Grandpa, what’s the farthest you can see?

[effortless]

Not my current myopia but an interesting question from a six year old. Above what height does the visual distance on the globe stop increasing. At about 35,000 I’ve always estimated my field of vision to be about 700 miles on the surface. Never been higher, I guess I could have done it mathematically but I’m too lazy.

[what next]

Hello!

... I guess I could have done it mathematically but I’m too lazy.

Mee too (lazy), but if you really want to impress your six year old grandson then you tell him that the fartest you can see with your naked eye is the Andromeda Galaxy (M31) which is 2.5 million light years away. Which in km would be: 23651826000000000000

[treadigraph]

Can't answer the question posed but in terms of seeing things at a distance...

While sitting high up on my local common in south London on clear winter days after sunset, I can see sun lit vapour trails right down on the western horizon. With the aid of ADSB I have often been able to work out which aircraft they are and the furthest I can see them is about halfway across the Irish Sea and down beyond Truro. This last observation was confirmed by a Martinair 747 which passed over me and its trail was still visible as it passed abeam Truro which is about 230 miles. Another good one was a Ryanair 737 out of Cork to Gatwick; spotted the trail abeam Milford Haven and watched till around Dorset when it disappeared as it began to descend. I probably could have seen the lights as it flew the approach onto 26 at Gatwick, but 30 mins or so after sunset it's beginning to getting a bit dark and I have mile of common to cross with attendant tree roots, cow pats and other unpleasant hazards in the grass!

During Lockdown with fewer aircraft about, one lengthy trail stood out in the early evening NW sky with a couple of turns in the trail, I spotted it abeam Chester and followed it down past Brum to London where it turned east heading towards Europe. A FedEx aircraft out of Dublin.

[WHBM]

While sitting high up on my local common in south London on clear winter days after sunset, I can see sun lit vapour trails right down on the western horizon. With the aid of ADSB I have often been able to work out which aircraft they are and the furthest I can see them is about halfway across the Irish Sea and down beyond Truro. This last observation was confirmed by a Martinair 747 which passed over me and its trail was still visible as it passed abeam Truro which is about 230 miles.
Oh, you are not allowed to say that, the air of London is officially desperately polluted. Must be right because the Mayor says so, so to avoid being asphyxiated in our beds we all have to give up our cars, the apparent source of it all, and travel only on public transport - which by the most amazing coincidence is a commercial operation of said Mayor, where they are short of money ...

Descriptions of low angle sightings of 200+ miles definitely not allowable.

[hoss183]

I remember that at 6ft the horizon is at 3 miles.
At 35,000 its 229 miles apparently calculator (https://dizzib.github.io/earth/curve-calc/?d0=30&h0=10&unit=imperial)
Correlates with treadigraphs observations

[Bergerie1]

I remember one morning flying east when coming up to Strumble in South Wales, on an incredibly clear day, being able to see the whole of the east coast of England from Kent to the Humber. Amazing, the mapmakers were right after all!!

[treadigraph]

Oh, you are not allowed to say that, the air of London is officially desperately polluted. Must be right because the Mayor says so, so to avoid being asphyxiated in our beds we all have to give up our cars, the apparent source of it all, and travel only on public transport - which by the most amazing coincidence is a commercial operation of said Mayor, where they are short of money ...

Descriptions of low angle sightings of 200+ miles definitely not allowable.
:)

Generally these severe clear days follow some cleansing heavy rain! On the pollution point, for 15 years I worked variously on the 16/17/18/19/20th floors of a tower block in Croydon with great views of London from Westminster to Heathrow and beyond; after heavy rain/wind, the early morning view in the sunshine was superb. By lunchtime a distinct yellowy-brown stain would be starting to make the buildings less distinct. I once flew in a C150 out of Lasham on a sunny day with a hazy sky. We climbed to about 3000' into an azure sky and a yellow tinge topped the smoggy crap below us...

[Pilot DAR]

I was up flying the other day to appreciate the autumn colours, and could see the cliffs at then north of Georgian bay 114 miles away from 3500 feet. I could just make out New York State across Lake Ontario to the south, 85 miles away, though the shore is not as prominent.

