Amoonalu asked in Science & MathematicsGeography · 10 years ago

# How far away can you see mountains from?

I'm writing a story about a girl who lives in a city that is about 800 miles away from a mountain range. I've been talking about how she can see the mountains on the horizon. In reality, would she be able to see the mountains from that far away?

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• Anonymous
10 years ago

Well, 800 miles is a bit far unless the mountains were really high up. I think your distance is too far for you to be able to see a clear horizon on the mountains. You may want to change the distance.

• Anonymous
10 years ago

Follow me on this, because I'll explain.

Let's say that you were looking at Mt. Everest, unobstructed from sea level with no atmospheric distortion of any kind, no haze, no nothing, just idealized optic conditions.

The equation to determine just how far someone could stand and see the tip-top (baring the atmospheric refraction in reality...), with the unit given in miles:

D = SQRT { (3 * H) / 2 }

So let's just call Everest 30,000 feet. Hence...

D = SQRT { [ 3 * (30,000) ] / 2 }

D = SQRT { [ 90,000 ] / 2 }

D = SQRT { 45,000 }

D = 212 miles

So you could see Everest from 212 miles away on a perfect day.

What would you need to see mountains 800 miles away? Follow --

You'd need:

H = [2D^2] / 3

H = [ 2 * (800)^2 ] / 3

H = [ 2 * (640,000) ] / 3

H = [ 1,280,000 ] / 3

H = 427,000 feet...

So your mountains would have to reach 81 miles, which is 20 miles beyond where we define the boundary between atmosphere and "outer space."

Probably should pick a smaller distance for your heroine.

• Anonymous
10 years ago

if you're at sea level, you can start seeing the top of a 4km mountain at a max distance of ~225 km.

To see a mountain from 800 miles away, the mountain would have to be about 155 miles high.

Ain't none on this planet.