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Group 1 Notes Week 2 Week 2 Notes for 1/23/12 Lunar Motion: It takes around a month for the moon to go around the earth, but there’s a bit of a complication with that. The reference point determines how long it takes for the moon to orbit. A solar month is 29.5 days, but a sidereal month is 27.3 days. The earth moves around the sun at the same time that the moon is going around the earth. By the time the moon gets lined up with a star again (from one orbit to the next), the moon has not gone around completely with respect to the sun. Sidereal Month is the time it takes the moon to return to the same alignment with a star. It takes a little bit longer for a Solar Month because the earth has moved around the sun. So a month is about 30 days, to keep in line with the Solar Month. The Moon keeps the same face pointed towards the earth – in other words, it revolves on its axis in the same amount of time it takes to go around the earth. So, a lunar day = a lunar year (rotation = revolution). Something happened to the moon to force it to have such a strange rotation/revolution ratio. It is not a coincidence – it is a phenomenon known as TIDAL LOCKING, a gravitational effect. The moon spun faster in earlier times, but the earth slowed it down over time, so that the same face is now permanently pointing towards the earth. So, we’ve never seen the “dark” side of the moon from earth. But it is not always dark – we just can’t see it when it’s in light (which is half the time). It is more correct to call it the “far” side of the moon. The geometry of the situation dictates the repetition of this pattern. This repetitive pattern can be used to tell time. The phase of the moon, as well as its place in the sky, can be used to tell time. Lunar Motion: Highlights • Takes the moon around 30 days to circle the Earth • Solar month=29.5 days º The sun doesn’t line up like other stars because it isn’t far away enough for it to have the effect of it converging in the distance. • Sidereal month= 27.3 days º Stars as a reference • The moon always faces the moon with the same side. • Moon revolves in the same time it takes it to rotate around the earth. • Tidal locking: The moon spins around on its axis at the same rate as it takes it to go around the Earth. • “The Dark Side of the Moon” though more accurately far side of the moon. • can tell time by the location of the moon and its phase. Eclipses are important when talking about the moon. A LUNAR ECLIPSE is when the moon is covered by the earth’s shadow (Earth is between Moon and Sun). A SOLAR ECLIPSE is when a bit of the earth is covered by the moon’s shadow (Moon is between Earth and Sun). The earth’s show easily covers the whole moon during a lunar eclipse. But the moon is smaller than the earth, so the moon’s shadow doesn’t block out the entire earth during a solar eclipse. The full shadow of the moon is called the UMBRA, which is totally dark because at this one point, the moon totally covers the sun. Surrounding the umbra is the PENUMBRA, which is only a partial eclipse. When the moon completely covers the sun, you can see a CORONA around the edge of the moon (and this is the only time when this is visible). During a total lunar eclipse, the moon looks reddish. Clearly a Lunar Eclipse covers a Full Moon. For a Solar Eclipse, you need a New Moon. These happen this way because of the position of the moon during these times. So, why are there only 2 solar or lunar eclipses per year? The problem is that the moon is tilted about 5 degrees from the Ecliptic Plane (the plane of the earth-sun orbit). Most of the Full and New Moons occur either above or below the Ecliptic. You only get total eclipses when the Full or New Moon crosses the Ecliptic. The line of intersection of these 2 planes has to point towards the Sun. This intersection is called the LINE OF NODES. But the line precesses in 346 days (a little less than a year), which is why you don’t get eclipses at exactly the same times each year. Lunar Eclipse Highlights: Lunar Eclipse- When the moon is covered by the earth’s shadow, so the earth is between the moon and sun. Has to be a full moon. Solar Eclipse- a bit of earth is covered by the moon’s shadow. The moon is between the earth and sun. Only covers a small area on earth. Umbra- full shadow Penumbra- partial shadow in a complete solar eclipse is the only time the corona can be viewed. Eclipses occur only a couple times a year because the moon, sun, and earth are not always on the same plane. Notes for 1/25/12 Predicting Eclipses: Figure out the 2x per year when the Line of Nodes is pointing towards the sun. The orbital plane of the moon precesses, which makes it hard to determine. The ECLIPSE YEAR is the precessional period of the orbital plane of the Earth/Moon system, which ends up being 346.6 days. With this knowledge, we can predict eclipses. With there being 2 eclipses per year, you get one every 173.3 days. The lunar cycle is 29.5 days. If you start with Day 0, you can figure out when these 2 sync up – it takes 18.3 years to get the same configuration. This is called the SAROS CYCLE. The Calendar Gregorian vs. Julian – based on the Roman model Romans and Babylonians used the First Point of Aries to mark the beginning of the year. But it didn’t work every year – after 4 years, it took an extra day to get back to the point. So the average approximation for the year is 365.25 days. One way to deal with this is the leap year, but this was seldom done. Some societies added an extra day or month, called INTERCALATION. The Romans changed their policy of monthly intercalation because it was politically controlled. In other words, they were non-astronomical reasons for intercalation. Because of this misapplication of the rules, the Romans got off by about 3 months. Julius Caesar, in 46 BC, standardized the calendar with an astronomer named Sosigenes of Alexandria. Thus, they added 3 extra months to the calendar, bringing the vernal equinox back to March 25th, and introduced the Leap Year (so that it wouldn’t be politically decided). This is the advent of the Julian Calendar, and it was used in the West for 15 centuries. But the year is actually 365.242199 days long. It was a close estimate, but not close enough over longer periods of time. By the 16th century, the vernal equinox had shifted to March 11th because of this discrepancy. Pope Gregory III decided to drop 10 days and bring the vernal equinox back to March 21st. But the calendar had to be tweaked – so, he changed the leap year. Every end-of-century (1600, 2000, etc.) divisible by 400 is a leap year, and only these end-of-century years are leap years. It makes the average year 365.2425 days, which is much closer. It will eventually get out of sync, too, but it will take much longer. This is the Gregorian Calendar, which we still use today. England and the American colonies didn’t use this system until 1752. And now to the Mayan Calendar… They had 2 basic calendars – the divine almanac (260 days long, for religions purposes) and the solar calendar (365 days). They also had a combination of these 2, which was called the Calendar Round system; it had a pattern than repeats every 52 years. But the one everybody’s talking about is the Long Count. It is a continual number of days for more than 5000 years. Every day for 5200+ years has a different name. This system doesn’t have to use leap years at all – it is a running count of days, which makes it easy to determine how long ago something happened. It begins counting in August of 3114 BC. When you run through all of the cycle, with each date named, it runs out on Dec 21st, 2012. A new cycle begins the next day. According to the Mayan calendar, we are in the 5th such cycle, so the 6th will begin on Dec 22nd, 2012. Highlights: Before the Julian Calendar, there were many calendars, then the Julian gave way to the Gregorian Calendar. The year is not exactly 365 days it is closer to 365.25 so using the stars to chart things it gets off. Intercalate: adding an extra day (or month) Leap Year: Adding one day every four years. Julian Caesar consulted an astronomer named Sosigenes of Alexandria in 46 B.C. found a way to sync it back up and get rid of intercalate. This brought the vernal equinox back to March 25 and introduced the leap year. The year however is actually 365.242199 days long. Pope Gregory XIII decided to drop 10 days and bring the Vernal equinox to March 21st.
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