Volume XIX No. 5 January 2008 ggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggg Analyzing the Analemma By Alberto Guzman T he Question: Where in the sky is the Sun at a fixed time each day? As a kid, I would have answered that at, say, noon, it was always at the same point south, south being down the street toward my school. Living in the tropics, plus being a kid, I had not looked closely enough to notice that sometimes the midday Sun shone the other way, from up the street. That north-south change became a lot more noticeable when we moved to New York. In July, the place was hot; the midday Sun burned from way up in the sky. You had to cross our new street to get any shade. In January, it was not hot; the Sun hung low over the southern horizon even at noon. The shadow of the facing building not only crossed the street, it reached a couple of floors up our building. You had to go to an avenue to catch some warming Sun. With these observations, I would have changed my answer to this: always along the southern meridian, high in the summer and low in winter. I had no reason to think otherwise until the historic Dennis DiCicco photograph of the "analemma" appeared (June 1979 Sky and Telescope). The photo here shows the pattern of Sun's location in the sky at a fixed hour early in the morning. (The photo is viewable at http://tinyurl.com/26ynu5.) The picture, then, demonstrates what Sundial makers and decorative gardeners seem to have known all along: the Sun's position at a given time of day traces out a figure eight over the course of the year, clockwise around the bottom loop, counter around the top. Rumor has it that this behavior has to do with Earth's axis inclination and elliptical orbit. We astronomy fans know that the axis inclination accounts for the south-to- north drift of the Sun from winter to summer. (Motion being relative, we are not embarrassed to talk about the "motion" of the Sun.) We will check that the ellipse and one other element explain the oscillation left and right, along with the form of the analemma. A Helpful Instrument Let us settle on noon and picture what is happening in the sky. It helps to have something pointing southward up into it, that is, toward the meridian. It would suffice merely to sight from the entrance to Sperry just over one of the parking lot lampposts, but let us take advantage of a physical guide. In the plaza of the McGraw-Hill Building, 48th Street and Avenue of the Americas in Manhattan, there is a steel sculpture in the form of a triangle atop a support. The bottom side of the triangle is inclined about 27° upward toward the south. Accordingly, it tracks the Tropic of Capricorn. On the shortest day of the year, it points at the transiting Sun. The long side, at right in the photo, is inclined about 50°, wherefore it traces the Celestial Equator. That side points at the midday Sun on the March and September equinoxes. As you have doubtless concluded, the steepest side, left in the photo, points at approximately 73°, along the Tropic of Cancer and therefore at the year's highest transiting Sun. Because the three sides all point south, the plane of the triangle intersects the sky along the meridian. By noting where the triangle points at the same time each day (more easily, at night) we could observe that the meridian's sky location (right ascension) at a given hour advances eastward in the sky by about a degree (four RA minutes) per day. We usually ascribe that observation to the starry background's rotating westward one degree per day. Thus, Antares transits at midnight around May 29th, so that the bottom of the triangle points just above it then. At the next midnight, Antares would lie about a degree west of the triangle's aim, then a further degree west the midnight after that, and so on. (Of course it is 360° in 365+ days, but never mind; one degree per day is fine for the government work Al Witzgall always claims to be doing.) Now let's bask again in the midday Sun. If the Sun moved eastward against the background of stars at the same rate as the meridian, then it would transit at the same time every day. But two factors affect the Sun's eastward advance. The first is the inclination of the ecliptic. The roughly 23° inclination of Earth's axis causes the Sun's path in the sky to incline at the same angle to the Celestial Equator. Even if the Sun moved at constant angular speed around the ecliptic, it would advance eastward in our sky faster at the two solstices, when it is moving directly east in the sky, than at the equinoxes, at which it is moving northeast or southeast. The eastward advance would therefore be faster than the meridian's in December and June, slower in March and September. The second factor is Earth's elliptical orbit. Like any planet, Earth has distance from the Sun increasing from perihelion (the point of minimum distance) until aphelion (maximum), then decreasing back until perihelion (as opposed to, say, going from max to min by dropping some, rising a little, then dropping