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070411.doc
Dazed about “Days” (Solar and Sidereal, That Is)!
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From Celestial North, this is IT’S OVER YOUR HEAD, a look at what’s up in
the sky over Puget Sound.
In everyday interactions, we typically use the word “day” to mean a 24-hour
period. But the term “day” in fact has two distinctly different scientific definitions.
Knowing the difference between the two helps explain, among other things, why
stars rise 2 hours earlier each month, and also sheds light on some really bizarre
differences in the length of the “day” on other planets.
Let’s begin by noting the Sun’s exact location in the sky. The time it takes
for the Sun to go around once and return to that exact same spot is the definition
of our familiar 24-hour day. Technically it’s known as a solar day because we
use the Sun as our basis for measurement.
Now another way to define a day is the amount of time it takes for the Earth
to complete one full revolution about its own axis. How do we know when the
Earth has rotated 360 degrees? Well, we look at the location of a distant star
and then wait for it to come back around to the same place in the sky the next
night. We call this a sidereal day from a Latin word meaning star. Many people
are surprised to learn that a solar day is not the same length as a sidereal day.
Why are they different? During a sidereal day, the Earth spins 360-degrees
on its axis. But at the same time, the Earth has moved about 1 degree in the
same direction in its orbit around the Sun. So for the Sun to appear to come
back to the same place in the sky, the Earth has to rotate an extra degree about
its own axis to catch up. The time it takes to make up this extra degree is the
difference between the length of Earth’s sidereal and solar days.
Copyright © 2007 Celestial North, Inc. All rights reserved.
070411.doc
Dazed about “Days” (Solar and Sidereal, That Is)!
Page 2 of 4
The Earth spins 1 degree every 4 minutes. So the sidereal day on Earth is
about 23 hours 56 minutes – four minutes shorter than the 24-hour solar day.
This means a given star will return to the same spot in Earth’s sky about 4
minutes earlier than the Sun does each day. Over a month, that adds up to two
hours, which is how much earlier a given star rises each month.
There is a very simple formula to calculate the length of a planet’s solar
day: it’s simply the product of its orbital period and sidereal day, divided by their
difference. This leads to some very interesting situations on other planets.
Mercury, for instance, orbits around the Sun in about 3 Earth-months.
Mercury spins once around its axis in about 2 Earth-months. That means that it
takes a given star 2 months to return to the same spot in Mercury’s sky. How
long does it take for the Sun to come back to the same position in Mercury’s sky?
Well, that’s just the definition of Mercury’s solar day. If we plug the numbers into
the formula, we get (3 months times 2 months) / (3 months – 2 months). That’s 6
divided by 1, meaning the length of Mercury’s solar day is about 6 Earth-months!
So in the time it takes for the Sun to appear to go around once in Mercury’s sky,
Mercury itself has spun fully 3 times around its own axis, and completed two full
orbits around the Sun! Mercury’s solar day is twice as long as its year!
Copyright © 2007 Celestial North, Inc. All rights reserved.
070411.doc
Dazed about “Days” (Solar and Sidereal, That Is)!
Page 3 of 4
The situation on Venus is perhaps even more strange. Venus has the
distinction of being the only planet that takes longer to spin around on its own
axis that it does to orbit around the Sun. Its orbital period is 225 Earth-days, but
its sidereal day is 243 Earth-days. What’s even more odd is that Venus spins
around backwards on its axis. So how does all that play into the length of a solar
day on this cloud-shrouded planet? If we do the math, we get an answer of –117
days. What does that mean? It means that on Venus, it takes almost 4 months
for the Sun to re-appear in the same place in the sky. But in this case, the minus
sign means the Sun rises in the west, and sets in the east! And even though
Venus’ sidereal day is longer than its year, its solar day is only about half the
length of its year!
By the way, this formula works for moons orbiting planets as well. If you
plug in the numbers for Earth’s Moon, you find yourself dividing by zero, since
the Moon’s orbital and rotation periods are exactly the same. That implies it
would take forever for the Earth to appear to go around in the Moon’s sky.
Though it seems crazy, since the Moon always keeps the same face toward
Earth, the Earth does indeed stay forever fixed in the same place in the Moon’s
sky!
We’re on the web at CelestialNorth.org, where you’ll find a page with
diagrams and further explanations of today’s topic.
Until next time, this is
________ and _________, with a reminder that the day is large and full of
surprises!
Copyright © 2007 Celestial North, Inc. All rights reserved.
070411.doc
Dazed about “Days” (Solar and Sidereal, That Is)!
Page 4 of 4
REFERENCES:
1. Diagrams and in-depth explanation of concepts in today’s show.
2. http://www.astro.washington.edu/labs/clearinghouse/labs/Skywatch/Lengt
hOfSiderealDay.htm
3. http://celestrak.com/columns/v02n01
4. http://www.newton.dep.anl.gov/askasci/ast99/ast99544.htm
5. http://nssdc.gsfc.nasa.gov/planetary/planetfact.html
6. http://www.badastronomy.com/bablog/2006/12/31/happy-new-yeararbitrary-orbital-marker/
Copyright © 2007 Celestial North, Inc. All rights reserved.