# How far can we see?

So how far can we see when we peer out into space or more prosaically, out at the horizon? Is there a limit? Obviously, the curvature of the earth will affect distance seen…20 miles?

If you’re talking about space, the answer is several thousand lightyears. Most of those pinpricks of light in the night sky are very distant. Also, once you get out of earth’s atmosphere, they are quite clear.

If, however, you’re talking about the horizon, the answer varies. It will be different depending on impurities in the atmosphere (smoke and water vapor, mostly). I live in the Ohio River Valley, and in the summer the combination of humidity evaporated off the river and smoke from local industries make visibility very limited.

Carpe hoc!

I read somewhere (no, I don’t remember where) that on a moonless night, with no obstruction, the human eye could make out a lit match from a distance of fifty miles.

IIRC, the furthest astronomical object that can be seen with the naked eye (from Earth) is the Andromeda Galaxy, 2.9 million light years away.
Alphagene

This is a simple trigonometric calculation (assuming the earth is spherical to avoid having to take into consideration exactly where you are standing) which depends on how high above the ground you are, and how high above the ground the object you wish to see is.

Assuming your eye is 6 feet above the ground, and you are looking at a spot on the earth’s surface, and the earth has a radius of 4000 miles (actually a little less), the angle between eye-center and spot center is about .043 degrees (arccosine of 4000/(4000 + 6/5280)). Take the tangent of that, multiply by 4000, and you get about 3 miles.

Now climb up on a hill to get your eyes 100’ above the ground, and you’ll be able to see over 12 miles.

If you are talking about how keen is human vision, it is very keen indeed.
An astronaut in low orbit can perfectly discern the trail of a middle-sized ship in the ocean under good visibility conditions.

There’s a somewhat simple formula that gives you your visual range according to your height above the ground, but I forgot it (shame on me!)

If I find it, I’ll post it.

The general rule(s) of thumb that I have seen regarding how to calculate distance to the horizon are:

Square root of your height/altitude in feet times 1.317 miles. (6 foot height gives 2.817 miles).

Or: Square root of your height/altitude in feet times 1.15 miles. (6 foot height gives 3.226 miles).

Or: Cecil quoted square root of your height/altitude in feet times 1.5 miles. (6 foot height gives 3.674 miles.)

Cecil’s correspondent in More of the Straight Dope used the formula from the other direction and his .574 miles inverts to 1.74 miles.

I suspect the difference in the values Cecil and I have been given (1.15 or 1.317 vs 1.5) are based on different attempts to define the length of arc on the Earth (which foils those attempts by not being a perfect sphere). (I further suspect that Cecil was using a figure that is easy to remember, going only to a single decimal place.)

Note that these are mostly in the ballpark with the answer Jens gave without requiring the final trigonometric conversion of tangent. If you actually carry around a calculator, you might want to find the various estimates of the Earth’s diameter at different locations and use the formula Jens provided. (The International Union of Geodesy and Geophysics set the equatorial diameter at 7,926.41 miles (3,963.205 mile radius) in 1967. I don’t know whether that has been updated.)

Tom~

E1skeptic: “An astronaut in low orbit can perfectly discern the trail of a middle-sized ship in the ocean under good visibility conditions.”

E1, I’d like to know where you heard this. If the Great Wall of China can’t be seen from outerspace (as has been frequently debunked) I don’t see how this is possible.

Carpe hoc!
(The Artist formerly known as pathunt)

The Great Wall of China can be seen from outer space. What is constantly being debunked is the idea that it is the only thing which can be seen. It isn’t. See:

## http://www.straightdope.com/classics/a2_092.html

“You can’t run away forever; but there’s nothing wrong with getting a good head start.” — Jim Steinman

Dennis Matheson — Dennis@mountaindiver.com
Hike, Dive, Ski, Climb — www.mountaindiver.com

"Think so? Tom Burnam, author of More Misinformation (1980), quotes a letter from astronaut Alan Bean on the subject:

‘The only thing you can see from the moon is a beautiful sphere, mostly white (clouds), some blue (ocean), patches of yellow (deserts), and every once in a while some green vegetation. No man-made object is visible on this scale. In fact, when first leaving earth’s orbit and only a few thousand miles away, no man-made object is visible at that point either.’"