more). Correspondingly, Sun's angular speed around the ecliptic is highest at perihelion, decreases until aphelion, then increases until perihelion. Because perihelion happens around January 3, close to the winter solstice, the Sun at the solstice is both moving at nearly its fastest speed along the ecliptic and advancing due east in our view. That makes sense of the bottom of the analemma. The midday Sun at its southernmost is outracing the meridian, getting increasingly out in front (east) of the line. The decreased speed along the ecliptic, compounding the ecliptic inclination, explains why the meridian begins to overtake the Sun with the approach of Spring. The situation in September is roughly mirror image to March. What is harder to match up is the low speed of the Sun at the summer solstice (almost aphelion) and the analemma's clear indication that the Sun is once more gaining on the meridian then. Why does the return to moving due east overcome the effect of minimal speed along the ecliptic? The Calculation For that answer, I turned to a spreadsheet. Kepler's Second ("Equal Areas") Law and the geometry of the ellipse imply the relative angular speed of the Sun along its path. From that speed, you can total up ("numerically integrate") the angle Sun travels in a given time from some reference, like its location at perihelion. The resulting table of angles (a kind of "ecliptic longitude", but that technical term is reserved for angle measured from the vernal equinox) is not too interesting, except maybe for this tidbit: While the Sun goes 180° in half the year, it goes more than 90° in the first and fourth quarters. (Let's leave the explanation to you.) From that table, which locates the Sun on the ecliptic, we make the spreadsheet calculate how far above and how far along the Celestial Equator the Sun is on a given day. Clearly the first number represents Sun's declination. The second is angular separation from perihelion, and is therefore something like 75° (5 hours) more than Sun's right ascension. The latter table is not so interesting, either, because our interest is not Sun's absolute position. Rather, we want its location relative to the meridian. So, we take Sun's angular position minus that of the meridian. Those values are of interest. If we have the spreadsheet graph them against time, we get this graph: If that graph were like a sine wave (in our earlier words, if it dropped from max to min without the intervening rise) then the Sun would spend half the year on each side of the meridian, and the analemma would be an oval instead. The shallow dip below zero and rise above zero explain why the upper half of the analemma crosses the meridian three times to create the upper loop. Since the spreadsheet has a table of solar declinations and one of corresponding locations relative to the meridian, how about a scatter plot of one table against the other? That plot is our payoff (at right): Experimenting Why does the analemma bulge to the right? What would happen to it if the axis inclination were different? What if perihelion happened around the spring equinox? You can experiment for yourself by downloading the spreadsheet. It is in Microsoft Excel, for Windows, from around 2003. If you can handle that, you can get the spreadsheet in the Tutorials & More section of the AAI website in the BEYOND BASICS section. You will find that it has cells for the axis inclination (set at 23.5°), orbit eccentricity (set at .017), and perihelion's day after the winter solstice (set at January 3 - December 21 = 13. This number is the "one other element.") Change those, look at the resulting figures, and you will have what science always offers: answers that beget questions. Stewart's Skybox by Stewart Meyers O n January 14th, MESSENGER (Mercury Surface, Space Environment, Geochemistry and Ranging probe) will fly past Mercury on the first of three flybys before settling into orbit around the planet in March of 2011 and, barring any equipment problems, transmit the first close-up images of Mercury in over thirty years. In honor of this month's flyby, Mercury will be the topic of this month's column. MESSENGER itself will be discussed in a future column. While Mercury has been known since the days when people first started to notice how things moved in the sky, it did not seem to make a major impression in the ancient world. Aside from the ancient Greeks and Romans linking it to their messenger gods (Hermes and Mercury, respectively), the planet was something like the Rodney Dangerfield of planets visible to the unaided eye. There are several reasons why this was the case. Since Mercury orbits very close to the Sun, it can be seen (without a telescope) only in twilight after sunset or before sunrise. And even then, its periods of visibility are much shorter than those of Venus. When it is visible, Mercury is not exceptionally bright like Venus is. This is due to both its distance from Earth and its small size (Mercury was the smallest planet in the solar system