The New Horizons' mission to Pluto has stirred the imagination and cast us to the frontier of interstellar space. Most everyone understands that the spacecraft and its primary target – the Pluto system which it swept through all too briefly last July – are way, WAY out there…far away from us here on Earth, and far from the Sun which they understand must supply its illumination. Natural curiosity inevitably asks the question: just how dim is the sunlight out there at Pluto? Specifically, did New Horizons' cameras need to employ any special techniques to compensate for the lower light levels as a result of being so distant from the Sun?
The Sun in the sky of Pluto. Detail of digital painting on exhibit at Griffith Observatory, Los Angeles, by Adolf Schaller and Donna Tracy. All images copyright Adolf Schaller and Donna Tracy.
The New Horizons spacecraft resumed its downlink of science data and images last Saturday, September 5th. A number of marvelous images have already been released and we’ll be devoting a post to them soon.
Meanwhile, let’s take a look at a question that has cropped up frequently since the historic July 14 flyby.
Everyone understands intuitively that a light source grows dimmer as one recedes from it. It’s a typical example of ‘common sense’ that is informed by experience. But the specific way a light source grows fainter with distance isn’t always immediately evident to intuition. That it grows dimmer with distance is an experience that informs ‘common sense’, but the experience itself doesn’t show ‘common sense’ how or why it happens. The phenomenon is noticed, but remains unaccounted for.
Nature doesn’t operate on whim. It operates in a regular or systematic manner. If there is any regular pattern in how light sources fade with distance, we could find out by performing a sufficiently careful observational experiment: all we have to do is measure how bright a constant source of light varies with distance. After looking over the data we might discover some regularity about how it works.
That’s a good and reliable way to do it, but it isn’t easy.
Although it may not be immediately apparent to our minds through the casual experience, the answer may be deduced from logical reasoning. We shift from the experimental to the theoretical domain in search of hypotheses that can account for the phenomenon. Experiment can be conducted to verify any hypothesis that tumbles out of just thinking about a problem but, as we shall see, it is a truly amazing thing that simple geometry can supply an answer to this and many other questions with impeccable precision.
Consider an area outlined by a square boundary of any size. The width of that square will vary in apparent size in direct proportion to one’s distance from it. The apparent width of the square appears to double if we move to a position half the original distance. We can also see that the apparent area has increased too, in a square progression with the linear dimension – its width – multiplied by itself: halving one’s distance to an object of a given area increases its apparent area by factor of 2x2=4. If we approach the same object to a third of the original distance, we would regard its apparent area has grown by a factor of 3x3=9, and so on. This is referred to as the inverse-square rule. With it one can determine the relative brightness of a given constant light source with distance.
The Inverse-Square Rule determines how a light source varies with distance.
Now that we are equipped with the inverse-square rule, the amount of sunlight Pluto receives from the Sun compared to what we receive is easy to ascertain. First, we need distances to compare. When New Horizons flew by Pluto it was 32.91 Astronomical Units (AU) from the Sun (with 1 AU = average distance of Earth from the Sun). That simply means that Pluto and New Horizons were 32.91 times farther away from the Sun than the Earth's average distance from the Sun.
[That distance, 1 AU = 92,955,807 miles or 149,597,871 kilometers. For the sake of readability in this post I will suppress my cringing and continue to use miles, yards, feet and inches instead of the far saner metric system for units of distance, for reasons that will become apparent shortly; readers – and students in particular – are encouraged to perform their own conversions as an exercise: Practice, practice, practice! Of course, you can save time by googling a convenient conversion engine or using a calculator without incurring the charge of laziness. One does not need to be good at juggling to understand how juggling works.]
In angular measurement, the apparent diameter of the Sun’s disk in our sky is about half a degree, or about 30 minutes of arc. By sheer coincidence, our Moon also happens to appear about the same size in the sky: about ½ degree. Of course, this does not suggest they are physically the same size. The Sun is enormous – about 400 times larger than the Moon. It just happens that the Sun is also 400 times farther away than our Moon is so that they appear to us on Earth to be about the same size in our sky.
An Astronomical Coincidence: The Sun and the Moon appear about the same size as seen from Earth despite their very different actual sizes.
We wish to compare how bright the Sun would appear at the distance of Pluto to its brightness as seen from Earth. Since Pluto and New Horizons were 32.91 times farther from the Sun, the apparent diameter of the Sun would be 32.91 times smaller as seen from Pluto. But the apparent area has fallen as the square of 32.91, or 32.91 multiplied by itself: The square of 32.91 is 1083.0681; the inverse of the square of 32.91 = 1/1083.0681. Let’s round that off to 1/1083.
