“Soon the earth will tilt on its axis and begin to dance to the reggae beat to the accompaniment of earthquake. And who can resist the dance of the earthquake, mon?” -Peter Tosh

Every year, there are two special days where every place on Earth receives the same amount of sunlight — 12 hours — split evenly between night and day: the equinoxes!

Equinoxes from timeanddate.com

Image credit: timeanddate.com.

Like all known objects that revolve around another due to gravity, the Earth rotates along its journey around the Sun. But on those two days of the equinox (from the Latin, meaning “equal nights”), the Earth’s axis-of-rotation makes a 90° angle to the imaginary line connecting the Earth to the Sun.

As a result, every place on Earth* spends exactly half the day basking in the sunlight and half the day out of view of the Sun, enjoying the night.

12 hours of day and night, everywhere

Image credit: F.K. Lutgens and E.J. Tarbuck, ©1998 by Prentice-Hall, Inc.

On that day, as the Sun rises during the equinox and ascends through the sky, rising towards its zenith, something unremarkable but very interesting happens right as it reaches its highest point above the horizon.

Equinox Sun

Image credit: Wikimedia Commons user Tauʻolunga.

At that very moment, the angle the Sun makes with your location on Earth exactly determines what your latitude is! Let’s go over why this is. On the equinox, the Sun will pass directly overhead to an observer on the equator. But to someone at any other latitude, because the Earth is curved, the Sun will never quite reach that maximally perfect overhead perspective.

The Sun on the equinox.

Image credit: © 2012 Millersville University.

If you’re exactly at the equator — like point A, above — then at its highest point in the sky, perfectly vertical objects will cast no shadow. But at any other latitude, no matter how close you make your measurement to the Sun’s maximum ascent in the sky, you will always see a shadow. When an object casts its shortest shadow during an equinox, however, that’s when things get really interesting. Because that’s when you can learn what your latitude is.

Animated gif of Stick's shadow

Image credit: Bora Shin.

You can figure out what your latitude is for yourself by taking a stick that’s exactly perpendicular to level ground, measuring its length, measuring the minimum length of its shadow, and just doing a little bit of geometry from there.

shadow length angle

Image credit: Astronomy GCSE, Waukesha South, and me.

The angle you measure when the Sun reaches its highest point on the day of the equinox — in degrees — defines for you what your latitude is at any location on Earth.

Shadow depended on location

Image credit: Larry Phillips original, modified by me.

And the same technique, applied during the equinox on any round world, would give you your latitude at that location. That, of course, is during the two equinoxes.

Larry McNish's Right Ascension / Declination site

Image credit: Larry McNish / RASC Calgary Centre.

But the two solstices are different. On the equinox, the angle the Sun makes with the Earth is perpendicular to the Earth’s axis of rotation, but on the solstices, that angle is at its maximum difference from 90°.

“How different is it,” you ask?

Sun angle in boston

Image credit: David Epstein at Boston.com.

It’s different by the amount that your planet is tilted by. In other words, that difference tells you, exactly, what the tilt of the Earth is!

Solstice Shadow difference

Image credit: retrieved from abovetopsecret.com; origin unknown.

So if you already know your latitude — which at this point, you can look up — you can figure out the tilt of the Earth on its axis. If you want to do it during this year’s June 20th (or December 21st, in parentheses) solstice, here’s what you do.

Shadow Board

Image credit: Larry Sessions and the Community College of Aurora.

Start with level ground, and make sure it’s as close to level as humanly possible. Take a straight object that’s as close to perpendicular to that level ground as you can make it; even someone who’s not great at it but who’s careful can usually get it within just a degree or two. Make sure you measure its length accurately, from the ground to its very top. And as the Sun reaches its highest point in the sky — not at “high noon,” mind you, but at its astronomical zenith — measure the length of the shadow that it casts. (You want to find the zenith angle, below right, and not the sun angle, below left.)

Sun and Zenith angle

Image credit: Julian Trubin, left, and unknown Greek source, right.

Those two measurements will allow you, because you have a right triangle, to figure out what the angle is between the vertical stick and the angle of the Sun. Mathematically, take the inverse tangent of the length of the shadow divided by the length of the stick, and you’ll get an angle in degrees.