until Pluto claimed the record, but Mercury regained the title when the IAU demoted Pluto to dwarf planet status in 2006). To the ancients, Mercury was not very impressive at all. It wasn't bright, stayed close to the Sun, and was usually dimmed by hazes near the horizon in our atmosphere. MTA (Mercury Transit Authority) In the early 17th century, Hans Lippershey in the Netherlands invented the telescope, though some revisionists claim Leonard Digges invented it fifty years earlier in England though their evidence is vague and practically non-existent. But it was Galileo who first thought of using one to look at the sky, instead of at ships sailing into port or enemy soldiers on the battlefield. When Galileo used it to look at Venus, he noticed that the planet had phases like the Moon. Unfortunately, when he looked at Mercury, his telescope showd very little detail. While this was due in part to the limitations of the instrument, Mercury's distance and small size played a role. It was not until 1639, when an obscure Italian astronomer by the name of Giovanni Zupus pointed his telescope at Mercury that it was confirmed Mercury also shows phases. But Mercury would prove to have another similarity to Venus that had nothing to do with phases. By the 1620's, astronomers who accepted the Copernican model of the solar system were aware of the correct order of the then-known planets from the Sun and they even knew their relative distances, though they did not know the actual distances. Using Tycho Brahe's observations, Kepler published an ephemeris of the planets in 1629. Looking through this table, French astronomer Pierre Gassendi noticed that Mercury was scheduled to pass in front of the Sun on November 7, 1631. So, he set up his equipment on the appointed date and time, projected an image of the Sun, and saw Mercury transit across the disk of the Sun. Gassendi also took the opportunity to measure the angular size of Mercury and arrived at a figure of 20 arc seconds (the modern value for Mercury on that date was 11 arc seconds). This was the first transit of a planet across the Sun that was scientifically observed. It would not be until 1639 that Jeremiah Horrocks would observe transit of Venus. In the late 1600's, Edmund Halley realized that, if a transit was observed from widely separated locations, it would be possible to work out the distance to the transiting planet and thereby work out how far all the known (at that time) planets were. While transits of Mercury are somewhat frequent, at a rate of 13 or 14 per century and only in May and November when the ascending or descending node (point in a planet's orbit when it crosses the ecliptic) occurs at inferior conjunction (when Mercury is on the same side of the Sun as the Earth), Mercury was simply too far from Earth to show a measurable parallax by that technique. Instead, astronomers used the much less frequent transits of Venus for the purpose. Even though the transits of Mercury have had little scientific interest, they are still well observed by amateurs using telescopes (with safe solar viewing techniques such as projecting the Sun's image on a screen, approved objective filters, and now hydrogen-alpha filters) as well as the modern solar observing satellites. The most recent transit was on November 8, 2006 and is depicted in this image from the SOHO satellite seen above. The next transit will be in 2016. Hot Side Hot, Cold Side Cold But that snub was not the end of astronomical interest in Mercury. In 1800, Johann Schroter observed Mercury and attempted to map the surface. However, due to the small size of Mercury, very little detail was seen, except for a possible shortening of a cusp when Mercury was in crescent phase. From what vague detail he could barely perceive, Schroter arrived at a rotation rate of approximately 24 hours. This was not confirmed when Sir William Herschel later observed the planet, as he saw nothing that gave any hint of rotation. The next wave of telescopic interest in Mercury would be in the late 19th century. Telescopes were better and astronomers had figured out that Mercury could be viewed in the daytime, when it was higher above the horizon and seeing conditions were somewhat more favorable. In 1882, Italian astronomer Giovanni Schiaparelli, who is better known for his Mars observations, studied Mercury and noticed vague markings on the surface. Based on these, he concluded that Mercury was in a tidally locked rotation with the Sun, like the Moon is with the Earth. In 1897, Percival Lowell, another name more associated with Mars than with other planets, examined Mercury and drew maps. And, just like his maps of Mars and Venus, Lowell also saw some linear features on Mercury. And, like his other maps, other observers never confirmed those features. And yet another individual who had a connection with Mars would get in on the act with Mercury. E.M. Antoniadi, a French astronomer, was working at Meudon Observatory and used its 33-inch refractor. With this telescope, Antoniadi