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8048 clicks; posted to Geek » on 16 Jan 2009 at 4:46 AM (8 years ago)   |   Favorite    |   share:    more»

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It's out beyond the neon lights.

its always just out of reach?

I know there must be somethin' better. But there's nowhere else in sight!

Not far enough.

I was told there would be no math.

The horizon is just under our field of vision after a couple dozen miles, but the Sun is 93,000,000 miles away.

I'm sorry for be such an asshole cynic, but that light takes about 9 minutes to even reach us. When you look at the sunset, God, Jeebus, Vishnu, Buddha, and Joseph Smith aren't looking down on you.

They never even knew (or will know) of your existence.

And even if they did know, they probably wouldn't even give a shiat.

/i hope my liver and kidneys give out before the cancer gets me.

Tree fitty.

That's line of sight distance, a different way to look at it is how far away it is if you walked on the ground, ie. the arc length: walking distance = R*acos[R/(R+h)]

They are similar for low h, but ground distance limits to the circumference/4 when you go very high instead of just approaching h+R/2.

Really you need both when working out wireless communication problems. The communication goes by line of sight, but the more practical number is how far away the horizon is on the ground (and the higher the tower is the larger the difference).

pnjunction: That's line of sight distance, a different way to look at it is how far away it is if you walked on the ground, ie. the arc length: walking distance = R*acos[R/(R+h)]

They are similar for low h, but ground distance limits to the circumference/4 when you go very high instead of just approaching h+R/2.

Really you need both when working out wireless communication problems. The communication goes by line of sight, but the more practical number is how far away the horizon is on the ground (and the higher the tower is the larger the difference).

Yeah, that measurement makes more sense to me. I was wondering what they were talking about at first when they mentioned the h+R/2.

Any calc majors out there want to give the equation for the area of the earth visible from a given height?

/ not that I really need it for anything

Unavailable for comment:

klparrot: Any calc majors out there want to give the equation for the area of the earth visible from a given height?

/ not that I really need it for anything

Why, are you buying a lot of paint? For small values of h it is close to the area of a flat disk, and given the Earth is lumpy anyway, that error is good enough for you.

So when we need to expand our horizons we now have the formula to work with! Enlightenment it seems is no good unless you show your working

Hrm. From my backyard here in Tigard, Oregon, I can see the peak of Mt. Jefferson, which according to the measurement tool in Google Earth is just under 70 miles away. Using the table in the article, I would have to be standing 1km above sea level. I'm actually only about 80m above sea level, which, according to the article, should only grant me 19.2 miles of vision. Either something's not right here, or the height of the mountain overrides the calculations.

/of course as a kid, I thought I could see Disneyland from my backyard with binoculars

Isn't it the bit where everything starts turning green and liney and a bit wire frame?

Korb: Hrm. From my backyard here in Tigard, Oregon, I can see the peak of Mt. Jefferson, which according to the measurement tool in Google Earth is just under 70 miles away. Using the table in the article, I would have to be standing 1km above sea level. I'm actually only about 80m above sea level, which, according to the article, should only grant me 19.2 miles of vision. Either something's not right here, or the height of the mountain overrides the calculations.

/of course as a kid, I thought I could see Disneyland from my backyard with binoculars

When the bad astronomy guy is speaking of distance you can see, he is talking about anything which is about flush with the ground. Of course you can see the top of the mountain, but that's because it's not flush with the ground at all.

A better way to think of it is "If there were no trees or houses around, could I see the base of the mountain?" The answer to that question is no.

Korb: Hrm. From my backyard here in Tigard, Oregon, I can see the peak of Mt. Jefferson, which according to the measurement tool in Google Earth is just under 70 miles away. Using the table in the article, I would have to be standing 1km above sea level. I'm actually only about 80m above sea level, which, according to the article, should only grant me 19.2 miles of vision. Either something's not right here, or the height of the mountain overrides the calculations.

/of course as a kid, I thought I could see Disneyland from my backyard with binoculars

The article is pretty cool.

When I was in the Navy, I had a tough time using the "official" methods of estimating distance using a periscope, because I didn't have all the mast heights of the hundreds of different ship classes memorized.

Instead, I would take the height of the periscope, and use that to get the distance to the horizon. Then I would estimate the distance to the target by eyeballing what percentage of the way to the horizon the target was. This method became less accurate as the target got over the horizon, (because that distance would depend on his masthead height), but my range calls were almost always more accurate than the other officers, except for the Captain's.