[Ex FSO GRIFFO]

Hey Mr 'T',

Whilst sitting at Sydney ATS Centre, we could see contrails in the setting sun to the 'far' west, travelling N / S and E / W , and we knew by the E/W ones that they were over Griffith (NSW) which is approx 260nm west of SY... the N/S ones transiting Melbourne / Brisbane....Had it not been for the Great Dividing Range to the West of SY, elevation approx 3,400ft AMSL, then we might have got further.....

Cheers

[cappt]

Great question, from 35K on a perfectly clear night the city lights start coming into view out the front from about 200 miles away. This would check out with Treadigraphs observation of contrails disappearing over the horizon around 230 miles away. Andromeda galaxy, great answer!

[roger4]

Hello!

Quote:
Originally Posted by effortless View Post (https://www.pprune.org/private-flying/636162-grandpa-what-s-farthest-you-can-see.html#post10906663)
... I guess I could have done it mathematically but I’m too lazy.
Mee too (lazy), but if you really want to impress your six year old grandson then you tell him that the fartest you can see with your naked eye is the Andromeda Galaxy (M31) which is 2.5 million light years away. Which in km would be: 23651826000000000000

Strictly, you aren't seeing the Andromeda Galaxy, you are seeing light that left Andromeda 2.5million years ago and has only just arrived on earth!

[effortless]

Thanks all, after discussion with the sprog, I found that he had been looking at a picture of the world from space. When the whole disc was visible, he worked out that he couldn’t see the whole surface of the hemisphere due to the angles. So the surface disappears round the corner, as he put it, long before the edge. That is if looking down on the pole, we couldn’t see the surface at the equator. So his question is, how far from earth does an astronaut stop seeng more of the earth.

[old,not bold]

Strictly, you aren't seeing the Andromeda Galaxy, you are seeing light that left Andromeda 2.5million years ago and has only just arrived on earth!
Yes well, that's true; just as it's true of "seeing" a lighthouse; you are seeing the light that left the lighthouse a short time** ago, not the lighthouse.

** 0.0000166 of a second, roughly. I think, if you're in a small sailing boat and the lighthouse is on the horizon. While the light is travelling towards you your boat will move 0.0000355 of a metre in whatever direction your CMG might be, which is something to take into account when doing a running fix using the lighthouse.

[DeanoP]

In the old days at Nav school, we were taught:

Radio Range Line of sight formula. = 1.22 X Sq. Root of Aerial Height + 1.22 X Sq.Root of A/C height.

Thus assuming you are looking at the sea level horizon at 24000ft. Line of sight = 189 nautical miles.

For terrain, substitute terrain height for Ae Ht. eg ground elevation 3000ft, A/C height 24000ft.
You can expect to see the top of the terrain at:
67 nm (terrain height)+ 189nm (A/C height) = 256nm

[Bergerie1]

The hardest question my three year old grandson asked some years ago was, "Grandpa, exactly what is electricity?" He is now doing some kind of a computer science degree at Cambridge. Perhaps he can now tell me!

[Pilot DAR]

Grandpa, exactly what is electricity?

It's smoke, 'cause when you let it out, whatever it is doesn't work any more.

[Mr Mac]

From our top field in Yorkshire we can see on a clear day with Binoculars' the Humber Bridge support, around 70 miles. As for A/C we can easily see north bound turning A/C with landing lights on from East Midlands Airport a similar distance. As for the high level stuff it always has amazed me both the view from the A/C, but also looking at the A/C as to how far away vertically they are.
Cheers
Mr Mac

[jtt]

From a height H you can see

w = R * acos(R / (H + R))

afar in each direction. R here is the readius of the earth (about 6360 km). The formula assumes that the earth is a perfect sphere (which it isn't, it's a bit thicker at the equator). If you're near to the ground increasing your hight has a large effect. If your eyes are 1 m above the ground you can see things about 3.6 km away, if they are at 2 m you can already see about 5 km. At 10 km height you can see all things about 350 km away. But the increase of radius of sight becomes smaller and smaller the higher you get. At 300 km (about the height of the ISS) the radius of sight is about 1900 km, at 1000 km it's 3350 km, at a million km (i.e. three times further away than the moon) it's 9960 km and at a billion km (from somewhere between Jupiter and Saturn) it's 9999 km. To be able to see all of a hemisphere you'd need to be infinitely far away (and the universe isn't infinite, and even if it where at that distance you'd only see the earth as a single, infinitely small point).