was able to disprove Lowell's canals. He also used it to observe Mercury from 1924 to 1929 and published his work in 1934. The drawings, considered the best made of Mercury, show faint irregular features. Based on his observations, Antoniadi thought that the synchronous rotation Schiaparelli reported was correct and that Mercury might possess a very thin atmosphere. Naturally, the pulp science fiction authors latched on to this finding and much ink (and cheap paper) was expended on stories set in some narrow band of Mercury between the incredibly hot sunlit side and the perpetually cold night side. In fact, this "twilight" area of Mercury even figured in a series of trading cards known as "Jets, Rockets, Spacemen" back in the 1950's. But the truth concerning Mercury's rotation would be revealed not too many years after the time of those cards. Oh, Radar After achieving success with detecting radar echoes from Venus, scientists decided to try to do the same with Mercury to derive a more accurate distance. In 1965, Gordon Pettingill and Rolf Dyce used the enormous radio telescope at Arecibo as a radar system and discovered that Mercury is not in a tidally-locked rotation, but actually rotates once in a little more than 58 days, which works out to two-thirds the orbital period of 88 days. This leads to some curious effects concerning the sunrise and sunset as seen from the planet's surface. For instance, the time interval from one Mercurian noon to the next is actually two Mercurian years. And it gets even stranger. Mercury has a rather eccentric orbit for a planet. When it is at perihelion, it is 20% closer to the Sun than it is at its mean distance. As a result, the increase in orbital speed when Mercury is at perihelion slightly more than compensates for the apparent motion of the Sun in the sky caused by the slow rotation. What this means, is that the Sun would appear to an observer on Mercury to slow down and reverse itself for a few Earth days. Then, as Mercury moved further from the Sun towards aphelion, the Sun would slowly resume its normal apparent motion for a hypothetical observer on Mercury. This strange rotation also explains why earlier astronomers thought Mercury had a synchronous rotation. Since Mercury rotates three times for every two orbits around the Sun, astronomers had been frequently seeing the same side of the planet. But they were right in one detail. Tidal effects from the Sun were responsible for Mercury's rotation rate. Highly Illogical Backtracking a bit, by the middle of the 19th century, planetary orbits could be calculated with enough precision to notice changes over time. In the case of Mercury, it was found that the point in its orbit where perihelion took place gradually shifted eastward. Factoring in the influences of all the major planets accounted for some of this effect, but there was a shift of 42 arc seconds per century that was unexplained. Urbain LeVerrier, the man who predicted the existence of Neptune thought he had the answer. In 1845, he proposed that the discrepancy was due to the planet Vulcan. No, this was not the arid, Earthlike planet in the 40 Eridani system that is home to a race of pointy- eared, green-blooded, highly-intelligent humanoids from the "Star Trek" franchise, but was a planet that was postulated to orbit closer to the Sun than Mercury and was thought to exert a gravitational influence that accounted for the 42 arc second shift. And, in 1859, LeVerrier received a report that Vulcan had been seen transiting the Sun by Dr. Edmond Lescarbault, a country doctor, carpenter, and an amateur astronomer in Orgenes, France. Even after visiting Dr. Lescarbault and seeing the crude equipment he used, LeVerrier bought the story like it was on sale with double coupons and Lescarbault even won the Legion of Honor. In fact, LeVerrier even computed an orbit and other parameters for the planet based on this sighting. These were a mean distance from the Sun of 18-½ million miles from the Sun, an orbital inclination of 12 degrees, a period of 33 days, and a diameter of 1,000 miles. This inspired more people, mainly French astronomers, to look for this planet. However, when others tried to confirm these sightings, they came up empty. During the total solar eclipse of 1860, special effort was made to look for Vulcan during totality. Nothing conclusive was found. Using his orbit calculations, LeVerrier predicted that Vulcan would transit the Sun on March 22, 1877. The date came and nothing happened. LeVerrier wasn't disappointed by this for long, as he died that year, still believing in Vulcan. Aside from sightings of objects near the Sun during the July 29, 1878 solar eclipse by James C. Watson and Lewis Swift, Vulcan quietly faded from history. The true explanation for the 42 arc second shift would not come until 1916, when it was discovered that the shift was a consequence of general relativity. Mercury's orbit, being closer to the Sun would be more susceptible to the relativistic effects of the warping of