Same Sun, Other Skies

Cover of Russian edition of Asimov's "Lucky Starr and the Big Sun of Mercury"
Russian edition of Isaac Asimov’s “Lucky Starr And The Big Sun Of Mercury
(Chosen because, of all the editions of this novel, it does the best job of delivering exactly what the title says.)

A section of the horizon was etched sharply against a pearly region of the sky. Every pointed irregularity of that part of the horizon was in keen focus. Above it, the sky was in a soft glow (fading with height) a third of the way to the zenith. The glow consisted of bright, curving streamers of pale light.
“That’s the corona, Mr. Jones,” said Mindes.
Even in his astonishment Bigman was not forgetful of his own conception of proprieties. He growled, “Call me Bigman.” Then he said, “You mean the corona around the Sun? I didn’t think it was that big.”
“It’s a million miles deep or more,” said Mindes, “and we’re on Mercury, the planet closest to the Sun. We’re only thirty million miles from the Sun right now. You’re from Mars, aren’t you?”
“Born and bred,” said Bigman.
“Well, if you could see the Sun right now, you’d find it was thirty-six times as big as it is when seen from Mars, and so’s the corona. And thirty-six times as bright too.”
Lucky nodded. Sun and corona would be nine times as large as seen from Earth.

Isaac Asimov, Lucky Starr And The Big Sun Of Mercury (1956)

That’s Isaac Asimov (writing under the pseudonym “Paul French”), being very Asimov about things, in one of his “Lucky Starr” science fiction juveniles. In Asimov stories, characters explain things to each other quite often; in his “Lucky Starr” stories, doubly so. This particular passage introduces my theme for this post—the Sun as seen from other planets of the Solar System.

First, there’s some basic geometry to deal with. The farther a planet is from the Sun, the smaller the Sun will appear in the planet’s sky—there’s a simple inverse relationship between planetary distance and the apparent width of the solar disc as seen from that planet. But it’s the apparent area of the solar disc that determines how much light and heat the planet receives from the Sun—that bears an inverse-square relationship to the distance between planet and Sun.

We can distil that down into a simple table if we list the average distance at which each planet orbits the Sun, giving that figure in Astronomical Units, one AU being the Earth’s orbital radius. In the table below, the second column of numbers, indicating the apparent width of the solar disc, is simply the inverse of the first column; the third column, showing the apparent area of the disc, is the square of the second. (I’ve rounded the numbers, so the relationship between the tabulated figures isn’t exact.)

PlanetSun dist. (x Earth)Sun width (x Earth)Sun area (x Earth)
Mercury0.38712.586.67
Venus0.72331.381.91
Earth1.00001.001.00
Mars1.52370.660.43
Jupiter5.20290.190.037
Saturn9.53670.100.011
Uranus19.18920.0520.0027
Neptune30.06990.0330.0011

That’s not the full story, however, because the planets have elliptical, rather than circular, orbits. So the apparent width of the solar disc will vary somewhat around the mean values listed above, getting larger and smaller during the course of each planet’s year. For most planets, the change is very slight. From the Earth, for instance, the solar disc has an average apparent width of 32 minutes of arc, which increases by about half a minute of arc in January, when the Earth makes its closest approach to the Sun (its perihelion), and correspondingly decreases by about half a minute in July, when the Earth is at the farthest point in its orbit (the aphelion). It’s not a particularly noticeable change. But two planets, Mercury and Mars, have significantly elliptical orbits, and I can improve my table by listing maximum and minimum values for their solar discs.

PlanetSun dist. (x Earth)Sun width (x Earth)Sun area (x Earth)
Mercury0.38712.14 – 3.254.59 – 10.58
Venus0.72331.381.91
Earth1.00001.001.00
Mars1.52370.60 – 0.720.36 – 0.52
Jupiter5.20290.190.037
Saturn9.53670.100.011
Uranus19.18920.0520.0027
Neptune30.06990.0330.0011

The area of the solar disc (and therefore the light and heat from the Sun) varies more than two-fold during the course of a Mercurian year! Mars undergoes a more modest change, but the Sun gets 40% larger in the Martian sky as the planet moves from the farthest to the closest point in its orbit.

Another thing we can tell from my table above is that Asimov got his numbers wrong. (Now, there’s a phrase I thought I’d never write.) We can defend his characters’ claim that the solar disc appears nine times larger on Mercury than on Earth, if we assume they’re talking about its apparent area at a time when Mercury was close to perihelion. But there are no circumstances under which the Mercurian solar disc can appear even thirty times larger than that seen on Mars, let alone thirty-six times.

