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Matt Rosenberg

Farthest Visible Distance?

By March 11, 2009

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John asks an interesting question on the forum. Basically, he is trying to determine the farthest distance visible between two points on earth. He suggests that perhaps it is mountaintop to mountaintop across some swath of ocean but does anyone know the answer? Please read his question and post an answer if you know!

Comments

March 12, 2009 at 11:54 pm
(1) Don Hirschberg says:

I don’t have an answer but a little eighth grade arithmetic establishes the order of magnitude. If we are looking from the top of a mountain 2 miles above sea level, and there were no obstructions, say over ocean water, our horizon would be about 126 miles distant. If the object mountain top were also 2 miles high this would set the maximum line-of-sight distance at 252 miles. Perhaps a laser beam could be seen at that distance, curiously, about one tenth the circumference of the earth. When we fly on commercial jets we can experience horizons more than 126 miles distant.

March 13, 2009 at 1:04 am
(2) Don Hirschberg says:

OOps. In my post above it should read 1/100th, not 1/10th the circumference of the earth.

March 16, 2009 at 12:33 am
(3) Kenneth Crook says:

In Yellowstone National Park, USA, on a ranger guided hike to the top of one of the 10,000ft mountains in the park (the parking lot at the start of the hike was at about 8,000ft) we could see the Teton Mountains 75 mile to the south. That was 35 years ago, I do not know if the air is still as clear today?

March 16, 2009 at 4:11 am
(4) Mary D says:

This problem is far more complicated than my maths can cope with but CWNP Antenna Systems may be able to help.

You need to go somewhere from where you can see over the earth’s circumference, have a clear flat surface, get up a high mountain or tower, and hope you can find another one over the horizon.

You might get close to your ideal view if you went to the top of Mt Kilimanjaro and look south east, or Mt Stanley and look wherever the flatest plain is. They are both spots, high up, with few high points closeby to interupt your view. You may actually be able to see these places from each other. I don’t know.

March 16, 2009 at 9:02 am
(5) vasu says:

angles ,measures, i say that trignometry can solve this problem

March 16, 2009 at 2:39 pm
(6) Harry Trendell says:

I used to be a Merchant Marine Officer on cargo ships before I got into teaching and the height of the ship’s bridge above the waterline was critical to the distance we could see to the horizon before the curvature of the earth came into play. This was generally around 7-8 miles on these ships. Lighthouses and their height above the water coupled with the power of the light itself figured into the visible distance we could “raise” the light at night. Daylight impacted this ability because the sunlight overpowered the lighthouse light, but they still operated the light during the daytime. So, I think Mr. Don is right about the 2 mile high mountains, if it were not for the atmosphere. This brings me to Montevideo, Uruguay. There is no “mountain” to “see” anywhere near the city of Montevideo. But, the tall Andes Mts. were on the other side of the continent and I always wondered if the early conquistadors, could see those Andes on really clear days in the 16th century?

March 16, 2009 at 11:54 pm
(7) ramesh parmar says:

the farthest visible distance on earth is the visible horizon from naked eye. I think that is the answer as fat I can think of.

March 17, 2009 at 8:07 pm
(8) Pierre-Luc says:

I would say that the fartest you can see is from Cerro Chirripo in Costa Rica on a clear day because you can see both Pacific and Atlantic ocean from it’s top.

Two years ago, a climbed Mount Sutton, QC and we could see what we thought it was Mount Washington, NH which is about 135 km away.

Here the picture :
http://www.panoramio.com/photos/original/19297206.jpg

November 30, 2009 at 10:39 pm
(9) Richard says:

Pierre-Luc, looking at your photo that definitely is Mt Washington and the Presidential Range… so you are seeing between 75 and 100 miles… Great shot BTW….

January 6, 2010 at 10:45 pm
(10) Kevin Poe says:

I can confirm that well over 100 miles is possible. Here at Bryce Canyon National Park in Southern Utah we can see from Paria View Point 8176 ft to Humphrey Peak above Flagstaff Arizona at 12,356 which according to Google Earth is 158.7 miles. But I’ve heard that you can see father from high mountains in the Andes — I just can’t find that info on-line.

January 15, 2010 at 7:45 am
(11) Chris Storey says:

This is a question I’m eager to see answered. It is certainly well over 120 miles. From the top of Skiddaw in England’s Lake District it is possible to see the Mountains of Mourne in Northern Ireland 120 miles away. Likewise from the top of Ben Nebvis in Scotland it is possible to see mountains in Northern Ireland over 120 miles distant. So there must be far longer views involving the World’s bigger mountains.