space-time by the Sun's mass than any other planet. This pretty much put an end to Vulcan, until the mid 1960's when Gene Roddenberry resurrected the name to use for Mr. Spock's home planet. The sightings during the 1878 eclipse were likely small comets near the sun, like those spotted by the SOHO satellite from time to time. But some good came out of all this. Heinrich Schwabe, while looking for Vulcan, found the sunspot cycle. Ready For Its First Close-up On November 11,1973, NASA launched Mariner 10, the first space probe to visit Mercury. After flying past Venus and making detailed images of the ultraviolet features in the clouds (and also using the planet's gravity to assist the flight - a first in space history), Mariner 10 made its first flyby of Mercury on March 29, 1974. Scientists were mildly surprised when the first images showd a heavily cratered surface that resembled the Moon. While craters were expected, the strong resemblance to the Moon was not. However, Mercury's similarity to the Moon was literally only skin deep. As Mariner 10 went past Mercury, it felt the effect of the planet's gravity and allowed its density to be calculated. The result was a mean density of 5.43 grams per cubic centimeter, as opposed to the Moon's mean density of 3.34 grams per cubic centimeter. This is thought to be due to Mercury having a very large iron core making up nearly half its volume. Another difference between the Moon and Mercury is that Mercury has a magnetic field. It is considerably weaker than Earth's, but it was detectable. Its origin is something of a mystery to this very day. Normally, a planet needs a liquid core and a rapid rotation to generate a dynamo effect to cause a magnetic field. Mercury rotates quite slowly and should not be able to generate a field. Yet, it somehow does. This magnetic field is thought to be responsible for Mercury being able to retain some gas from the solar wind to give it a very tenuous atmosphere. Upon closer examination of Mariner 10 images, Mercury turned out to have some very unusual surface features. For instance, numerous cliffs and scarps were seen. These were thought to have formed when Mercury's interior cooled and the crust contracted. Also, a region of jumbled-looking topography was found and named "chaotic terrain". It was later learned that this feature is on the exact opposite side of the planet from the enormous Caloris basin, one of the larger impact features seen in the solar system with a diameter of 1300 kilometers (806 miles). It is thought that the shock of the massive impact traveled all the way through the planet and affected the surface on the other side. Mariner 10 made two other flyby visits to Mercury on September 21, 1974 and March 16, 1975. Unfortunately, due to the nature of Mercury's orbit, the same hemisphere of the planet was photographed each time. Recent Developments The end of the Mariner 10 mission in 1975 did not mean the end of studying Mercury. True, it had to be studied by ground-based means, but discoveries were still made. In 1991, Martin Slade of JPL (NASA's Jet Propulsion Laboratory) had a brilliant idea to improve the quality of radar studies of Mercury. The 70-meter Goldstone antenna of NASA's Deep Space Network was used as a radar transmitter. The reflected signal, however, was detected using the Very Large Array (VLA) collection of radio telescopes in New Mexico. This combination resulted in the ability to gauge how different parts of Mercury reflected the radar signal. To everyone's surprise, a very reflective area was found at the north pole of the planet. Further study seemed to indicate that the reason for the high reflectivity might be the presence of water ice. This might seem odd, but there is a way a planet like Mercury might be able to hold onto water ice. It is thought that there are craters at the north pole of Mercury where the Sun don't shine (at least at the crater floor). These perpetually dark craters can become quite cold. When a comet hits Mercury, some of the vaporized comet material might reach the cold polar craters and condense out, creating icy deposits. However, it is not totally certain that this is what actually happens on Mercury. Further investigation might settle the issue. Another discovery made possible by improvements in radar astronomy concerns the interior of Mercury. Over a five-year period, Jean-Luc Margot of Cornell University used a technique similar to that used by Martin Slade to measure the rotation rate of Mercury to very high precision. Margot found a kind of variation in the rate, known as longitudinal libration which results from solar gravity tugging on Mercury, was double what it would be if Mercury was solid all the way through. This is thought to be evidence that at least the outer core of Mercury is in a molten state. While this would help explain the magnetic field (though there is still the problem of the slow rotation rate), this raises the mystery of why there should be any liquid core to Mercury at all, since a planet