Curious Questions: How far can you see on a clear day?

A walk to a local hilltop prompts Martin Fone to wonder just how far you can see, assuming perfect atmospheric conditions.

It is worth all the effort, clambering laboriously to the top of a hill or viewing platform to gaze in awe on the vista around me. I often wonder just how far I can see if I am blessed with a clear day. I recognise that Alan Jay Lerner’s song, On a Clear Day (You Can See Forever) from the eponymous 1965 Broadway musical, is a tad hyperbolic, but were The Who with their I Can See For Miles from their 1967 The Who Sell Out album, nearer the mark?

Does the old midwestern joke that people living out on the prairies can see their dog run away for days contain a scintilla of truth? Inevitably, the answer is not as simple as it may seem.

The first complicating factor is the fact that the Earth is spherical, something that had been recognised, at least by scientists, for over two millennia. Eratosthenes, a Greek from Alexandria, who died in 194 BCE, realised the planet was a globe and even calculated the circumference of the 36th parallel running through Greece and Crete. Strabo, the first century CE geographer, pre-empted Columbus by some 1,500 years in surmising that by sailing west from Spain you would end up in India in the east. By the time Pliny the Elder wrote his Naturalis Historia in 77AD, the Earth’s spherical shape was common knowledge; ‘we all agree on the earth’s shape. For surely we always speak of the round ball of the Earth’ (II.64).

While you are standing on terra firma you might be forgiven for thinking that the planet is flat. However, a little bit of observation will demonstrate the errors of your ways. Look out of an upper storey window of a building and then compare what you see with your view from the ground. Assuming that there are no annoying obstacles in the way, if the Earth was flat, your view should be identical. However, that distant object on the horizon you could see from the window would have disappeared when you looked at it at ground level. The Earth’s natural curvature, around 8 degrees per mile, has taken the object out of the line of your sight.

If you are lying on the ground with your eyes about a foot off the ground, the maximum distance you would see before the Earth’s curvature intervened is around a mile. Stand up, and assuming your eyes are around five feet off the ground, the distance is extended to around 3 miles.

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Let’s put it another way: if you were planning to run a 5-kilometre race on a perfectly flat track, you would not be able to see the finishing tape from the starting blocks. The higher you are, though, the further the horizon line will be. Standing 1,000 feet above sea level, it would be 38.7 miles away and 208.8 miles away from the top of Everest.

“Buildings like London’s Shard are tall enough to counter the effect of the Earth’s curvature and so can be seen from points between the South Downs to the Thames Estuary, over 40 miles away.”

These distances can be calculated with help from Pythagoras’ theorem; I always wondered at school what I was going to use it for. If we assume the Earth is perfectly round with a radius of 6,378,137 metres, we can construct a theoretical triangle with the centre of the earth forming one point, the horizon a second point which we assume to be at right angles to it and the observer’s height above sea level the third. Fortunately, these days there are computer programs that can do all the hard work for you. Of course, the planet is not perfectly spherical and so some inaccuracy is introduced into the results, but they are good enough to satisfy the idlest of curiosities.

However, there are other factors to consider, not least the quality of the air. The molecules in the air attenuate the light, so that even in the most perfect conditions, the maximum distance you would see is reduced to around 150 miles. Such perfect conditions are extremely rare as tiny particles suspended in the air form a light haze and reduce visibility further. Ironically, fine settled weather, which would normally encourage you to climb up to a viewing point, results in little in the way of air movement and so more particles hang around. The result is visibility can be disappointingly poor and those distant hills are often obscured by a haze.

How far you can see is also determined by the size of the object you are looking at and that is down to your visual acuity. If you are blessed with 20/20 vision, (by which ophthalmologists mean you can see from 20 feet something you should see from that distance), when you are standing at sea level, an object needs to be over 4.4 feet square to be seen over the horizon. Buildings like London’s Shard are tall enough to counter the effect of the Earth’s curvature and so can be seen from points between the South Downs to the Thames Estuary, over 40 miles away.

You also need a clear sightline, if you want to see as far as you can. This is often harder to achieve than you would imagine as obstacles — some natural, other man-made — interpose themselves between you and the horizon.

Assuming you have all the ingredients in place, a high vantage point, a tall object to view, clear sightlines and excellent air conditions, then computer models suggest that the longest sightline in the world is the one that runs from Mt Dankova in Kyrgyzstan to Hindu Tagh in China, some 558 kilometres.

No one has ever photographed this sightline to prove the point. Marc Bret, though, took a picture at dawn on July 16, 2016 of the longest sightline to be captured on film, from Pic de Finestrelles in the Spanish Pyrenees. The furthest object visible was Pic Gaspard in the French Alps, 443 kilometres away. Marc’s website, Beyond Horizons, has this and several other astonishing pictures.

Look upwards and there are no annoying obstacles to disrupt your vision. Distances are transformed dramatically. The moon, large, bright and often clear enough for us to see some of the details of its surface, is 239,000 miles away, while the sun, whose rays we chase with an obsession verging on mania, is around 93 million miles from our planet. Of the planets orbiting with us around the Sun, Saturn at 746 million miles is the furthest we can see with the naked eye. Squint hard enough and you might even see its rings.

Distances are even more astronomical when you consider the constellations. The Andromeda Galaxy is a rotating cluster formed of around one trillion stars, twice the number of the Milky Way. Even though it is 2.5 million light-years away, the light emanating from its burning stars is so bright that it is the furthest object from Earth seen with the naked eye.

I cannot help wondering, though, when I gaze into the impenetrable blackness of the night sky, just how far I am seeing. There has to be something there for you to see before you can measure it, a deeply philosophical thought to ponder on. You never know, Alan Jay Lerner may just be right.