I’m suggesting views in Africa from/towards Kilimanjaro or Mt Kenya. Or views from the Pacific towards the Andes.

January 28, 2010 at 4:58 pm
(12) Chris says:

telescope peak in death valley national park has one of the highest vertical rises in north America and rises above very low plains. I’m not sure about any official numbers but according to Wikipedia, you can see for over a hundred miles in many directions, even past Mt. Whitney to the west and Mt Charleston to the east. Both of which are taller that it. Maybe you could see one from the other?

March 21, 2010 at 10:47 am
(13) cpm says:

so one Xmas day-driving over the Berkeley hills to Livermore early-we could see top of Sierras clear enough to see rock formations. There was heavy tule fog in Central Valley, so I think there was some kind of atmospheric lens working. This was a distance of over 150 miles and it was spectacularly acute view.

April 1, 2010 at 10:48 am
(14) Owen says:

I have an apt. in Erie Pa. on the 9th floor approximatley
150 ft above water level. I have a deck facing directly
north; I was wondering if with a good spotting scope,
would it be possible to see the Canadian shore on a
clear day. I want to do this,but don,t want to spend the
money and then find out it can,t be done.

Any help with this would be greatly appreciated.

June 22, 2010 at 4:39 pm
(15) jhon b rutherford says:

i believe that mt. kilimanjaro in africa is first for seeing the farthest. tall mountain in the middle of the desert. obvious. second is mt. diablo located in the california bay area. on clear days, many have been able to see the sierra mountain range, which is roughly 200 miles away!

September 12, 2010 at 1:58 pm
(16) Chellappa says:

I have seen practically all the great peake of Himalayas when I fly from Delhi to any north eastern destination like Bagdogra, Guahathi or Dibrugarh . (in fact the pilot draws yr attention !
The pilots inform the distance as above 150 km.
But one shoud remember that he is at aheight of 30 000 ft & the Himalayan range is well above 7 km (24 -25 000 ft,
The visibiliy is excellent fxcept monsoon months !(June to Sept)
The(////

January 1, 2011 at 10:19 pm
(17) Steven says:

Okay but what about a Just a 5mW Green laser pointing at like the moon. Could someone in Wisconson or Canada see the laser beam. Could you see the beam at night if it was pointing at a distant star.

October 30, 2011 at 2:47 pm
(18) kiko says:

i have just seen the photo with visibility more than 270 km , it shows mountain corno grande in italy and the apennines, the photo is taken form hill sveto brdo velebit in croatia, i just found it on the internet and im skeptical is it what i see is real, it looks more like a clouds then a mountain http://www.summitpost.org/apennines-from-velebit/40455

January 6, 2012 at 8:25 am
(19) Wimpie says:

Man, this is so interesting to me. What I would like to know, is if one would try to go around the world, and touch every continent, with these naked eye visibility hops, what would the route be, and will it be possible ? Also, how long will the aggregated ‘line of sight’ distance be compared to the circumference of the earth ? This is really WOW !!

January 6, 2012 at 8:29 am
(20) Wimpie says:

Hey, here’s a fantastic challenge. If we could figure out the route, and have somebody at each viewpoint, and have a conference call, we could have a theoretical visible “line of communication” around the world….who’s up for it …

February 20, 2012 at 6:42 am
(21) Name says:

You can seen from Whiteface near Lake Placid NY to Mount Washington, NH, which is approximately 131 miles. The book, The Worst Weather on Earth, lists a few more that may be a bit longer from Mount Washington.

With Higher mountains and longer / larger valleys, there are further views in California and the Western Mountain regions – a hiking guidebook or website would probably yeild much farther descriptions there (or in other areas of the world where there were higher mountains).

March 15, 2012 at 5:26 pm
(22) jimmy says:

Mt Snowdone in Wales. You can see 144 miles from the summit, all the way to Scotland.

April 28, 2012 at 8:48 am
(23) Keith Halley says:

No one has mentioned Fermat’s Principle of Least Time, which deals with the refraction and reflection of light, and which holds that light will travel by the fastest path available to it. This means that even mountains below the horizon can been seen under certain atmospheric conditions. (I think temperature inversions come in here). There is a famous photograph of Mt Canigou, in the Pyrenees, seen from Marseille, often used to illustrate this Principle. And it may have been the cause of a reported sighting of the coast of Norway from Ben Rinnes, in North-East Scotland.