At Pluto’s distance of 33 Astronomical Units, the Sun’s disk is reduced to about 1/33 of its apparent width as seen from Earth, but its apparent area is reduced by a factor of 1083.
That is the fraction of sunlight Pluto receives from the Sun compared to what Earth receives per unit area of surface; in other words, the Sun at Pluto would appear less than a thousandth as bright as what we see blazing in our sky on a clear day.
(Astute readers may wonder if the inverse-square relation applies to gravity as well…and indeed it does! At that distance Pluto experiences a gravitational attraction toward the Sun 1/1083 – again, less than a thousandth – that which our planet experiences).
A Sun less than a thousandth as bright as what we see in earthly skies may seem hugely fainter than what we are used to, but consider that this is still MUCH brighter than our own full moon, which has an apparent brightness as seen from Earth about 400,000 times less than that of the Sun. (It must be remembered, of course, that the Moon is not a generator of visible light like the Sun; it is simply a globe of rock and dust which reflects the sunlight that falls on its surface: the Sun is the dominant lamp that illuminates all of the objects in its planetary system. And, to be sure, the distances to both vary slightly since both the Earth’s yearly orbit around the Sun and the Moon’s roughly monthly orbit around the Earth aren’t perfectly circular. Sometimes the Moon appears slightly smaller than the Sun and vice versa. But they both remain fairly similar in apparent size, and we can speak of an average brightness of the Full Moon for our purposes: about 400,000 times fainter than the Sun).
Now, suppose we wish to tinker out how many of our full moons would equal the Sun’s brightness as seen from Pluto. We simply take the number of full moons that equal our own Sun’s brightness – 400,000, and divide it by the number we acquired from our inverse-square calculation. All we have to do is replace the 1 in 1/1083 with 400,000:
400,000/1083 = 369.3
Therefore, the Sun from Pluto would appear as bright as about 370 full moons – but all of that light would be concentrated into a very tiny disk of blazing light only 1/33 the diameter of the Sun we see in our sky!
We’ve seen that the Sun's apparent size in Pluto's sky is about 33 times smaller than its apparent 0.5 degree angular size in our sky. (Since 1 degree of angle corresponds to 60 minutes of arc, one can also say that the disk of the Sun in our sky measures about 30 arc-minutes across). Therefore its disk would appear to be only 1/66 of a degree or less than 1 minute of arc across.
To appreciate just how small that angular size is, consider that the apparent width of the disk of the full moon – which coincidentally happens to be about the same as the apparent size of the Sun, or about half of a degree – is about the same size as a pencil eraser held at arm's length from your eye. (You can check that for yourself...but please use the MOON for the measurement: trying to test it with the Sun can cause instant and permanent blindness. NEVER, EVER look directly at or anywhere near the Sun with the naked eye! The Moon is a convenient and appropriate target for that measurement, so there is no reason not to employ it).
A pencil eraser held at arm’s length from the eye approximates the width of the full moon.
Without undue stretching, my arm length measured from my eyeball to the pencil I hold in my hand is roughly 23 inches. If I place that pencil 23x33=759 inches or 63.25 feet (or 21 yards) away from my eye, the eraser will appear about as large as the disk of the Sun would as seen from Pluto.
A pencil eraser placed 63 feet away from the eye approximates the apparent size of the Sun’s disk as seen from Pluto.
That’s almost exactly the distance between a pitcher and a pencil held in the catcher’s mitt on a professional league baseball diamond.
A pencil eraser placed at the catcher’s glove 3 feet behind home plate at a distance of 63 feet from the pitcher’s eye approximates the 1/66-degree size of the Sun’s disk as seen from Pluto. To compare that with the apparent ½-degree size of the Sun as seen from Earth, the pitcher holds up his own pencil at arm’s length, 23 inches from his eye.
The pitcher should easily be able to make out the pencil in the catcher’s glove at that distance, but the eraser would be difficult for his eye to resolve as anything more than a dot. Most people do not have the visual acuity to see pick it out. Very young children often have such acuity, but it’s notoriously difficult to confirm it from their reports, for obvious reasons. Nevertheless, there are amazing examples of such eagle-eyed ability.
One evening as dusk descended on the sky, I was aiming and focusing my 11x80 binoculars on Jupiter and its moons while my nephew, who was about 6 or 7 years old at the time, stood next to me awaiting his turn to get a look at it through the binoculars. When I told him he’ll be able to see Jupiter’s moons through them, he remarked “I can see them”. Startled, I turned to him to find he was looking up at the bright star-like point that was indeed Jupiter. I asked him, “You can see them?” And he repeated, as if it was the most ordinary thing in the world, “I can see them.” I asked him how many he saw, and he counted them out, “one, two…three, four.” I prompted him, “How many are on each side?”…and he said, “There is one on this side…” (indicating the left side with hands) and continued, counting them out, “one…two, three” on that side (indicating the right side), adding, “They are all lined up”.