of Mercury's size, regardless of proximity to the Sun should have solidified completely billions of years ago. Margot has proposed that the outer core contains other elements, such as sulfur, mixed in with the iron, which would lower the melting point substantially. Again, this is another finding that requires more detailed investigation. Not all the recent discoveries were made by radar. In 1998, Jeffrey Baumgartner of Boston University decided to apply a then-new technique that had been used to create high-resolution images of Earth orbiting satellites to observing Mercury. The method, which is now familiar to those members of AAI who use CCDs or digital cameras, involves taking numerous short exposures, selecting the sharpest images, combining, and processing them. For the Mercury observations, the 60-inch reflector at Mount Wilson Observatory was used. Some images were of the hemisphere photographed by Mariner 10 and these showed that the images had real detail, not artifacts. Other images were taken of the hemisphere that went unseen by Mariner 10. While the images had nowhere near the resolution of spacecraft images and show only broad details, it appears that the unseen hemisphere has features similar to the other hemisphere. But we will have to wait for MESSENGER to get more detailed images. After years of study, much has been learned about Mercury. But, there are probably many other discoveries to be made. There might be a few surprises even from MESSENGER's first flyby this month. A Short Modern Look At The Universe By Dr. Lew Thomas When Did It Begin? Y ou have perhaps heard it said that the universe began about 14 billion years ago. How do we know this....or, do we really know? It was originally based upon what is known as the Hubble Constant. In 1931, Edwin Hubble along with Milton Humason stated that the universe was expanding; that all the galaxies shared a motion of separation one from each other and that this expansion could be measured by observing the shift of their Fraunhofer lines toward the red end of the visible spectrum. The effects of gravity were superimposed upon the motion of nearby galaxies, of course. For example, the Andromeda Galaxy is actually approaching us. However, when this gravitational effect is subtracted, a red shift remains. And when you reach distances such as those between the galactic groups, the red shift dominates. The farther away a galaxy is from us, the greater is the red shift. Hubble and Humason reported this by constructing a graph which plotted red shifts, or recessional velocities, against distances to each galaxy measured. This work began back in 1924, when Hubble began to use the newly fabricated 100 inch telescope at Mt. Wilson in California. Humason was then driving a mule train to haul equipment and astronomers up a dirt road leading to the summit. Humason later became what amounted to a janitor at the observatory. His curiosity earned him a position as assistant to the nighttime astronomers, helping them point the huge telescope to collect their data. Humason absorbed information so quickly and learned skills so rapidly that he finally became a full fledged astronomer at Mt. Wilson. This is a success story that demonstrates what can be accomplished when one is highly motivated. These two astronomers concentrated on galaxies in clusters to which the distances could be estimated by assuming that each cluster was made up of about the same variety of galactic types. The more galaxies in each group, therefore, the brighter was the assemblage. By the inverse square law, the distance could then be estimated independently of the red shift. When the red shift vs distance plot was made, it was observed that the more distant a galaxy was, the greater was its red shift. This was in keeping with the theoretical model of the universe put forward by Albert Einstein. In his field equations from general relativity, at first he predicted a static universe. This is one which is bounded in space and time, yet still infinite in both. This is a difficult concept. By analogy, one may liken it to the surface of the earth upon which you can travel infinitely far, but whose surface is still bounded. Einstein was troubled by his result which forced him to introduce a repulsive force. This was a strange force between particles which increased as the distance between the particles increased! A Russian mathematician, Alexsandi Friedman, in reviewing Einstein's work, pointed out that in one of the mathematical operations, Einstein had divided by a complicated expression which could take on a value of zero. In mathematics, simply dividing by zero, without knowing how the expression may approach zero has no meaning*. Einstein revised his result and found that a valid solution predicted a universe which was either contracting or expanding -- and without any repulsive force! Einstein later remarked that he considered his repulsive force mistake the worst blunder of his career. Now, measurements were needed to choose between a