The trouble is, I never called out masthead height or the number of "ticks" on the periscope. I just called out the range. That really bugged some people.

BONUS ROUND: Calculate how Our SarahTM can "see Russia from my backyard", when the nearest Russian coastline is about 1000 miles away.

DIFFICULTY: No using the variable "batshiat crazy"

About three states away for me.

jbc: Not far enough.

Here's a math problem for you, don't ponder it too long or your head'll explode, but how many drugs would you have to consume, in what period of time, to be on the street and go... 'Well, I gotta have the Horizon!'

galactus5000: Isn't it the bit where everything starts turning green and liney and a bit wire frame?

Jack31081: Here's a math problem for you, don't ponder it too long or your head'll explode, but how many drugs would you have to consume, in what period of time, to be on the street and go... 'Well, I gotta have the Horizon!'

Thanks. Now I'm gonna have to listen to the entire discography today at work!

jbc: Not far enough.

"The car is a Plymouth Horizon. It is not a joy to ride!"

1.415 * square root (height in feet) = radio horizon for VHF/UHF in miles.

DeathRaySanta: Calculate how Our SarahTM can "see Russia from my backyard",

No silly. She doesn't see Russia, she sees Putin raising his head, which is miles across and very tall, which means she can see his eyes as they come over the horizon...

// sorry, I don't have the image....a little help here?

My horizion is farther than Stevie Wonder's horizion.

100?

4?

Q?

George Washington?

I just have to say GREAT JOB to Dansker
Loved the sketch!

My daughter was doing this exact problem earlier this week. 10th grade.

AHHH...Trig. What memories!

chanceman: My horizion is farther than Stevie Wonder's horizion.

Only until it stops raining.

pnjunction: Really you need both when working out wireless communication problems. The communication goes by line of sight, but the more practical number is how far away the horizon is on the ground (and the higher the tower is the larger the difference).

Hmm...thinking about it, you'd need a pretty high tower for there to be a significant difference between line of sight and ground distance. It's probably only significant to satellite communications.

Dansker:

Please stop mocking Korb's tiny, tiny house. The job market has been very difficult on this side of the Atlantic, and some Americans have to duck to avoid hitting their head on their roof as they crawl through their door.

And women wear those 3" heels for the extra .2miles of visibility

DeathRaySanta: BONUS ROUND: Calculate how Our SarahTM can "see Russia from my backyard", when the nearest Russian coastline is about 1000 miles away.

Simple. Her house is roughly 101,000 meters tall. If you compare this to Korb's house (vide supra), which is perhaps 2 meters tell, assuming Korb is not a midget, the constrast is quite striking. It clearly illustrates the economic gaps in the US right now.

mtman900: When the bad astronomy guy is speaking of distance you can see, he is talking about anything which is about flush with the ground. Of course you can see the top of the mountain, but that's because it's not flush with the ground at all.

The Bad Astronomer is a Farker, by the way.

Only if you assume the Earth is perfectly smooth where you are looking.

DeathRaySanta: BONUS ROUND: Calculate how Our SarahTM can "see Russia from my backyard", when the nearest Russian coastline is about 1000 miles away.

DIFFICULTY: No using the variable "batshiat crazy"

9/10 on this one. You assume (correctly) that most Farkers don't know that Sarah actually said you can see Russia from Alaska (truth) and Tina Fey said she could see Russia from her house (fallacy)

chimp_ninja: Simple. Her house is roughly 101,000 meters tall. If you compare this to Korb's house (vide supra), which is perhaps 2 meters tell, assuming Korb is not a midget, the constrast is quite striking. It clearly illustrates the economic gaps in the US right now.

mtman900: When the bad astronomy guy is speaking of distance you can see, he is talking about anything which is about flush with the ground. Of course you can see the top of the mountain, but that's because it's not flush with the ground at all.

The Bad Astronomer is a Farker, by the way.

I love the disclaimer at the bottom of that link: these calculations have disregarded topography and the curvature of space-time, both of which would have a negligible effect

Great stuff

Korb: Hrm. From my backyard here in Tigard, Oregon, I can see the peak of Mt. Jefferson, which according to the measurement tool in Google Earth is just under 70 miles away. Using the table in the article, I would have to be standing 1km above sea level. I'm actually only about 80m above sea level, which, according to the article, should only grant me 19.2 miles of vision. Either something's not right here, or the height of the mountain overrides the calculations.