He was right! I said, “Take a look”, indicating the binoculars. His previous observation was no spoiler to the view at 11 magnifications delivered by the binoculars: no doubt he could easily discern more than the major bands and the Great Red Spot on Jupiter’s disk that I was pointing his attentions to. He said he could see other spots on Jupiter besides the big dark one (the Great Red Spot) but also remarked casually that the two moons closest to Jupiter – which were situated close to one another – were now ‘much easier to see’. It explained perfectly why he paused in his counting: his eyes had been challenged to separate those two close points into independent objects.
That stunning visual acuity remained with him into his early teens, when he reported during another viewing session preparing to view the planet Venus which was blazing low against the fading twilight glow of sunset: he casually remarked that he could discern its crescent phase! Having noted examples of his sharp vision on innumerable occasions since that first Jupiter observation, I had no reason to doubt him. That young man is eagle eyed!
Under ordinary conditions in a well illuminated baseball stadium, day or night, the light reflected off the rather dark eraser on the end of the pencil is a rather inadequate target for the eye. A better target would be a white spot of the same size against a black background. Most of us would then easily be able to discern it. It would still look like a point, but most would have no trouble seeing it. And, of course, if we looked at a light source the same size as the eraser - say, a small pen-light of that size aimed at our eyes in darkness - we would have no problem at all in detecting it...but only as a bright point of light. A candle flame is considered to be a very modest light source suitable for illuminating one’s immediate environs in darkness, say, reliably within the confines of a typical bedroom. But it is said that a candle flame itself can be seen from well over a mile.
Needless to say, the surface of the Sun is tremendously bright and puts out a prodigious amount of light. As tiny as its disk would appear at Pluto's distance of 33 AU distance, it would still be painfully bright to look at and cause damage to your retina if you looked directly at it, even at such an immense distance.
In any case, it’s easy to see that at Pluto's distance, sunlight would be more than adequate for fairly ordinary exposure settings. Imagine that there are 370 full moons in our night sky at once, all of them compressed into a spot only 1/66 of a degree across! Such an illumination level would make the outdoors considerably brighter than it is when, for example, the pall of a strong thunderstorm darkens our sky at midday. It would be considerably better illuminated than typical indoor household room or office settings. Consider that only a few full moons’ worth of illumination is all that is needed to read a book comfortably. Try reading printed text under the illumination of a full moon to give you an idea of what it’s like.
The apparent brightness of the Sun as seen from Pluto is equivalent to the amount of light delivered by 370 full moons. The blank face of the giant moon at right depicts the average brightness spread over the entire disk.
So, under 370 such full moons-worth of illumination, you should easily take photos with your favorite camera using ordinary settings while standing on the surface of Pluto...if you could get away with it before the camera's electronics and battery - along with the photographer - froze to death within seconds. So bring a warm spacesuit…but make absolutely sure that it is well insulated, especially in the outer soles of your space-boots: if they leak any heat, you could find yourself sinking right through the nitrogen or carbon monoxide ice surface and miss that valuable selfie with Charon in the background…
A few weeks ago New Horizons mission planners announced they had selected the next target for their intrepid spacecraft: a visit to the Kuiper Belt Object called 2014 MU69, situated about 4.1 billion miles or 44.1 AU from the Sun, about a billion miles farther out than Pluto is. I encourage you to calculate how bright the Sun would be at 2014 MU69 compared to its apparent brightness at Pluto and to us here on Earth. How many full moons would that be equivalent to?
At the time of New Horizons’ flyby of Pluto, radio transmissions traveling at the speed of light from the spacecraft required 4 hours and 25 minutes to reach Earth. How long will it take those transmissions to reach Earth from the spacecraft when it reaches 2014 MU69?
As far as these targets are from us, they are but a tiny fraction of the distance to the nearest star, over 4 light-years away. 1 light-year is, of course, the distance light travels in a year’s time. That is equivalent to 5.87 trillion miles, or 63,241 AU! How bright would the Sun be at such a distance?
In a future post we’ll explore the brightness of stars and how the Sun compares to those we can see in our night sky (for example, how far we would have to travel away from our Sun before it was too faint for our human eyes to see it. The answer might surprise you!)…and with our imaginations we’ll explore how real alien suns might appear in the skies of actual alien worlds which have been discovered. But before we do, we’re not quite done with the Sun and the Moon: first, we’ll take a look at this month’s “Super-lunar eclipse”…