contracting and an expanding universe. Hubble and Humason provided the necessary data. The slope of the velocity (red shift#)) vs distance curve is the Hubble constant (H). The curve was assumed to be straight and the expansion rate was believed to be linear. The Hubble constant is usually expressed as km/sec per megaparsec. If the slope is really constant over eons of time, the Hubble constant gives a measure of the age of the universe. Let this age be To and so: To = 1/H (1) Now a megaparsec equals 3.086 x 1019 kilometers and there are 3.15576x107 seconds in a year, so that for H = 1 km/s/megaparsec 1 km/s/mpc = (1 km/sec) / 3.086x1019 km = 3.240x10-20 / sec = 3.240x10-20 x 3.15576x107 = 1.0268x10-12 / year = 1.0268x10-12 / 109 = .001027 /billion years (2) If H = 50 km.s/megaparsec, from (1) and (2) we obtain To = 1/(50 x .001027) = 19.4 billion years (3) We can simplify the arithmetic by revising (3) to express 1/H = 973.7 billion years per 1 km/sec/megaparsec (4) and then To = 973.7/H 1000/H billion years (5) where H = number of km/sec/megaparsec. (6) We say that if H = 50 then the universe must have begun about 20 billion years ago; that 20 billions ago all the matter and energy that is in the universe today was concentrated together in what has been called the primeval atom. All of these calculations assume that the Hubble constant can be determined as a single number, that the expansion of the universe has been constant, and that the sum total of all matter and energy in the universe is a constant. An alternate means for determining the age of the universe is to estimate the age of the galaxies based upon our theories of the creation, evolution, and death of stars. The best models of this process today yield from 12 to 20 billion years. Assumptions And Difficulties In Using The Hubble Constant The Hubble constant determines both the age and size of the universe. Certainly if we know the expansion rate and if this be constant, the time that the universe began would be known. Also, knowing these same items will determine the size to which the universe has so far expanded. However, there are certain subtle assumptions involved in using the Hubble constant quite apart with the determination of its value . We have tacitly assumed the following: 1) the cosmological principle, 2) the effects, if any, of gravity upon the expansion, and 3) the total amount of mass plus energy in the universe is constant. The cosmological principle states that the universe is homogeneous on a large scale. That is, the universe is expanding equally in all directions and consequently the mean density of the universe is decreasing evenly in all parts of space. The radius ® of the universe, if you will, is therefore undergoing a constant change throughout all space. Based upon these assumption, three models of the universe are possible, namely 1) A steady state universe in which )R = 0, 2) an expanding universe in which )R > 0, or 3) a contracting universe represented by )R < 0. The General Theory of Relativity mathematically allows all three possibilities. With the discovery of the cosmological red shift, solution #2 must be chosen. The question now becomes, is )R constant or variable with time. In other words, has the universe always expanded at the same rate? Here we must consider the effect of gravity. If there is enough mass in the universe, the expansion must slow down. Just like a rocket fired from the earth with less than the earth's escape velocity, that rocket must return to its starting point (neglecting gravity sources other than the earth as well as the earth's accelerating motion in space). If the expansion velocity is equal to or has exceeded the escape velocity of the universe, then the expansion must continue forever. If the gravity between the particles of the universe (galactic groups) of the universe is sufficiently weak, then the expansion velocity will virtually not be affected. In 1998, estimates of the distance to remote galaxies was made using the light output of embedded Ia supernovas as standard candles. Independently, the red shift of these galaxies was measured. The result indicated that in the past (remote galaxies) the expansion rate of the universe was less as it is now (nearer objects). The tentative conclusion is that the universe will expand forever and at an accelerating rate. An acceleration in the expansion of the universe would imply that either some gravity source(s) beyond our field of examination is pulling apart he matter in this region of space or that some repulsive force exists within our universe. Now, as we have said, the General Theory allows all three situations listed above, and we must reply on the measurements to chose the right one. Clearly the universe is expanding at an accelerating rate if the measured red shifts are cosmological. The discovery of the acceleration of the expansion of the universe has revived the notion of a cosmological constant great enough to produce this effect. What had been rejected by Einstein has