[Andrew Stephens]

Yo nn maths dudes.

I was driving along this afternoon and for a split second the sky was blue and the clouds white and fluffy. And I was thinking...
"I wonder what the total volume of sky is that you can see from a point on the earths surface?" To work that out I figured I would need to know the distance to the horizon. The height of the atmosphere and some basic maths.

Can anyone here tell me.

I was wondering just how much room I could see and how much of the human race I could fit into just my un obstructed view?

[osiris]

I'm just guessing here, but a lot? Like, really a lot.

[mattyb]

The height of 'the sky' isn't fixed. Sometimes you can see the moon for example, sometimes you see stars.

And just in case you didn't know, stars are REALLY REALLY far away.

/working late before an intervention, bored atm

[GSixZero]

Quickly figuring, and ignoring some subtleties, it's on the range of 150 million cubic kilometers, if you assume the sky is 85km high, (the height of the highest clouds).

[Andrew Stephens]

Originally Posted by GSixZero 

Quickly figuring, and ignoring some subtleties, it's on the range of 150 million cubic kilometers, if you assume the sky is 85km high, (the height of the highest clouds).

[zaphod]PHREEEEEEEEEEEEEEE-OWWWWWW[/zaphod]

workings?

[richwig83]

Thread hijack: What would the viewable area be??

[BlueSky]

I hear the sky is bigger in Montana.

[osiris]

Originally Posted by Andrew Stephens 

[zaphod]PHREEEEEEEEEEEEEEE-OWWWWWW[/zaphod]

workings?

That's infinitely improbable.

[GSixZero]

Ra = atmosphere is 85km thick, more or less depending on how much you want to count.
Re = Earth has radius 6,356km (http://en.wikipedia.org/wiki/Earth_radius)

If you have no height, you can assume the visible atmosphere is comprised like a sphere of radius Ra+Re, that is partially filled to a height of Ra. I didn't figure it out, but I'd guess that adding the extra atmosphere that you can see by being ~2meters off the ground is negligible.

You can use this calculator: http://www.onlineconversion.com/obje...ial_sphere.htm

[mattyb]

Wouldn't the radius just be 85km? If you're on the North Pole and you look straight up, that would be for a distance of 85km. Why would the half a sphere of your vision have anything to do with the earth's radius?

Or has the long day at work clouded my mind?

[alligator]

Interestingly enough, nobody subtracted the guy's height from the distance to the edge of the clouds.

[Andrew Stephens]

I was thinking about it geometrically. Imagine a line from ground level to the horizon (how far away is the horizon?) this forms the base of the section of sphere. (cut and paste from here) This can be determined in a number of ways but perhaps the easiest is by using Pythagoras theorem of right-angled triangles. Using this, the distance to the horizon is:

SQRT (h+2rh)


Where h is the eye height above sea level and r is the radius of the earth (roundly, 4,000 miles).

Using feet throughout (for a six foot eye height) the calculation becomes:

SQRT (6+(2*21120000*6) = 15920 feet.

So I can see under a sphereoid with a flat base around 6 miles in diameter.

[Andrew Stephens]

Originally Posted by Andrew Stephens 

I was thinking about it geometrically. Imagine a line from ground level to the horizon (how far away is the horizon?) this forms the base of the section of sphere. (cut and paste from here) This can be determined in a number of ways but perhaps the easiest is by using Pythagoras theorem of right-angled triangles. Using this, the distance to the horizon is:

SQRT (h+2rh)


Where h is the eye height above sea level and r is the radius of the earth (roundly, 4,000 miles).

Using feet throughout (for a six foot eye height) the calculation becomes:

SQRT (6+(2*21120000*6) = 15920 feet.

So I can see under a sphereoid with a flat base around 6 miles in diameter.

oh except the base isn't flat because of the earth's surface being curved! doh!