A few months ago in an episode of Numb3rs, the protagonist used a clever trick to locate where a photo was taken. He had the datestamp of the photo, and because it was a sunny day, the shadows were easily visible. In the photo was a basketball hoop (10ft high) which was supported by a pole extending up from the ground. The surface of the ground was made of pavers which were of a known size. Using this information he was able to locate the photo. So a few questions: 1. Is this plausible? 2. How accurate would it really be? 3. Long shot here, but where would one start digging for algorithms to actually do this? Regarding the first question of plausibility, it seems to me it is. You may have to make assumptions about which hemisphere you are looking at, but that's ok. But the whole reason I'm posting here is that although I am decent at writing computer programs (hence the algorithms question), my math, esp. physics, esp. astronomy skills are pretty meek. If the answer is no, and there's some extra piece of information you would need, please mention, as I may be misremembering the episode. This is my first post to Sciforums, please let me know if I've misfiled/broken rules.
Well, obviously you'd be able to determine which directions "in" the photo are North South East and West by looking at the direction of the shadow and comparing it to the time of day it was taken. Then you can go look for basket ball hoops that are aligned in just that direction, which you might be able to on some maps, and then you could visit those to find out which one looks like the picture. Otherwise I can't think of anything, except if you had a detailed 3D map of the area you're searching Please Register or Log in to view the hidden image! I don't know shite about physics or math, tho
Let us assume that the photo was taken somewhere in continental USA. There are four time zones in continental USA. It would seem to me that there would be four possible locations for the photo, one in each time zone. Suppose the time stamp on the photo was noon, and the shadow of the basketball pole was oriented exactly North/South, making it also noon based on actual solar time. This would indicate that the photo was taken in the center of one of the four time zones. The length of the shadow would indicate the latitude (see below), but there would be four possible longitudes, one in each time zone. Now assuming a more arbitrary time. The direction of the shadow indicates true solar time. North/South indicates noon solar time. The angle between the shadow and a North/South line indicates some solar time other than noon. I think there is a 15 degree difference for each hour (one degree of longitude for every four minutes). This value can be found somewhere (Maybe in the NY Times World Almanac. Surely on some web site). Do not use my guess without checking it. The difference between the time stamp time and true solar time would indicate how far you were from the center of a time zone. The longitude of center of each time zone is published somewhere. I think the same one degree of longitude for each 4 minutes of time difference is correct. Once again, this value can be verified. If you could not assume continental USA, there would be more than four possible longitudes. You could rule out longitudes where there were oceans or seas. You could rule ignore some longitudes due to its being unlikely that basketball is played at those longitudes. Note: At true solar noon, there is a latitude at which a vertical pole casts no shadow because the pole is pointed directly at the sun. That latitude is known for each date. If there is a shadow, you can make a right triangle, with the pole and the shadow as two legs. The hypotenuse is an imaginary line between the end of the shadow & the top of the pole. If the angle between the hypotenuse and the pole is L degrees, then you are L degrees of latitude North or South of the latitude at which the pole casts no shadow. If the end of the shadow is North of the pole, you are L degrees North. At times other than true solar noon, the calculation might be more complicated. The angle of your triangle might not be the same as the degrees of latitude north of the no shadow latitude. I worked the above out from first principles and am not sure about times other than true solar noon.
But, Dinosaur, you can't tell which direction is south and North on the picture except by guessing based on the timestamp and the direction of the shadow. I.e. you won't have a clue as to the "true solar time" :l
You need at least date & time the photo was taken, time zone, & the compass direction of the shadow. As previously posted, Without knowing the time zone you can at at best narrow the location down to 4 or more possibilities.
There are some universal timestamps, eg, Coordinated Universal Time (UTC) in GPS. I think locating a place from the length/direction of the shadow is mathematically impossible. From what you said, its more likely that he used the shadow to get a rough idea of the whereabout of the place, looked for the features in the pavement and other background objects to pinpoint the place. Actually, I have done something similar before. Some guy post two photos: one showing a rock, the other a view from the rock towards a coast. By targeting an island shown in the background and with the help of Google maps and Google Earth and then guessing from the angle of shot towards the coast, I successfully found this rock. Here, I have the information that this location is within a certain city. Why the hunt? This is my Geocaching adventure without a GPS receiver.
First, thanks to everyone for contributing their brain power to this little problem. Here are some assumptions we can make for solving this problem: We do not know what time zone we are in, but we are in the continental US We do not know what way is North in the photo We can measure, let's say down to the inch, the length of the shadow The time we are given is accurate to the minute I agree it doesn't seem possible to know where exactly the photo was taken without knowing what angle the shadow is at. However it seems like one should be able to produce an arc of possible locations. E.g. given that you have a shadow of a particular length at a particular time, there's a series of points on the Earth where that shadow could have been cast. The series of points would, I imagine, form an arc that corresponds in some way to the curvature of the Earth. Does this seem correct in principle? With that information one could overlay on sat maps and look at possible locations. You would have four time zones but perhaps you could rule some out based on historical weather information. E.g. if it was cloudy over one time zone's arc you could rule it out.
Think about a point where a vertical pole casts no shadow at a particular time. This can only occur at Solar noon at a particular latitude. There is a circle of fixed latitude where the length of the shadow can be zero. Of course, this cannot happen in continental USA. It can only occur between the tropic of Cancer & the Tropic of Capricorn. The special latiutude varies with date. The above is mentioned to present a context for an analysis. Suppose the photo was known to be taken at noon in the tropics in a region about 3000 miles wide, approximately the East/West dimension of continental USA, and there was a shadow whose length was known. At solar noon, a pole North or South or of the no-shadow location would cast a shadow whose length would depend on the distance from the special no-shadow point. Similarly, poles East or West of that point would cast shadows whose length depended on distance from that special no shadow point. Those four points would be on a closed curve, possible a circle, but more likely an ellipse or ellipse-like curve. Thus at noon in the tropics in a given time zone, there would be a closed curve of possible locations centered in the middle of the time zone. Without knowing the direction of the shadow, one could only know that it was on a closed curve around the no-shadow point in some unknown time zone. That would leave a lot of places requiring comparison with the photo, but I suppose it would be doable. For times other than noon in the tropics, I suppose there would be a different closed curve of possible locations. I suppose a similar analysis could be applied to places north or south of the tropic region. Sorry I was too busy to proof read or use a spell checker on the above.
Ok, I see what you are saying. I've been doing some more thinking and reading about this the last few days, and I've decided the problem is too hard to tackle with my current understanding of astronomy and relevant algorithms. Thanks for trying to help.