So the correct answer for your grandson (who seems to be a very smart boy;-) is that there's no point in the universe where you can see all of a hemisphere of the earth. And if he's already very far away going away further (even a lot) does help less and less - from the moon he can already see 99% and to see 99.9% he'd need to go ten times further away (beyond Mars). Also tell him to try to become good at math which will allow him to find the answer to such (and many more) questions.

[Fareastdriver]

In the days when civil airspace stopped at 29,000 ft I could fly my Vampire over the centre of London around midnight and look at the lights of Paris one way and an illuminated map of England the other.

[effortless]

Thanks jtt but you are missing his point. Certainly you can see the whole disc but you cannot see the surface of the whole hemisphere. It is round the corner.

[FullOppositeRudder]

This doesn't fit the properties of the discussion exactly, but last night we had an excellent overhead at dusk pass of the International Space Station which continued visually right down to the distant treeline on the south eastern horizon. Looking back at my tracking program for that pass, at that moment it was 2,150 km distant at an altitude of 434 km with a calculated elevation of about 2.5 degrees. Part of the fascination with this object is my involvement with the on-board amateur radio experiments, the rest is just the fascination of it being there, just as it was in October 1957 like watching the very first LEO object (Sputnik 1 launch vehicle) cross the sky. My grandmother was both skeptical and fearful - "Whatever next!" she said. None of us could have predicted what this would lead to in the years since that time and right up to our present era.

[visibility3miles]

I'm told that the sailors of old always knew that the hulls disappeared from view first, and the mast tops and crows nest's last, so they knew the earth was curved rather than flat when, for example, Christopher Columbus sailed away.

https://www.quora.com/What-is-the-distance-to-the-horizon-from-sea-level?share=1
Originally Answered: How far is the horizon at sea level? (https://www.quora.com/How-far-is-the-horizon-at-sea-level?no_redirect=1)As mentioned by others, the distance to the horizon at sea level (assuming you mean looking out over calm water) depends on what elevation you are viewing from. A good approximation for this when your observing height is relatively small compared to the radius of the Earth (in effect, not from the ISS!) is 𝑑=2𝑅ℎ‾‾‾‾√d=2Rh, where d is the distance to the horizon, R is the radius of the Earth, and h is the observation height.

As Chris Spencer (https://www.quora.com/profile/Chris-Spencer-120) wrote, this can be approximated as 𝑑=3.57ℎ‾‾√d=3.57h where h is in meters and d is in kilometers, or 𝑑=1.22ℎ‾‾√d=1.22h where h is in feet and d is in miles.

This would be great if we were on an airless planet, but in fact the distance to the horizon changes depending on the amount of atmospheric refraction, a function of temperature and pressure. In most cases, the atmosphere bends light rays downward, moving the horizon farther out. The equation is quite complicated and depends on knowing the atmospheric conditions quite precisely. However a reasonable approximation is either to increase the distance by 8%, or to replace the Earth’s radius by its effective radius, approximated to be 7/6 R. In which case the formulas become 𝑑=3.86ℎ‾‾√d=3.86h and 𝑑=1.32ℎ‾‾√d=1.32h.

Assuming an average overall height in the US, this would mean that the horizon IS 2.87 miles away, but appears to be 3.11 miles away.

[visibility3miles]

And, given my screen name, you know I was not supposed to fly if the visibility was less than three miles...

[kiwi grey]

From the car-park on Te Mata Peak (elevation ~400m, near Havelock North, Hawke's Bay, NZ), I have on an exceptionally clear day been able to see both Mt Ruapehu and Mt Taranaki.
Mt Taranaki is on the other side of the North Island and ~250km from Te Mata Peak
:O

[MarianA]

So his question is, how far from earth does an astronaut stop seeing more of the earth.