Before I go through the list of planets in more detail, I need to give a couple of definitions. The apparent surface brightness of the solar disc is called its luminance, and (perhaps counterintuitively) it doesn’t change with distance within the planetary system. The reason the solar disc sheds less light on more distant planets is because it is smaller, as detailed in my table above, not because it’s dimmer, area for area. The amount of light a planet receives from the Sun is called illuminance, and it’s what gives us the sense of whether our surroundings are dimly or brightly lit, and what determines the settings our cameras need to use to get a properly exposed picture. The SI unit of illuminance is the lux (say “looks”, not “lucks”), and sunlight on a clear day on Earth provides about 100,000 lux.

Now, let’s go through my list of planets, one at a time:

Mercury

Sunlight on Mercury is going to be brighter than anything we experience on Earth—five to ten times brighter. But, although science-fiction illustrators tend to depict the Mercurian sun as huge in the sky, it wouldn’t actually be that large. You can easily cover the solar disc, seen from Earth, with just the tip of your little finger. The Mercurian sun could be obscured with a couple of finger-tips, even at its largest.

Mercury’s slow rotation has an interesting effect on its daylight. It’s locked into what’s called a spin-orbit resonance. One Mercurian “year” lasts 87.97 Earth days; one Mercurian rotation takes 58.65 Earth days, meaning that the planet rotates exactly three times on its axis for every two orbits around the Sun. This means that, for any point in Mercury’s orbit, the planet returns to that point one orbit later with an extra half-rotation. So if some point on the surface experiences noon at a particular orbital location, it’ll experience midnight when it returns to that orbital location after one Mercurian year, and then noon again the next year, and so on. If it’s noon at a particular location when Mercury is passing through perihelion, it will be noon during perihelion every two Mercurian years (and midnight on the alternate years). So there are two points on the Mercurian equator, on opposite sides of the planet, that experience the brunt of the solar heating during Mercury’s closest approaches to the Sun. One of these hot points, on the equator at 180 degrees longitude, lies some distance to the southeast of a huge Mercurian impact basin, which has accordingly been named Caloris Planitia, or “Plain of Heat”.

There’s more fun to be had with Mercury’s spin-orbit coupling and eccentric orbit, but it strays away from the chosen topic of this post—I’ll come back to it another time, perhaps.

Venus

Venus, at about three-quarters of Earth’s distance from the Sun, sees the solar disc about a third larger than it appears from Earth. So light levels in orbit around Venus are close to double what we’d experience while in orbit around the Earth, and about two-and-a-half times the illuminance at the surface of the Earth on a clear summer’s day. That difference occurs because our atmosphere, even on a clear day, absorbs and reflects some sunlight before it arrives at the surface—but not nearly as much as the atmosphere of Venus, the surface of which lies under a perpetual dense overcast.

The light level at the surface of Venus, under all that cloud, was measured by the Venera series of Soviet-era landers. Venera-9, which made the first successful landing in a location with the Sun high in the Venusian sky, reported an illuminance of 14,000 lux, which is about what you receive if you stand in the shade under a bright, blue sky on Earth. Results from Venera-13 and Venera-14 were a bit lower, if the numbers quoted in a slightly batty paper entitled “Hypothetic Flora of Venus” can be considered reliable. Again with the Sun fairly high in the sky, the Venusian light level reached a value of 3,500 lux, about a thirtieth of a sunny day on Earth, and representing just a seventieth of what arrives at Venus’s cloud-tops. Even that low figure can be considered bright, by Earthly standards. 3,500 lux is the equivalent of the illuminance provided by the lights positioned above surgical operating tables, sufficient to carry out extremely fine work. (Our eyes adapt readily to a range of lighting conditions, and most of us barely notice that the normal level of illuminance indoors is usually at least a hundred times lower than that outdoors.)

Not that we’d be doing much fine work on the surface of Venus, given that the massive greenhouse effect from its dense atmosphere pushes the surface temperature up over 450ºC. (It’s traditional at this point to say “hot enough to melt lead”. Consider it said.) But if we were standing on the surface, the illumination would be equivalent to that of a diffusely lit but extremely bright room. A day-night cycle would last 177 Earth days (Venus rotates very slowly), and the sun would rise in the west and set in the east (Venus has retrograde rotation). But we wouldn’t be able to determine the exact moment of sunrise or sunset, since the location of the Sun would be no more than a brighter patch in the sky—“a smear of light”, says NASA, though I haven’t been able to track down a simulation of Venus’s atmosphere that might provide more detail on that.

