WEBVTT

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Suppose you placed a camera
at a fixed position,

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took a picture of the sky

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at the same time everyday 
for an entire year

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and overlayed all of the photos 
on top of each other.

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What would the sun look like
in that combined image?

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A stationary dot?

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A circular path?

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Neither.

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Oddly enough, it makes this 
figure eight pattern,

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known as the Sun's analemma,

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but why?

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The Earth's movement 
creates a few cycles.

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First of all, it rotates on its axis
about once every 24 hours,

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producing sunrises and sunsets.

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At the same time,
it's making a much slower cycle,

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orbiting around the sun
approximately every 365 days.

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But there's a twist.

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Relative to the plane of its orbit,

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the Earth doesn't spin 
with the North Pole pointing straight up.

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Instead, its axis has a constant tilt
of 23.4 degrees.

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This is known as the Earth's axial tilt,
or obliquity.

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A 23-degree tilt may not seem important,

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but it's the main reason that
we experience different seasons.

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Because the axis remains tilted
in the same direction

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while the Earth makes its annual orbit,

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there are long periods each year

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when the northern half of the planet
remains tilted toward the Sun

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while the southern half is tilted away

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and vice versa,

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what we experience as summer and winter.

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During summer in a given hemisphere,

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the Sun appears higher in the sky,
making the days longer and warmer.

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Once a year, the Sun's declination,

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the angle between the equator

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and the position on the Earth
where the Sun appears directly overhead

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reaches its maximum.

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This day is known as the summer solstice,
the longest day of the year,

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and the one day where the Sun 
appears highest in the sky.

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So the Earth's axial tilt

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partially explains why the Sun 
changes positions in the sky

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and the analemma's length

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represents the full 46.8 degrees
of the sun's declination

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throughout the year.

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But why is it a figure eight
and not just a straight line?

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This is due to another feature
of the Earth's revolution,

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its orbital eccentricity.

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The Earth's orbit around the Sun
is an ellipse,

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with its distance to the Sun
changing at various points.

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The corresponding change
in gravitational force

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causes the Earth to move 
fastest in January

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when it reaches 
its closest point to the Sun,

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the perihelion,

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and the slowest in July
when it reaches its farthest point,

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the aphelion.

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The Earth's eccentricity 
means that solar noon,

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the time when the Sun 
is highest in the sky,

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doesn't always occur 
at the same point in the day.

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So a sundial may be as much
as sixteen minutes ahead

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or fourteen minutes behind
a regular clock.

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In fact, clock time and Sun time
only match four times a year.

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The analemma's width represents
the extent of this deviation.

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So how did people know 
the correct time years ago?

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For most of human history,

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going by the Sun's position
was close enough.

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But during the modern era,

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the difference between sundials
and mechanical clocks became important.

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The equation of time, 
introduced by Ptolemy

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and later refined based 
on the work of Johannes Kepler,

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converts between apparent solar time and
the mean time we've all come to rely on.

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Globes even used to have 
the analemma printed on them

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to allow people to determine 
the difference

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between clock time and solar time
based on the day of the year.

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Just how the analemma appears
depends upon where you are.

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It will be tilted at an angle
depending on your latitude

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or inverted if you're in 
the southern hemisphere.

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And if you're on another planet,

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you might find something 
completely different.

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Depending on that planet's 
orbital eccentricity and axial tilt,

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the analemma might appear as a tear drop,

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oval,

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or even a straight line.