Observation of a neutrino burst from the supernova SN1987A”. Physical Review Letters, 58, p. 1490-1493, 1987. https://doi.org/10.1103/PhysRevLett.58.1490

[2] Bratton, C. B.; Casper, D.; Ciocio, A.; Claus, R.; Crouch, M.; Dye, S. T.; Errede, S.; Gajewski, W.; Goldhaber, M.; Haines, T. J.; Jones, T. W.; Kielczewska, D.; Kropp, W. R.; Learned, J. G.; Losecco, J. M.; Matthews, J.; Miller, R.; Mudan, M.; Price, L. R.; Reines, F.; Schultz, J.; Seidel, S.; Sinclair, D.; Sobel, H. W.; Stone, J. L.; Sulak, L.; Svoboda, R.; Thornton, G.; van der Velde, J. C. “Angular distribution of events from SN1987A”. Physical Review D, 37, p. 3361-3363, 1988. https://doi.org/10.1103/PhysRevD.37.3361

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

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

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.

References:

[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