May 21, 2012 at 2:07 pm
(24) Adam Mark says:

Old topic but fascinating. Enjoyed reading all the posts/experiences. Perhaps my greatest experience with this was flying towards Albuquerque on a crystal clear day @ 30,000 ft. on the TX/NM border (over Clovis) and making out the snowy Sangre De Cristo mts. to the NW some 150 miles.

May 27, 2012 at 11:10 pm
(25) Drake Murphy says:

I was on Mt. Tamalpais (The biggest mountain within easy driving distance of downtown San Francisco, and I could see 61.93 miles to a mountain called Cobb Mountain (4740 ft) 2 counties away. prevailing winds had blown away all particulates in the air. (sorry sierra foothills!)

June 1, 2012 at 6:17 am
(26) do the math says:

The distance across St. George’s Channel, between Holyhead and Kingstown Harbour, near Dublin, is at least 60 statute miles. It is not an uncommon thing for passengers to notice, when in, and for a considerable distance beyond the centre of the Channel, the Light on Holyhead Pier, and the Poolbeg Light in Dublin Bay, as shown in fig. 23. The Lighthouse on Holyhead

FIG. 23.
FIG. 23.

[paragraph continues] Pier shows a red light at an elevation of 44 feet above high water; and the Poolbeg Lighthouse exhibits two bright lights at an altitude of 68 feet; so that a vessel in the middle of the Channel would be 30 miles from each light; and allowing the observer to be on deck, and 24 feet above the water, the horizon on a globe would be 6 miles away. Deducting 6 miles from 30, the distance from the horizon to Holyhead, on the one hand, and to Dublin Bay on the other, would be 24 miles. The square of 24, multiplied by 8 inches, shows a declination of 384 feet. The altitude of the lights in Poolbeg Lighthouse is 68 feet; and of the red light on Holyhead Pier, 44 feet. Hence, if the earth were a globe, the former would always be

p. 29

[paragraph continues] 316 feet and the latter 340 feet below the horizon, as seen in the following diagram, fig. 24. The line of sight H, S, would be a

FIG. 24.
FIG. 24.

tangent touching the horizon at H, and passing more than 300 feet over the top of each lighthouse.

Many instances could be given of lights being visible at sea for distances which would be utterly impossible upon a globular surface of 25,000 miles in circumference. The following are examples:–

“The coal fire (which was once used) on the Spurn Point Lighthouse, at the mouth of the Humber, which was constructed on a good principle for burning, has been seen 30 miles off.” 1

Allowing 16 feet for the altitude of the observer (which is more than is considered necessary, 2 10 feet being the standard; but 6 feet may be added for the height of the eye above the deck), 5 miles must be taken from the 30 miles, as the distance of the horizon. The square of 5 miles, multiplied by 8 inches, gives 416 feet; deducting the altitude of the light, 93 feet, we have 323 feet as the amount this light should be below the horizon.

p. 30

The above calculation is made on the supposition that statute miles are intended, but it is very probable that nautical measure is understood; and if so, the light would be depressed fully 600 feet.

The Egerö Light, on west point of Island, south coast of Norway, is fitted up with the first order of the dioptric lights, is visible 28 statute miles, and the altitude above high water is 154 feet. On making the proper calculation it will be found that this light ought to be sunk below the horizon 230 feet.

The Dunkerque Light, on the south coast of France, is 194 feet high, and is visible 28 statute miles. The ordinary calculation shows that it ought to be 190 feet below the horizon.

The Cordonan Light, on the River Gironde, west coast of France, is visible 31 statute miles, and its altitude is 207 feet, which would give its depression below the horizon as nearly 280 feet.

The Light at Madras, on the Esplanade, is 132 feet high, and is visible 28 statute miles, at which distance it ought to be beneath the horizon more than 250 feet.

The Port Nicholson Light, in New Zealand (erected in 1859), is visible 35 statute miles, the altitude being 420 feet above high water. If the water is convex it ought to be 220 feet below the horizon.

The Light on Cape Bonavista, Newfoundland, is 150 feet above high water, and is visible 35 statute miles. These figures will give, on calculating for the earth’s rotundity, 491 feet as the distance it should be sunk below the sea horizon.

The above are but a few cases selected from the work referred to in the note on page 29. Many others could be given equally important, as showing the discrepancies

p. 31

between the theory of the earth’s rotundity and the practical experience of nautical men.

The only modification which can be made in the above calculations is the allowance for refraction, which is generally considered by surveyors to amount to one-twelfth the altitude. of the object observed. If we make this allowance, it will reduce the various quotients so little that the whole will be substantially the same. Take the last case as an instance. The altitude of the light on Cape Bonavista, Newfoundland, is 150 feet, which, divided by 12, gives 13 feet as the amount to be deducted from 491 feet, making instead 478 feet, as the degree of declination.

