Measure the tilt of the Earth today!

A person without a shadow should keep out of the sun, that is the only safe and rational plan. -Adelbert von Chamisso

A few years ago, there was a rumor going around that the Earth’s axis had shifted, and that we were no longer inclined to the Sun at 23.5°.

Well, guess what? Today, June 21st, like most June 21sts, is the Summer Solstice for the Northern Hemisphere. This means, for everyone (like me) living North of the Tropic of Cancer, this is the one day of the year where the Sun reaches its absolute highest point in the sky.

(If you’re South of the Tropic of Capricorn, this will apply to you on December 21st.)

This is particularly interesting, because not only do you receive the greatest amount of daylight on the Summer Solstice, but because the Sun reaches its highest point in the sky, shadows of completely vertical objects reach their shortest length at (astronomical) noon on this day, as opposed to any other.

Back in ancient times, this idea that different latitudes had shadows of different lengths allowed us to measure the circumference of Earth for the first time.

But we know the size of Earth quite well now, and we’re also pros at measuring latitude and longitude.

This means that we can use our stick and its shadow, combined with our knowledge of our latitude, to measure the tilt of the Earth!

How’s that? It’s pretty simple. All you have to do is measure what length your shadow is from a vertical object over the course of a day.

You’ll find one point — that corresponds to astronomical noon — where the shadow is shorter than all others. If you use a little geometry, you’ll realize you know the length of the shadow and the actual height of the stick, and so can figure out what angle the Sun is at when it reaches its highest point during the solstice.

And that’s it! Just subtract this angle from your latitude and you’ve measured the Earth’s axial tilt! This is probably the easiest way to do it, and it works for everyone North of 23.5°. (Or, it would if we all had a sunny day!) And don’t worry too hard if you missed today; you’ll get some really close answers if you do it any time this week!

So happy Summer Solstice, but for those of you who have Winter Solstice today, I was ready for you six months ago!

Comments

  1. #1 6EQUJ5
    June 21, 2010

    Earlier today we saw the Summer Solstice. (I was awake at 1128 UTC.) The other hemisphere saw the Winter Solstice. To those few people straddling the Equator at the time, it was just a solstice.

    In the northern hemisphere, our days are now getting shorter and our nights longer, but usually we don’t hear this from network news weatherbozoes until the equinoxes. No one knows why.

  2. #2 bifyu
    June 21, 2010

    Those of us in the tropics experience this twice a year on dates straddling the solstice. In Hawaiʻi they’ve named this “Lahaina Noon”. The sun is passes directly overhead (though not actually at 12p) and there are no shadows for the vertical stick-like objects. It’s kind of a nifty demonstration.

  3. #3 Jeffrey
    June 23, 2010

    Nice post! But are you sure about that formula?

    “Just subtract this angle from your latitude and you’ve measured the Earth’s axial tilt!”

    I keep noodling around with it and I can’t get it to work.

    How’s this strike you?
    tilt=latitude + sun angle-90

    Consider right at 23.5 lat. The sun’s angle will be 90 degrees.

    20 degrees north of that, the sun’s angle will be 20 degrees lower.

    At the equinox, when the tilt toward the sun is zero, at the poles, you get tilt=90+0-90=0.

    Do I have this wrong?

  4. #4 Jeffrey
    June 23, 2010

    Never mind. You’re defining “sun angle” as the difference between vertical and where the sun is, while I was thinking of it as the angle between the horizon and the sun.

  5. #5 Spaceman Spiff
    June 25, 2010

    Sorry to be picky, but as a matter of fact the Earth’s obliquity isn’t 23.5 degrees (hasn’t been for ~500 years), but 23.438 degrees, and it bobs between 22 and 24 degrees over time. See, e.g., http://en.wikipedia.org/wiki/Tropic_of_Capricorn

    Why most textbooks use the number that was determined during the explorations of the Renaissance, I haven’t a clue.

  6. #6 saç ekim merkezleri
    June 26, 2010

    Hi all;
    Why does the inside of the human skull have really sharp blades of bone sticking out? Seems like there should be evolutionary pressures against it.

    Are chromosomes in a cell, all linked together in one long chain, or are they free floating seperate pieces?
    Mary lou…,

  7. #7 Brittnie
    September 22, 2010

    Hi, This hasn’t much to do with the blog but I really need help. I’m doing a astronomy project using stonehenge as a reference and I can’t find a way, without measuring my shadow, to find the Sun’s angle compared to the date. Like The sun is at a 90 degree angle on the spring and fall equinoxes and at a 60 degree angle on summer solstice and a 120 degree angle on winter solstice but what about other dates? If you can help PLEASE send me an e-mail @ pibrittniebee@aol.com
    THANKS! :)

  8. #8 stumpy
    May 15, 2011

    Wondering if anyone can write about the significance of 23 degrees and a Celtic Cross.

  9. #9 Gus
    February 20, 2012

    I searched for “obliquity” on thefreedictionary.com and it said it was 23.27º

  10. #10 woodpig
    coombs
    July 2, 2012

    we have lived in the same house for 16 years, and every year at the summer solstice,the light that normally comes thru our south facing back door window,disappears. This year it has not disappeared, leading me to believe that indeed the earth’s axial tilt has changed. How do you argue with that.

  11. #11 praveena
    walkeshwar
    July 30, 2012

    really nyc pics but i do suggest to show and specify the tilts actually both the tilts

  12. #12 Randell David Fleet
    El Paso,Texas
    December 26, 2012

    News stations do not report the days of the solstices because of there association with Pagans maybe.

  13. #13 Jahi
    United States
    January 20, 2013

    I have 2 diametrically opposed hung doors in my house.
    Last year and maybe the year before #1 would swing open
    by itself when almost closed and #2 was normal (stay where put). This year #2 swings shut when opened and #1 stays put.
    I always wondered what caused this to happen. I can entertain a 22-24 degree shift possible, but with the polar ice melt and weight shift we may be experiencing an even larger axis shift here in 2013. Check predictions for 2013.

  14. #14 Harshvardhan Singh
    Ghaziabad, India
    January 8, 2014

    It’S A VERY USEFUL WEBSITE FOR STUDENTS. EVERY TYPE OF INFORMATION IS HERE.

  15. #15 Tom Devitt
    Twickenham UK
    July 15, 2014

    I have a vertical post in the centre of my back garden. oN JUne 21st, for the past three years, I have marked the line of the shadow on the ground for each hour from 08:00 BST to (almost) 20:00. (Surrounding buildings prevent any earlier or later shadows.).I have marked each shodow line with garden wire and copied them on to a card. When I measure the angles (with a protractor) I get following increases of angle per hour from 08:00 to 18:00 , 15,15,20,25,25 25,25,20,15,5. How can I calculate what the angles should be. My latitude is 51.43924 and longitude is -0.348626. My age is 77 and you would think I had more sense, but I dont trust the government and what they tell us about time, or anything much else for that matter. I would like to work it out for myself! Thomas O. Devitt PhD