How far is the horizon from the observer at sea level?

Answer 1

The answer would depend upon the observer's height, or more accurately, the height of the observer's eyes from sea level. For simplicity's sake, let's use the numbers 1.5m for eye height, 6,375,000m for the radius of Earth, and of course, assume that the planet is a perfect sphere, our observer has perfect eyesight, etc.

The line of the observer's vision when it meets the horizon forms a tangent to the surface of Earth. If you draw a line from this point to the center of the planet, and another line from the observer to the center, you form a right triangle. One leg is 6,375,000m and the hypotenuse is 6,375,001.5m. So the other leg can easily be computed using the Pythagorean Theorem:

d = sqrt[ (6,375,0001.5)^2 - (6,375,000)^2 ] = 4373.21

So to our observer, the horizon is about 4.37km away.

Note that this is the limit of vision for objects with zero height, e.g. something painted on the ground (assuming again our observer has perfect eyesight). S/he can see objects even further away if they do have height. For example, two observers with identical height will be able to see one another at twice the distance, though it will only be one another's foreheads poking a tiny bit above the horizon.

Large objects such as buildings, or ships sailing in, may be seen at a much greater distance, and this distance is also made much greater if the observer moves to higher ground. For example, even going to the top of a small, 10m building (only a single storey) will extend the horizon to 12.1km, and standing atop a 50m cliff extends it to 25.6km.

Answer 2

The distance to the horizon in nautical miles is 1.25 times the square root of the height above sea level of your eyes in feet. So if you're standing on the beach and your eyes are nine feet above sea level, the horizon is 1.25 times three = 3.75 nautical miles away.

Answer 3

'Horizon' is an illusion. It does not exist. When you reach where you think is horizon, it is again that much far away -like carrot on a stick. I guess Horizon is as far as you can see.
Have a friend sail into see, keep in touch through cell phone. Call him when you can last see him and ask him how much has he sailed -if the boat has odometer.
There is your answer.

Answer 4

This is a hard one for my simple mind,, I know it has to do with Quadrant being a verticle angle measured from the horizon at sea level.
I suspect firefly up there has your best answer.

Answer 5

It varies a bit based on the height of the observer.

Answer 6

Around 18 kms on a clear day.

Answer 7

I think it's 20 miles. My dad told me that when I was a kid, so I don't have any proof. That's just the only thing I've ever heard about it.

Answer 8

it depends on the position of the sun. it usually seems like a few miles