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070411.doc Dazed about “Days” (Solar and Sidereal, That Is)! Page 1 of 4 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.