Supposing the astronaut is looking out the cupola of the ISS 400km above the surface of the earth I calculate a distance to the horizon of just under 2300km.

https://cimg7.ibsrv.net/gimg/pprune.org-vbulletin/600x400/cupola_f56c0cb9865d7d6954217b39efe1497f02584f0e.jpg

That means she sees the horizon 2300km from her vantage point.

The distance along the curvature on the ground an ant would have to travel will be slightly different. More different as your altitude above earth increases. Looking down from the moon almost the whole hemisphere will be visible and distance along the line of sight would be dominated by the distance from earth in the first place.

The math is just using the pythagorean theorem:

https://cimg6.ibsrv.net/gimg/pprune.org-vbulletin/200x200/horiz_8773dc64e6540bf775069173beba63d5fd47433e.gif

r=6400km
v=400km

The distance d from the Observer O to a point H on the horizon is given as the square root of

2*r*v+v^2

[goldox]

A few years ago one of the first 360 degree high-res photos of London was taken from (I think) the top of the Telecom Tower.
I remember scrolling and zooming around the image for ages being fascinated at what could be seen.
Looking due west I eventually zoomed as far as possible, and although quite hazy could clearly see tails of BA aircraft, airport buildings, and of course the tower.
I was mightily impressed.

[goldox]

Found it!
Height of viewing platform of BT Tower is 177 metres.
Distance to LHR tower is 20 miles.
Can't do any maths from this, not my thing....:O



https://cimg4.ibsrv.net/gimg/pprune.org-vbulletin/1232x577/lhr_from_bt_tower_b288e2fd7c468bc8acd3c75b7f9a01eafbc133cc.p ng

[Midland 331]

A gin-clear December afternoon in Richmond, N.Yorks, U.K..

Aircraft seen con-trailing over Grimsby to the south-east, and Isle of Man to the west, all verified on FR24.

Heading up The East Coast to Teesside in the days of the "hang a left at Clacton" experimental rmilitary airspace routing, it was great to see the "bump" of Kent, then the tapering shape of The Wash, all weather map-style.

[GS-Alpha]

If you want the distance the ant travels (maintaining that the Earth is a sphere), you just need angle C. This can be calculated using the Sine rule:

OH/SinC = CO/SinH

SinH = Sin90 = 1

So SinC = OH/CO => AngleC = aSin(2298/6800) = 19.7515 degrees.

Distance the ant travels = Circumference of the Earth x 19.7515/360 = 2 x pi x 6400 x 19.7515/360 = 2206km.

(Something tells me the ant won’t survive the voyage).

[netstruggler]

As you move away from earth more and more of its hemisphere becomes visible.

But to see absolutely the whole hemisphere you'd need to be infinitely far away, such that the rays of light towards your eyes become parallel.

Luckily the universe allows for getting infinitely far away (perhaps).

[pilotmike]

For most applications, a simple approximation to within about 1%, which is close enough for most situations on Earth is:

D (Nautical Miles) = Square root of Height (Feet).

So to answer 'effortless's original question, the distance visible from 35,000' is around 190NM or 220 miles, not 700 miles. Apologies for making it appear so simple, when it can be made to sound so mathematically involved and over-complicated.

[scifi]

For those lucky enough to be really high above the earth, the amount of 'earth' that you can see is equal to 180 degrees minus the angle of the size of the earth.
So if earth subtends an angle of 30 degrees, you are actually seeing 180-30 , = 150 degrees of it.
Even when your earth only subtends an angle of 1 degree, you are still only seeing 179 degrees of it.
.

[Jan Olieslagers]

Grandpa, what’s the farthest you can see?

"Oh, that depends on many things, my big dear.
I've happened to not see your grandma just around the corner.
I've happened to see a B747 27 furlongs away."

With any luck, that will get him on about what a furlong is. Or a B747.

[treadigraph]

Had a lovely view of the ISS one night - noticed it was coming on the Portuguese coast around Porto so nipped up to my bedroom which faces SSE. Could see it clearly all the way across the Europe until it disappeared behind the flats opposite, probably near Warsaw or somewhere like that. In doing so it passed over the newly risen fullish moon and afterwards I could mentally trace its curved path from horizon to horizon - the earth is flat? Had another great view from Fort William - it was over Penzance when we spotted it!