Dating the Eiffel Tower

Posted: December 31, 2012 by tchannon in Analysis, methodology


Images (c)Google and providers, usage non-commercial and for education

This is a pair of aerial photographs of the Eiffel Tower, Paris. I am going to demonstrate how to estimate the height and also estimate the date of a photograph.


Parameters for the pair of photos, inserted here to be adjacent, read on first.

Measurement is difficult, great care and thought is needed. Best done several times. Perhaps a sequence of images is available, other object in the photo you can check.

Those in the southern hemisphere might have to change details, let us know.

What follows is a stroke of luck and Tim is passing on a wrinkle, plenty to spare. (‘ere, take a gross). If it helps someone somewhere sometime, great.


I am using Google Earth but other photo measurement can be used (eg. import to Draftsight where you can draw and measure angles, but you need accurate ground scale)

You also need a Nautical Almanac or tables or web resource of which there are few. By magic I discovered the astronomical software Solex is is brilliant for this task. (runs on i86, assumes ‘nix under Wine or Windows) Cost, free, says is the Light version, ignore, that is the only version.
Send Prof. Aldo Vitagliano a postcard, up to you.

The easier task, estimate height when the photo date is known

The Eiffel tower is on roughly flat ground and we can be pretty sure it is vertical. Counter intuitively provided we can deduce the point on the ground directly beneath the top of the item we are measuring, a certain amount of sideways in the aerial image doesn’t matter: the shadow is on the ground.

The Google earth measurement tool has a useful property, start a measurement at the lower point and measure upwards (towards north). In this case from the guessed centre of the tower based to the top of the roof. Repeat draw upwards, simple reason, the angle is then automatically the right way around for what we need, otherwise rotate value by 180 degrees. (actually works correctly even if the image is rotated)

You have shadow length and an angle of a sundial.

Fire up Solex. Don’t care which ephemeris.

Set the date to the photo date and 1 day step. This puts you at zero hours on the morning of the day.


This is the default on start-up, I’ve indicated what needs changing.

Set the latitude and longitude. Do not forget this or you will curse. (for Google Earth the centre lat/long is at the bottom of the image)


And this is it as used. I’ve underlined all the things you watch and indicate all the keys you need. That is all, simple.

Time spins, sun position changes. By trial and error you get the hockey stick, sorry, answer you need. (that ought to confuse outsiders)

Azim is sun azimuth in the sky which means the angle of the shadow relative the absolute north.

alt is altitude of the sun in the sky, about shadow length.

Explaining how you twiddle what in words is difficult, experiment, only thing to break is your patience.

Eiffel tower. This is a rough demonstration. Images at top left for 2001.

Image date is bottom left in format MM/DD/YYYY if you see eg. 1/1/1999 the date is unknown, first Jan is dodgy any year.

Set the date.

Get the lat/long and set.

To get the height move time within the day of the photo so that the azimuth is as the angle shown by Google Earth. (you get time of day in UT incidentally) Sanity, do the shadows look right for that time of day?

tan(57.156 alt) * 190.6 metres_shadow = 295 metres_height

Maybe you can be more accurate or account for various errors.

What is the date of a photograph?

This is very hard, sometimes impossible. Getting within a few days is good.

You need to know the year of the photo, research, deduction, any method.

You highly preferably need to know the season. Why? Date is ambiguous, two different dates with the same values, or one at umm… equinox is it?

Unfortunately you also need to know the height of the object where once again no holds barred on figuring it out. A good one is another photo at a known date. Another is some other object of a known height, use that instead.

The right hand Eiffel tower images approximate a date but is actually shown at bottom left of image, so we know the right answer.

arctan(height_of_object / length_of_shadow) = altitude

You have azimuth from Google and now the solar altitude from the  shadow vs. height ratio.

Match with Solex for the right range of likely date. You will find this tricky to do. There is logic. Day at a time for one thing, fine setting for the other.

In this case a few days out. Good enough for demo and typical of what you might manage.


The method is useful but difficult, here though are definite practical tools and instructions. No-where else on the Internet but the Talkshop.

Why am I doing this? Yeah right, mad. There is a reason to do with the Surfacestations project. Better to write it up separately than confuse a very large article where dating a photograph is needed.

Snippet mentioned by wickedpedia, Eiffel Tower is the first place cosmic rays were measured.

Post by Tim Channon

  1. tchannon says:

    If you don’t want this at the top Rog, flip the date.

  2. Caz says:

    You may be interested in this free online Ephemeris Tim. Very simple to generate tables.

    I doubt many photoshop users are aware that it is quite easy to detect fake photographs with such a tool.

  3. tchannon says:

    If that does what I assume, tables are a useful method. (online Java is not available here)

    Anyone remember nomographs, wonderful things. Go dig, ah yes
    Related to the more familiar slide rule and yes I can see one right now.

    Presumably you are writing about wrong shadows and lighting so whilst I have ways of uncovering iffy images, not an expert with the lighting issue. Perhaps you can tell us more.