Many have urged that refraction would account for much of the elevation of objects seen at the distance of several miles. Indeed, attempts have been made to show that the large flag at the end of six miles of the Bedford Canal (Experiment 1, fig. 2, p. 13) has been brought into the line of sight entirely by refraction. That the line of sight was not a right line, but curved over the convex surface of the water; and the well-known appearance of an object in a basin of water, has been referred to in illustration. A very little reflection, however, will show that the cases are not parallel; for instance, if the object (a shilling or other coin) is placed in a basin without water there is no refraction. Being surrounded with atmospheric air only, and the observer being in the same medium, there is no bending or refraction of the eye line. Nor would there be any refraction if the object and the observer were both surrounded with water. Refraction

p. 32

can only exist when the medium surrounding the observer is different to that in which the object is placed. As long as the shilling in the basin is surrounded with air, and the observer is in the same air, there is no refraction; but whilst the observer remains in the air, and the shilling is placed in water, refraction exists. This illustration does not apply to the experiments made on the Bedford Canal, because the flag and the boats were in the same medium as the observer–both were in the air. To make the cases parallel, the flag or the boat should have been in the water, and the observer in the air; as it was not so, the illustration fails. There is no doubt, however, that it is possible for the atmosphere to have different temperature and density at two stations six miles apart; and some degree of refraction would thence result; but on several occasions the following steps were taken to ascertain whether any such differences existed. Two barometers, two thermometers, and two hygrometers, were obtained, each two being of the same make, and reading exactly alike. On a given day, at twelve o’clock, all the instruments were carefully examined, and both of each kind were found to stand at the same point or figure: the two, barometers showed the same density; the two thermometers the same temperature; and the two hygrometers the same degree of moisture in the air. One of each kind was then taken to the opposite station, and at three o’clock each instrument was carefully examined, and the readings recorded, and the observation to the flag, &c., then immediately taken. In a short time afterwards the two sets of observers met each other about midway on the northern

p. 33

bank of the canal, when the notes were compared, and found to be precisely alike–the temperature, density, and moisture of the air did not differ at the two stations at the time the experiment with the telescope and flag-staff was made. Hence it was concluded that refraction had not played any part in the observation, and could not be allowed for, nor permitted to influence, in any way whatever, the general result.

In 1851, the author delivered a course of lectures in the Mechanics’ Institute, and afterwards at the Rotunda, in Dublin, when great interest was manifested by large audiences; and he was challenged to a repetition of some of his experiments–to be carried out in the neighbourhood. Among others, the following was made, across the Bay of Dublin. On the pier, at Kingstown Harbour, a good theodolite was fixed, at a given altitude, and directed to a flag which, earlier in the day, had been fixed at the base of the Hill of Howth, on the northern side of the bay. An observation was made at a given hour, and arrangements had been made for thermometers, barometers, and hygrometers–two of each–which had been previously compared, to be read simultaneously, one at each station. On the persons in charge of the instruments afterwards meeting, and comparing notes, it was found that the temperature, pressure, and moisture of the air had been alike at the two points, at the time the observation was made from Kingstown Pier. It had also been found by the observers that the point observed on the Hill of Howth had precisely the same altitude as that of the theodolite on the pier, and that, therefore, there was no

p. 34

curvature or convexity in the water across Dublin Bay. It was, of course, inadmissible that the similarity of altitude at the two places was the result of refraction, because there was no difference in the condition of the atmosphere at the moment of observation.

The following remarks from the Encyclopædia Brittanica–article, “Levelling”–bear on the question:–

“We suppose the visual ray to be a straight line, whereas on account of the unequal densities of the air at different distances from the earth, the rays of light are incurvated by refraction. The effect of this is to lessen the difference between the true and apparent levels, but in such an extremely variable and uncertain manner that if any constant or fixed allowance is made for it in formula or tables, it will often lead to a greater error than what it was intended to obviate. For though the refraction may at a mean compensate for about one-seventh of the curvature of the earth, it sometimes exceeds one-fifth, and at other times does not amount to one-fifteenth. We have, therefore, made no allowance for refraction in the foregone formulæ.”