Now, take your latitude, which you can look up on google if you like, and do the following for a June (December) solstice:

  • If you live North of the Tropic of Cancer (South of the Tropic of Capricorn), subtract your measurement from your latitude; that’s the tilt of the Earth!
  • If you live South of the Equator (North of the Equator), subtract your latitude from your measurement; that’s the tilt of the Earth!
  • Or, if you live between the Equator and the Tropic of Cancer (between the Equator and the Tropic of Capricorn), add your latitude and your measurement together; that’s the tilt of the Earth.
Solstice and tropics

Image credit: Kurdistan Planetarium.

And that’s how you, yourself, can measure what the tilt of the Earth on its axis is! If someone tells you “the poles have shifted,” as some conspiracy theory sites may tell you, now you know how to test it for yourself!

That’s one of the coolest things you can measure on the Solstice, and you don’t even need any astronomical equipment to do it. You could also do this on any planet, so long as you knew the appropriate latitudes, to measure the tilt of any world.

Obliquity of the planets

Image credit: Calvin Hamilton.

So enjoy the solstice this Wednesday, and to those of you who try it, I’d love to know how close you come to the “accepted” modern value of 23.44°. If our axial tilt has changed, I want to be the first to know!

* — Technically, the very highest latitudes near the North and South poles receive slightly more than 12 hours of daylight, since the angular size of the Sun becomes important for the day-night boundary extremely close to the poles. But, as far as I know, none of my readers are South Pole researchers or Santa Claus; if you are, my apologies!

Comments

  1. #1 Brent Jackson
    Auckland, New Zeland
    June 19, 2012

    Great article. Instead of using a stick (which might be difficult to get vertical) you could use a hanging weight instead.

  2. #2 MandoZink
    June 19, 2012

    This trick is also useful to use to determine the height of a tall object, and can be used on any sunny afternoon. Working in the civil engineering dept of a large airport, my boss sent me out with a theodolite to determine the height of a tall pole near a runway end off of our property. I noticed the ground was very flat and a nearby fence post was casing a very distinct shadow. Rather than set up the theodolite and take readings, I quickly measured the height of the fence post and the length of its shadow. I then measured the shadow of the taller pole and used the fence post/shadow ratio to determine the taller pole’s height. It was quick and easy.

  3. #3 Eric Lund
    June 20, 2012

    Be careful that you do this at actual solar noon, which can be quite different from civil noon. There is always a longitude correction (4 minutes per degree). If daylight savings time is in effect (most places in the US, Canada, Europe, and the former Soviet Union; for the December solstice this will be true in certain Southern Hemisphere countries), that will shift the time by one hour. And if you live in a place where the time zone is set for political and/or economic convenience rather than by longitude, things can be really far off: as much as three hours in parts of western Alaska and western China.

  4. #4 OKThen
    Planet Earth
    June 20, 2012

    I really appreciate a post like this. (for sure I much appreciate your other posts, especially leading edge physics and astronomy). But a post like this is about the basics, that Pythagorous, Galileo, an aboriginal person and you and I can appreciate.

    All you need is to have is the sun, a stick, a shadow and an inquisitive mind capable of careful observation.

    In a post like this, you Ethan remind me of some things that I already know; but you explain it in a simpler and clearly way than I could. And you don’t stop there; you go on to make connections between equinoxes, solstices, tilt of the Earth and of other planets.

    Today, this story isn’t one of the Earth shaking physical theories that is being debated and may one day change our understanding of our place in the world and universe. But yesterday, this story was just that: an Earth shaking physical theory that changed our understanding forever.

    This simple story is part of the essential foundation of our great scientific heritage. Thank you for retelling it so well.

    May I suggest that you build a calendar index. The idea is that certain of your posts are especially important to read in certain months of the year. This one in Mar, June, Sept, and Dec.; other posts are important for other months. Maybe I’m oversimplifying; just a thought. (I was going to edit out this thought, but oh well.)

  5. #5 OKThen
    Planet Earth
    June 20, 2012

    p.s. I’m going to have to go outside today and carefully dirve a large stick in the ground. I will have to place stones to mark the time of day, the shadows of solstices and equinoxes, and so on.

