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friendofgunnar
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posted September 07, 2007 11:01 PM |
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Astronomical Puzzle
I haven't worked out the complete solution to this yet but here's a puzzle to chew on:
"Is it possible for two people on direct opposite sides of Earth to see Venus at the same time?"
Assume for the sake of the puzzle that once the sun is fully risen all planets and stars become fully submerged by it's light.
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baklava
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posted September 07, 2007 11:07 PM |
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Why not? It just depends on the angle of looking. Earth is round, hence it should be possible
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Geny
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What if Elvin was female?
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posted September 07, 2007 11:11 PM |
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Edited by Geny at 23:12, 07 Sep 2007.
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Sure, it's possible, they just watch US Open on the TV at the same time.
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Binabik
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posted September 07, 2007 11:15 PM |
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It would have to be at exactly sunrise or sunset. Im my opinion the sky would be way too bright to see Venus.
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kookastar
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posted September 07, 2007 11:52 PM |
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Here's an article about viewing Venus in the daytime {SanFrancisco}
http://www.fourmilab.ch/images/venus_daytime/
I must concur I've seen a venus looking "star" in the daytime, although never did check to see if it was venus...
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Binabik
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posted September 08, 2007 12:25 AM |
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Yea, now that I think about it, I think I've seen a "star" during the daytime also. But FOGs question assumed that you can't see it when the sun has risen.
If you assume it can be seen during the day, the question still remains if two people on opposite sides of the earth can see it at the same time. Ignoring light/dark, celestial bodies can never be in a viewable position by more than half the earth at one time. If Venus can be seen during the day by one person, a person on the opposite side of the earth can't see it because they would have to look "through" the earth to see it.
The only time two people on opposite sides of the earth can see a celestial body at the same time would be if the object is in a perpendicular direction to a line/plane connecting the two people. Even then, the only reason they can both see it is because they are standing and their eyes are above ground level. At ground level they can't see anything that's "inward" from a tangent line to the earth. In other words, at ground level, two people on opposite sides of the earth can never see ANY object at the same time. (ignoring that the earth's atmosphere bends the light slightly)
In order to see Venus during daylight, it must be ideal conditions. So can both people meet these ideal conditions at the same time considering the above?
um, just thinking "out loud"....
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friendofgunnar
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posted September 08, 2007 12:31 AM |
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Quote:
Yea, now that I think about it, I think I've seen a "star" during the daytime also. But FOGs question assumed that you can't see it when the sun has risen.
by the way, the puzzle assumes that you can't see it when it's "fully" risen. (I started thinking about this when I saw venus today while the sun was still in the process of rising)
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Binabik
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posted September 08, 2007 12:37 AM |
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I've been trying to figure this out for the last hour or more without drawing pictures.
I'm still debating if the two people can see ANY object at the same time.
And you also have to take into account that when you see Venus, it's reflected light from the sun, so you have to consider the angle of reflection.
I'm sure the answer can be easily found in the net, but thinking it through is more fun. (even if it's more nerdy)
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Gnoll_Mage
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posted September 08, 2007 10:12 PM |
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Binabik's right to say that we could only ever see something if we were directly opposite on the Earth because we both have height. But this is so small compared to the Earth that I'd be surprised if it were possible to both see anything at all if you were opposite. Maybe I'm missing something...
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Binabik
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posted September 08, 2007 10:20 PM |
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If I did the math right (which is very questionable), I figured with a perfectly round and smooth earth, the two people could not see anything closer than 2,843,938km away.
I used a tall person with eyes 2m above the earth. The tangent line to the earth is an angle of 89.936 degrees.
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Gnoll_Mage
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posted September 08, 2007 10:37 PM |
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My maths comes up with 8,006,215,028m, something like 4x your answer, but I don't trust mine either... 
Venus is always more than about 50 million km away from Earth, according to Wikipedia. It looks as if it is physically possible to see it, now the question is, is there some other factor that comes into play.
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baklava
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posted September 08, 2007 10:38 PM |
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Yes but Earth isn't perfectly round... It's elipsy (or whatever the adjective of 'elipse' is )
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you got the blues."
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Gnoll_Mage
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posted September 08, 2007 10:58 PM |
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Elliptic / elliptical  . I took the smallest radius Earth ever has when I was measuring the distance between the people, but I forgot to take into account the fact that the Earth would then be larger at other points. But fiddling with ellipses is too much like hard work for late in the evening 
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Binabik
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posted September 08, 2007 11:05 PM |
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Edited by Binabik at 07:36, 10 Sep 2007.
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I'll double check my numbers later, but you are probably right considering it's been more than 25 years since I've taken any math
Regardless of whose numbers are right, it's a very acute angle.
This is super exaggerated, but the purple area is the area where both people can see.
One side of the earth will be the light side and the other the dark side. With an extremely long angle, looking toward the sun side would be looking directly into the sun.
I think the "un-roundness" of the earth is insignificant.
edit: the 8 million km is correct.
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friendofgunnar
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posted September 09, 2007 07:56 PM |
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The more I think about the problem the more complex it seems to be.
I also got 8.013 million kilometers for the convergence point for the tangents. Given that the atmosphere refracts light, and that people can either climb buildings or even jump (and also that Venus is the same size as Earth), it seems that two people could see Venus at the same time. However, now we have to take the sun into account.
Anyway, let's assume that the earth is perfectly round so we can get past this
I'll post my answer sometime tomorrow if anybody wants to give it a crack before then.
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Binabik
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posted September 11, 2007 01:22 AM |
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There's another factor that hasn't been mentioned. Venus would be right against the horizon. The acuity of the human eye must be taken into account.
From Wikipedia:
Cycles per degree (CPD) measures how much an eye can differentiate one object from another in terms of degree angles. It is essentially no different from angular resolution. To measure CPD, first draw a series of black and white lines of equal width on a grid (similar to a bar code). Next, place the observer at a distance such that the sides of the grid appear one degree apart. If the grid is 1 meter away, then the grid should be about 8.7 millimeters wide. Finally, increase the number of lines and decrease the width of each line until the grid appears as a solid grey block. In one degree, a human would not be able to distinguish more than about 12 lines without the lines blurring together. So a human can resolve distances of about 0.93 millimeters at a distance of one meter.
If you calculate this out, the distance between Venus and the horizon is so small that it is very doubtful that anyone could distinguish between Venus and the Earth. This is especially true when you consider that the people would be looking through maximum atmosphere with lots of distortion.
Here's a visual aid. The orbits are to scale, and the planet diameters are 2000X scale so you can see them. Imagine two people standing on the north and south pole of the Earth (assuming no tilt). They can spin around and look in any direction. Unlike what I said earlier, they would not be looking into the sun, but they will still have that very narrow angle between Venus and the horizon.
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friendofgunnar
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posted September 11, 2007 09:41 AM |
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I think though that Venus, being a light "source", would be identifiable even in that small angle.
I ran across this as the top google hit:
"Cycles per degree is used to measure how well you can see details of an object separately without being blurry."
Not seeing something and seeing something blurry are two different things.
Is there an expert in the house?
Actually, I've got venusrise here in an hour or two. Let's see if I'm motivated to stay awake for it...
edit
probably not
An easy way to test this would be to have two observers, one with a telescope/binocs and the other without. They'd both watch the horizon and see if they could spot venusrise at the same time. I'd be willing to bet that they'd see it within seconds of each other.
I've got an opportunity to test it in a week or so.
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