/of course as a kid, I thought I could see Disneyland from my backyard with binoculars

well, basically, its reversed. In your case, you are the object on the ground, and the mountain is the plane.

It's right there.

CheddarPants: It's out beyond the neon lights.

thats only true in the city

Bonanza Jellybean: Unavailable for comment:

I read a short story recently...it's the story of a photographer who went completely insane trying to take a close-up photograph of the horizon

Does gravity have any impact on the distance that can be seen?

I mean at 5'11" I am sure that the distance that I can see is only impacted minimally by gravity. But as the article states, what about when you are on a plane? Doesn't gravity extend the radius seen by a few hundred feet?

I a "D" in Calculus. I have to take it again in the Fall.....

Dangl1ng: Does gravity have any impact on the distance that can be seen?

I mean at 5'11" I am sure that the distance that I can see is only impacted minimally by gravity. But as the article states, what about when you are on a plane? Doesn't gravity extend the radius seen by a few hundred feet?

I a "D" in Calculus. I have to take it again in the Fall.....

I have a terrible memory for this stuff even though I read a lot of books about science (in the middle of "Parallel Worlds" by Michio Kaku right now), but the gravity of the Earth is probably not nearly sufficient to have a significant impact on the light relecting off of the ground to your eyes. But that's just my totally non-scientific judgement based on a poor memory of reading about science, etc.

/need more coffee

If there were a neutron star (or some other hideously dense object) in between you and the object you were looking at then yes, I believe the light would be affected by gravity. Although, if you are in an airplane flying over the Earth and there is a neutron star close enough to do that, you probably won't be worried about gravity distortion of light!

/as Dr. Neil DeGrasse Tyson would say "that would be bad"

I just can't shake the notion that for very large h, d should go to h+R. That equation doesnt seem to agree, though his numbers do...

What am I missing

The formula does not factor in atmospheric refraction.

moogrum: I just can't shake the notion that for very large h, d should go to h+R. That equation doesnt seem to agree, though his numbers do...

What am I missing

Hmm..good observation (I made the mistake of saying it goes to h+R/2 in a previous post, oops). According to limit theorem it just goes to h as h goes to infinity, which makes sense because at infinity R is going to be insignificant. I think you have to use a some kind of approximation for just 'large' h.

The only thing I can come up with is that if you look at the line before the cancels the R^2 from each side. If you consider that d^2 is going to much larger than R^2 and drop the R^2 from just that side, you're left with:

d^2 = h^2 + 2Rh + R^2 = (h+R)^2 ==> d = h + R

I'll leave it somebody with more of a math background than my engineering one to discuss the validity of dropping the R^2 from one side and not the other, seeing as how you could make the same argument that R terms are insignificant on the other side and end up with the d=h that the limit theorem provides.

The formula does not factor in atmospheric refraction.

Here's an interesting case where occasionally you can see hundreds of miles:
Corsica as Seen from Nice (new window)

I've heard of cases where people in Michigan can see Chicago due to refraction. St. Joseph, MI is 48 miles across the lake but the only time that I've seen Chicago is at sunset, from the top of the dunes with the city backlit by the setting sun (it's a stunning view from atop the Grandmere Dunes).

And the Wilkes' U.S. Exploring Expedition had to deal with serious polar refraction (new window) when exploring Antarctica for the first time. They were mapping the area around what became Wilkes Land but knew that distances were deceiving them.

ecmoRandomNumbers 2009-01-16 12:52:20 AM
The horizon is just under our field of vision after a couple dozen miles, but the Sun is 93,000,000 miles away.

I'm sorry for be such an asshole cynic, but that light takes about 9 minutes to even reach us. When you look at the sunset, God, Jeebus, Vishnu, Buddha, and Joseph Smith aren't looking down on you.

They never even knew (or will know) of your existence.

And even if they did know, they probably wouldn't even give a shiat.

/i hope my liver and kidneys give out before the cancer gets me.

Wow. Take your Prozac and keep you bitter opinions to yourself.

Fark. I bet you NEVER get laid.

The rule of thumb that I learned was to take the square root of your height above the ground, then add another 25% of the result to itself. Then call it miles. So if I'm on the roof and my eyes are 16 feet off the ground, the horizon is 5 miles away.

When I was in the Navy, it was something to be aware of. On some days the horizon looks like it's a long, long way away, on others, it looks pretty close. The height of the eye of my ship was about 65 feet. The horizon was about 10 miles away. Useful information when you're a lookout and trying to correlate a radar contact to a surface ship.

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