    I have a barren worthless spot of in my yard prefect to build a small aboriginal astronomical instrument.

  6. #6 Darethehair
    Morden, Manitoba, Canada
    June 20, 2012

    I used a variation of this a few minutes ago. I used an old telescope to ‘point’ to the Sun (NOT look through it!) at solar noon today. I then measured the angle of the Sun with an inclinometer (sitting on the telescope tube). Did a bit of math and got 23.38° (a bit off the actual value, but close).

  7. #7 Ethan
    June 20, 2012

    For what it’s worth, I got a minimum zenith angle of 22.2°, to the best I could measure it.

    Since my latitude is 45.45°, that means my measurement for the Earth’s tilt is in the 23.2° – 23.3° range. Not bad, and while it isn’t perfect, it definitely goes to show there *hasn’t* been a dramatic pole shift!

  8. #8 Remo
    June 20, 2012

    Ethan, I don’t believe your footnote is correct.

    Everywhere in the world, both north and south, has a day of sunshine longer than 12 hours on the equinox. At the extremes, the North and South Pole both basked in 24 hours of daylight from March 18 thru March 22. And a little less extreme Longyearbyen receives an extra 36 minutes, and even Singapore which nearly straddles the equator receives an extra 6 min, 30 secs. (ref: http://www.timeanddate.com/worldclock/astronomy.html?n=737&month=3&year=2012&obj=sun&afl=-11&day=1 )

    Moreover, it is not just that .25 degrees you gain ’cause the sun is a ball, not a point, and half the ball peaks over the horizon. Remember, the earth rotates 1 degree every 4 minutes. And the path of the sun in Singapore is almost vertical at the equinoxes. At least with Singapore, even if you throw in the extra .5 degree from the sun peaking over the edge of both the east and west horizons, you are still stuck with an extra 4 min and 30 secs of sunshine. And it only gets worse as you push up and down from the equator.

    Just a little physics challenge for you and your readers. Answer tomorrow.

  9. #9 OKThen
    June 21, 2012

    Remo is correct. Thanks.

    See this chart http://en.wikipedia.org/wiki/File:Hours_of_daylight_vs_latitude_vs_day_of_year.png
    It’s a rather nice graph that shows Remo’s point. Nice.

  10. #10 Wow
    June 21, 2012

    You also have refraction causing sunlight to bathe the earth “before” the sun rises (in a geometrical sense).

  11. #11 Remo
    June 21, 2012

    Kudos to OKThen and Wow. It is atmosphere refraction.

  12. [...] can use this event to measure your latitude the Earth’s tilt, if you have a stick and a protractor and clear skies and the ability to take an inverse tangent. [...]

  13. #13 Bashir Bomai
    Nigeria
    July 28, 2012

    I don’t get to see all these great events because I live in Africa.I never get to see the aurorae nor some of the stars and planets however,on a very clear night,I get to observe a part of the Milky Way Spiral arm.Included are the Peliades,Orion(quite magnificent).I also get to see Mars,Jupiter,Venus,the Dipper,and some other Constellations.I really need to see the manifestation of the Northern or Southern Lights.I love the article above and I find it very educative,enlightening and will carry out some of the experiments for myself.

  14. [...] Another great activity, courtesy of Jonathan Blake of the Naturalistic Paganism yahoo list, is measuring your latitude on the equinox using only the sun, a stick, and some basic calculations. [...]

  15. [...] solstice has come and gone at 11:11 a.m. London time (6:11 a.m New York time). That’s the moment when the north pole of the Earth points most away from the sun, and the south pole points…. Because it’s followed by a weekend and then Christmas Eve, it marks the end of the 2012 [...]

  16. #16 Jabez Hart
    United States
    January 4, 2013

    There are postings on you tube about earthquakes changing the tilt slightly in the past few years. Are these founded?
    Some such state that the unusual extreme storms and weather of the past couple of years are directly related to this. Is this so? Certainly earthquakes have recently increased in frequency and intensity. There also are groaning kinds of sounds heard in the sky around the planet , also so recorded. Is this so as well? Wondering here about the increased US drought too. Any thoughts?