Mars

Because of Mars’s elliptical orbit, the solar disc varies in apparent size with the seasons, ranging between about 60% and 70% of its width seen from Earth. This means the illuminance at the surface of Mars on a clear day can vary between 47,000 and 68,000 lux—to the adaptable human eye, indistinguishable from daylight on Earth. The solar disc appears largest when Mars is at perihelion during its southern hemisphere summer, and smallest during southern hemisphere winter. The southern hemisphere therefore experiences more extreme seasonal temperature changes than the north.

The Martian day is not much different in duration from an Earth day—about 40 minutes longer—and planetary scientists who study Mars refer to the Martian day as a “sol” (from the Latin for “sun”) to avoid confusion. There’s no confusing a Martian sunset with an Earth sunset, however:

The dominant colours are reversed, with a blue sun in a red sky. The effect is due to the particular size of fine dust particles suspended in Mars’s atmosphere, which produces a diffraction pattern that preferentially reinforces the forward-scattering of blue light. (A similar effect is sometimes produced by smoke aerosols on Earth.) You can find the detailed optical explanation here.

Jupiter

The next planet out from the Sun is Jupiter. While there’s nowhere for an observer to stand on a gas giant planet, it has a retinue of moons that might provide convenient locations from which to observe the Sun.

Such hypothetical observers would see a solar disc shrunk to about a fifth of its width as seen from Earth, providing only about a twenty-fifth of the light. That is, however, still about 5,000 lux—a not-too-overcast day on Earth, and easily sufficient illumination for the finest of work. And still comparable to the surface of Venus.

Saturn

By the time we reach Saturn, the solar disc has a tenth of its Earthly width, and sheds about hundredth of the light—1,400 lux, which is the equivalent of a solidly overcast day on Earth, or the sort of lamp one uses for fine work indoors. Still not particularly dim, then.

Again, our hypothetical observer would need to station themselves on one of Saturn’s moons in order to have a clear view of the Sun. Any moon would do, with the exception of Titan, which is swathed in a thick atmosphere. And we have some pretty detailed calculations of what the Sun would look like from the surface of Titan. I quote from the linked paper:

At visible wavelengths, the sky appears as nearly featureless orange soup most of the time, with little if any increased brightness toward the Sun’s azimuth.

My linked paper also provides some helpful graphs, suggesting that the overall reduction in illuminance when the Sun is overhead on Titan is somewhere between five-fold and ten-fold—so down to around 150-300 lux, in round numbers. That’s what we get under the absolute densest of massive cumulonimbus storm clouds on Earth, and the range of lighting used in corridors and stairwells indoors. So some of us would need to reach for our reading glasses on even the brightest day on Titan. The illuminance is cut a hundred-fold by the time the Sun has reached the horizon on Titan (say 15 lux, getting down to the limit for reading newsprint), and the setting sun would be absolutely invisible. But Titan’s atmosphere scatters light so well that the sky would continue to illuminate the landscape with full-moon brightness (about 0.2 lux) even when it was thirty degrees below the horizon.

Uranus

At Uranus, the solar disc has a twentieth of its width on Earth, and provides only around 350 lux—a little brighter than the surface of Titan, but still a profoundly overcast day on Earth.

Neptune

By the time we reach the outermost planet of the Solar System, the solar disc is down to a thirtieth of the width we see on Earth, and providing just 140 lux. Still, that’s the equivalent of 700 full moons, and you’d have no more difficult finding your way about in the vicinity of Neptune than you’d have finding your way down a stairwell on Earth.

We reach a significant threshold at Neptune, however. The solar disc is now just one minute of arc across, which is the limit of resolution of the human eye. Looking at the sky from one of Neptune’s moons, the Sun would appear as an eye-wateringly intense point of light, rather than a clear disc. But it would have the same surface brightness as the Sun seen from Earth—you could still damage your retina by staring at it with the naked eye (though the naked eye would of course not be an option out at the edge of the Solar System).

If we move farther from the Sun than Neptune, the solar disc can never appear any smaller to our eyes—it will always appear as a little point of light, smeared by the physical limitations of our eyes into a tiny spot one minute of arc across. At first a searingly bright star, and then progressively dimmer as we move farther and farther away.

But that’s a topic for another post.

Comparison of sizes of solar disc seen from various planets
Click to enlarge

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