It will be seen from the above that, in practice, refraction need not be allowed for. It can only exist when the line of “sight passes from one medium into another of different density; or where the same medium differs at the point of observation and the point observed. If we allow for the amount of refraction which the ordnance surveyors have adopted, viz., one-twelfth of the altitude of the object observed, and apply it to the various experiments made on the Old Bedford Canal, it will make very little difference in the actual results. In the experiment, fig. 3 for

p. 35

instance, where the top of the flag on the boat should have been 11 feet 8 inches below the horizon, deducting one-twelfth for refraction, would only reduce it to a few inches less than 10 feet.

Others, not being able to deny the fact that the surface of the water in the Old Bedford and other canals is horizontal, have thought that a solution of the difficulty was to be found in supposing the canal to be a kind of “trough” cut into the surface of the earth; and have considered that although the earth is a globe, such a canal or “trough” might exist on its surface as a chord of the arc terminating at each end. This, however, could only be possible if the earth were motionless. But the theory which demands rotundity of the earth also requires rotary motion, and this produces centrifugal force. Therefore the centrifugal action of the revolving earth would, of necessity, throw the waters of the surface away from the centre. This action being equal .at equal distances, and being retarded by the attraction of gravitation (which the theory includes), which is also equal at equal distances, the surface of every distinct and entire mass of water must stand equi-distant from the earth’s centre, and, therefore, must be convex, or an arc of a circle. Equi-distant from a centre means, in a scientific sense, “level.” Hence the necessity for using the term horizontal to distinguish between “level” and “straight.”

June 1, 2012 at 6:26 am
(27) dothemath says:

The distance across St. George’s Channel, between Holyhead and Kingstown Harbour, near Dublin, is at least 60 statute miles. It is not an uncommon thing for passengers to notice, when in, and for a considerable distance beyond the centre of the Channel, the Light on Holyhead Pier, and the Poolbeg Light in Dublin Bay Pier shows a red light at an elevation of 44 feet above high water; and the Poolbeg Lighthouse exhibits two bright lights at an altitude of 68 feet; so that a vessel in the middle of the Channel would be 30 miles from each light; and allowing the observer to be on deck, and 24 feet above the water, the horizon on a globe would be 6 miles away. Deducting 6 miles from 30, the distance from the horizon to Holyhead, on the one hand, and to Dublin Bay on the other, would be 24 miles. The square of 24, multiplied by 8 inches, shows a declination of 384 feet. The altitude of the lights in Poolbeg Lighthouse is 68 feet; and of the red light on Holyhead Pier, 44 feet. Hence, if the earth were a globe, the former would always be 316 feet and the latter 340 feet below the horizon. The line of sight H, S, would be a tangent touching the horizon at H, and passing more than 300 feet over the top of each lighthouse.

June 30, 2012 at 5:22 pm
(28) Dave says:

While driving in southern New Mexico, on a very clear day with just a few puffy clouds locally, I observed the tops of thunderstorms to the east that were at least 250 miles away, as confirmed by the use of cellphone weather satellite and radar features. They were not at the absolute limit either, so greater distances are apparently realistic.

July 18, 2012 at 3:49 pm
(29) Andy says:

A good article with some numbers is found at http://blogs.discovermagazine.com/badastronomy/2009/01/15/how-far-away-is-the-horizon/.
I read somewhere that the furthest distance one can see anywhere in the world is from the Wrangell mountains to Denali NP in Alaska. I don’t know the reference anymore but a computation using http://en.wikipedia.org/wiki/Highest_mountain_peaks_of_Alaska and http://www.movable-type.co.uk/scripts/latlong.html yields 270 miles between Mt Blackburn and Mt Foraker.

October 22, 2012 at 3:44 pm
(30) David says:

You may challenge my answer.
I believe the farthest visible distance is infinity-n, where n is defined by the limitations of the optics available to the naked eye when setting two opposing mirrors with the viewer between those opposing mirrors.
Without the mirrors, you could find the actual two farthest viewable points from a global 3 dimensional map.

February 24, 2013 at 9:27 pm
(31) Kevin Wainwright says:

Mt Kenya (17,057′) is easily observable from Mt Kilimanjaro (19,365′) on a good day – I witnessed this myself last month when I climbed Mt Kilimanjaro. The two peaks are 214 miles apart, which is well within the theoretical distance of 329 miles at which two peaks of these heights would become invisible to one another due to the curvature of the earth. I have heard it said that these two points are the most highly separated points on earth that are visible one from the other (assuming clear weather).

April 8, 2013 at 5:53 am
(32) TR Proven says:

I’m seeking the answer to how far a 21 foot object is visible to the 20/20 vision looker. I know there’s a coverage distance on the retina before the object is visible but none of the forums seem to talk about it.

As of the mountain range discussions are about very large objects. this is a small object.

Thanks

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