  17. #17 BOB
    bundaberg.queensland australia.
    January 4, 2013

    WERE IN AUSTRALIA,CAN ONE STAND,AND WHATCH HE’S OR HER’S,SHADDOW GO UNDER YOUR FEET,AND RE APPEARS AGAIN,AT 21 DEC,AT NOON

  18. #18 Vince Whirlwind
    January 5, 2013

    Bob, time to put down the Bundy.

  19. #19 wlm
    January 5, 2013

    Sorry to burst everyone’s bubble, but there are at least 5 reasons why, if you follow Prof. Strassler’s method to measure your latitude, you’ll probably get it WRONG! (Or, at least, it’ll likely be inaccurate.)
    1. The Earth is not round. It’s an oblate spheroid: it’s approximately ellipsoidal in shape with the poles along the minor axis. A line that runs from your feet through the center of the Earth doesn’t measure your latitude. Rather, it’s determined by a line that runs perpendicular to the tangent plane of each point on that (hypothetical) ellipsoidal spheroid. And its angle varies from that of a sphere depending on where you are relative to the equator and the poles. There have been several measurements and approximations of the “best fit” ellipsoid to use; the one currently used most widely is the WGS84 ellipsoid. (Some countries, such as Great Britain and Australia, still use other ellipsoids for some local maps that fit better under their particular portion of the earth, but this one is the “best fit” for the planet as a whole, and is the basis for the GPS system.)
    2. The gravitational geoid does not conform exactly to that WGS84 ellipsoid; rather it has ripples and waves, varying from place to place, by up to several hundred meters above or below the smooth WGS84 ellipsoid. (The geoid is the theoretical equipotential gravitational surface where “mean sea level” would be if there were no waves or tides and water covered the entire planet.) So if you hold a weight on a string, it’s likely that it will not point toward the exact center of the earth; it will point perpendicular to the tangent plane of the geoid wherever you happen to be. Depending on where you are, this can be a significant source of error.
    3. The Sun is not a point light source, but a sphere. You can account for this somewhat by taking measurements at exactly the time of day when it is at its zenith. But because the sun’s shadow has both an umbra and a penumbra, the exact placement of its shadow becomes “fuzzy” – hard to measure exactly.
    4. Light from the Sun is subject to distortion caused by diffraction by the atmosphere, which can vary by season and due to unpredictable weather effects. Again this can be mitigated by making measurements only when the sun is at its zenith. But this only works in the temperate and equatorial zones, where the zenith is well above the horizon; near the poles, diffraction will always be a problem. It’s why it is impossible to predict the exact time of sunrise and sunset, even when using models of the Earth’s atmosphere to include corrections for pressure differentials with altitude. (Predictions of the time of observed sunset can often be off as much as 5 minutes; there have been cases on the West Coast of the U.S. where the “standard” predicted time was off by almost 10 minutes, due to some extreme pressure and temperature inversions and extensions of the atmosphere causing unusually high bending of the photons’ paths.)
    5. Earth’s rotational axis moves relative to Earth’s surface, by a surprising amount. It wobbles! The poles can move by meters over the course of just months. There are maps kept by the Earth Rotation Service showing a curly-cue path over the course of several years. This is in addition to the much slower, but not insignificant, tectonic movement of the Earth’s crust – which is also sometimes intermittent, not steady. (Remember, the Earth has a solid inner core, a liquid outer core and a semi-molten lower mantle. Those things move at different rates, with their own convection and frictional and tidal effects, underneath us. And they are massive enough to have an effect on Earth’s rotational axis.) Over surprisingly short periods of time, these geophysical changes can alter the alignment of the rotational axes vs. the ellipsoidal axes of the crust of the planet.

    All of these kinds of effects have to be taken into account by serious astronomers and geophysicists, as well as map makers and civil engineers! It’s yet another example of Nature throwing curve balls at us in our attempts to model how the World really works. And why science always needs to go back to the actual evidence rather than relying on simplistic models and rationales to explain things.

  20. #20 Michelle Brown
    October 15, 2014

    A friend and I made a video where we calculated the tilt of the Earth from measuring my height/shadow length since we were at the south pole at winter solstice. You can see it here: https://www.youtube.com/watch?v=tTnn91KyJ-4

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