Assuming a clear day and 360 degree view, what percentage of the earth's surface can I see from 33,000 feet?

Answer 1

0.0782% -

Converted to miles for convienence, your altitude is 6.25 miles, and assume Earth's radius equals 4000 miles. Note that the 3 points of your position, a point on the horizon, and the center of Earth form a right triangle with a hypotenuse of 4006.25 miles (your distance to the center of Earth) and one side of 4000 miles (the distance from the point on the horizon to the center of Earth) Therefore the distance you can see to in miles would be equal to the square root of the difference of the square of the hypotenuse and the square of the long side, i.e:

d = SQRT(4006.25^2 - 4000^2)

I get about 223.7 miles. So the area that you can see is that squared times pi (area of a circle of course). I get about 157,202 square miles. That divided into the area of Earth, which is

4 * 4000^2 * pi =~ 201.062 million sqare miles

gives about 0.000782, or 0.0782%

I made a simplification that result in negligible error, that being that the distance from you to the horizon equals the distance from ground level directly below you to the horizon, which isn't exactly correct. If you like, you can use the Pythagorian Formula again to get a less approximate number (which still won't be exactly correct due to the curvature of Earth within that circle), but, rounded to 3 decimal places, I think you'll end up with the exact same result.

Sound good?

Answer 2

The whole area of globe S=4pi*R^2, R=6370 km; now you are above the surface at the point A, being h = 33000ft = 10 km; you also can see a point B on horizon, so AB is tangent to the globe. If point O is center of the globe, then cos(a)=R/(R+h), where a is angle AOB.
The area visible to you s=Integral{for t=0 until a} of R*dt*2pi*sint*R = 2pi*R^2* Integral{for t=0 until a} of sint*dt = -2pi*R^2*cost {for t=0 until a} = -2pi*R^2*(cos(a)-1) = 2pi*R^2* h/(R+h); thus q=s/S=0.5*h/(R+h)= 5/6380=0.0784%

Answer 3

The previous two answerers have the correct method, but they have allowed rounding errors to creep into their results.

By taking care to avoid those, the answer is 0.07858 per cent, so they were only tiny errors anyway.

Answer 4

in many situations verse 9 is taken out of context , neglecting to point the verses before and after it. the following is the the instant context, “yet ?do no longer be called ?Rabbi; for One is your instructor, and also you're all brothers. 9 “do no longer call all people in the international your father; for ?One is your Father, He who's in heaven. 10 “do no longer be called ?leaders; for One is your chief, that is, Christ.” Jesus is dealing with a a lot different challenge. he's retaining the hypocrisy of the Pharisees and instructors of the regulation. In verses 6 and 7 which at modern-day precede the rejection of the titles of honor, Jesus explains in what experience His rejection is meant: "and they love the position of honor at feasts and the suited seats contained in the Synagogues, and salutations contained in the market places, and being called rabbi." the following Jesus is commenting on their superiority complexes. they have effectively set God aside and positioned themselves in His position; for this reason the comments on being humbled and being exalted. Bible Christians call their ministers "Pastor." Pastor ability shepherd. In John 10:14-16 Jesus says, "i'm the reliable shepherd. i understand my own and my own understand me, because the daddy is time-honored with me and that i understand the daddy, and that i lay down my existence for the sheep. and that i have different sheep which aren't to any extent further of this fold. i need to carry them also, and they are going to heed my voice. So there'll be one flock, one shepherd." If we reason that we received't call a clergyman Father because we "have one Father who's in heaven," then can we no longer also reason that we received't call a minister Pastor because there is purely "one Shepherd?" placing apart and grabbing carry of one scripture verse is volatile. it would want to be deceptive or perhaps risky. Even an honest and nicely-intentioned Christian can subconsciously bend a verse to verify his or her own needs. that is taken into consideration mandatory to appreciate the Bible as God meant. St. Augustine once stated, "no longer what one scripture says, yet what all of Scripture says." we are able to take it a step more desirable and say, no longer what Scripture says yet what Scripture ability.

Answer 5

approximately 300 miles around,then the curvature of the earth drops off.