Of course, they are talking about after leaving oribt, so I concede that it might be possible to see the Great Wall from the “low orbit” E1 was talking about. Still, the trail of a mid-sized ship would be much more difficult to see, due to it being pretty much the same color as the surrounding ocean.

Carpe hoc!
(The Artist formerly known as pathunt)

Disclaimer: I have no 1st hand knowledge of what you can or cannot see from orbit, having never been there

But the topic is kinda interesting to think about. LEO might, I suppose be as low as 100 miles - I believe things can orbit at that height for at least a few days before deorbiting due to aero drag. So let’s say that’s our height.

Now, 100 miles is a ways, but really, it’s not that far. For instance, I live in colorado, and there’s absolutely no missing a particular mountain that’s 60 miles from my house. Even at 100 miles away, on a clear day most of it is below the horizon, but you can see the top part with little trouble. A mountain is much bigger than manmade objects of course, but the top of this one is pretty narrow (I’m guessing maybe 50 meters?), and you can see some amount of detail.

The other thing to consider here is that angular size isn’t the only factor at work. If something is glinting, for example, or luminous, you can see it easily even when it doesn’t subtend enough arc to be visible normally. Maybe that’s the deal with ship wakes; they glint in a way that’s different from the surrounding water. (I’m not saying this is really true, just tossing it out as an idea).

I hereby propose that everybody save up and buy me a ride into space (and BACK, dammit! ) and I’ll give you all a first hand, detailed report about what I could and could not see.

k0myers

Difficult, but not impossible. If you want to get into all the physics behind refraction, etc, etc, we will have a looooong debate here. I clearly remarked “under good visibilty conditions”. That means the right illumination (angle of incidence and intensity), proper atmospheric conditions, etc. I was just trying to stress the fact that our vision is VERY good.

And, thanks Tomndebb. The formula I was referring to is the same Cecil gave: square root of your height/altitude in feet times 1.5 = visual range in statute miles.

So how does that relate to how far we are supposed to sit from our tv screen? Which varies with the set size…right?

E1skeptic, due to all that unfortunate “Great Wall” discussion, I might have come off a little rude. I’m sorry. I really would like to know where you might have heard about the ship’s trail. If you could remember and pass it along, I’d really appreciate it. Thanks.

Carpe hoc!
(The Artist formerly known as pathunt)

We can see as far as the lens of our eyes.
Any light that strikes the lens is detected, regardless of how far it has traveled.
No light, no sight.
As stated above, we can see for millions of light years. Forever, as they say.
Lucky us, huh.
Peace,
mangeorge

Mangeorge is right in a sense. If it’s bright enough, we’ll see it. But regarding how far we can see small detail, the answer is related to angular size.

Because that concept is not easy to grasp, we use analogies such as “the light of a cigarrete butt at a distance of a mile in a clear night”.

MrKnowItAll: No offense taken, thanks for the apology, anyways. I don’t remember right know the reference for my previous statement. I will look it up, and let you know ASAP.

What I could find, though, is the following statement in the book “Everyday Wonders”, by Barry Evans:

I’m already looking for my “Guiness” to check it out myself.

Peace.

All these formulas seem to under estimate the distance that a person can see. I work as a weather observer and one of my jobs is to determine visibility. On a clear day I can easily see the visibility marker 6 miles away. I can also make out individual houses in the town across the strait 20 miles away. I can also see the mountains 50 miles away and certainly could see them from much farther away.

vlad621 writes, “All these formulas seem to under estimate the distance that a person can see. … I can also see the mountains 50 miles away and certainly could see them from much farther away.”

I don’t doubt for a moment that you can a mountain from 50 or more miles away, but that does not imply the formulas are wrong. You forget that horizons are additive.

k0myers

Well i remember being up on Fremont Peak in the Gabilan mountain range.(About 3,395 ft. in elevation). It’s near the small town of San Juan Bautista in California.We were able to see all the way across the San Joaquin valley, and see several snow capped peaks of the Sierra Nevadas (on a clear day) You can also spot Mt. Diablo (Its near the bay area), and you can see all the way to Arroyo Seco which is about 90 miles or so (probably more but thats the most recognizeable spot in the area to those of us up on that mountain).