returned. We call it dark energy. This dark energy is assumed to be constant throughout all of time and is a repulsive force. As the acceleration continues, the binding force of gravity is weakened as distances between galaxies increases. Therefore an acceleration must result. This acceleration is not limited by the speed of light which applies only to material objects moving in space. The expansion is of space itself. Red shifts indicating recessional velocities greater than light speed are permissible and many have been measured. The question of whether or not the Hubble constant can be relied upon to measure vast distances has been answered. It cannot. Red shift is still used as a distance metric, however. As an example, the galaxy-quasar association of NGC 4319 and Markarian 205* along with recent red shift studies indicate that these objects show significantly different red shifts. Notwithstanding, using ground based measurements, they appear associated by a luminous and filamentary "connection". If this connection be real, it seriously challenges the concept of always using the red shift as a cosmological yardstick. Moreover, it has far reaching implications regarding our present day concepts of cosmology and cosmogony. The magnitudes and computed distances of these two objects are given in the following table. The distances are based upon a Hubble constant of 75 km/s/mpc. OBJECT MAGNITUDE RECESSIONAL2 DISTANCE VELOCITY km/s Mpc Mly ------------ --------------------------------------------------------------------------- ----------------------NGC 4319 13 1700 22.7 7 Mrk 205 14.5 21000 280 910 With this important question in mind in 1993 Dr. Karl Hricko and this author imaged this apparent cosmological pair using the Hubble Space Telescope operated by the Space Telescope Science Institute of NASA. The pointing and imaging of the galaxy and quasar were perfectly accomplished. Careful examination of the images seem to indicate that the apparent connect is a foreground tidal tail of NGC 4319 produced by another nearby galaxy. A relatively unprocessed infra-red image* of the pair is shown here. The quasar is just to the lower left of the galaxy. Three Solutions In the next figure, we show three solutions resulting from different values for the cosmological constant, qo. Here the radius (R) of the universe is plotted against time. Curve 1 is the "critical solution or boundary between a closed and open universe; in which qo = 0.5 . This is the case when the mean density of the universe exactly equals the critical density. In other words, the universe is expanding with a velocity just equal to its escape velocity. For qo = 0.5, the age of the universe is undefined. TC = 0.667 To (7) Curves above #1 represent an open universe or one in which the expansion will continue forever. The age of an open universe would be TOPEN or TC< TOPEN < To (8) Curves below #1 are for a closed universe in which gravity would eventually reverse the expansion and the universe will collapse upon itself. Curve #2 is an example of this. The age of a closed universe, which we believe is not represented by present data, would be TCLOSED < 0.667 To (9) The ordinate labeled "today" is our present position in time. The dotted line is the empty universe in which gravity is so weak that it has no effect upon the expansion. This expansion would therefore be uniform, and under these conditions the universe began at To (this is the age of the universe often called the Hubble Age). All other decelerating models yield a younger universe. Curves above the straight line for the open universe, like #3, represent an acceleration in the expansion rate and would yield a universe older than To. This is the case which present data indicates applies and the age would be TACC > To (10) If the universe were closed, at some time in the future it would come together again in what has been called "the big crunch." Whether or not this would result in another Big Bang is open for speculation since we do not know what caused the previous Big Bang that, we believe, created our present universe. Our projection of the fate of the universe hinges upon which of these curves represents reality. We now think TACC applies. To correlate this discussion with that of relativity, we state that: An open universe = Negatively curved space or 0 curvature if R is large enough A closed universe = Positively curved space A uniform expansion = Space of zero curvature. Now to the third assumption, which we believe applies, that the sum total of all mass and energy is a constant across time. No one knows whether this is true or not. As a matter of fact, in 1930, Bondi, Gold, and Hoyle proposed a "steady state" universe. In this model, it was argued that as the universe expanded it would become less dense unless new matter were created to hold the density constant. Their hypothesis assumed a constant density universe with matter-energy coming into existence at just the correct rate to maintain a constant density as the expansion proceeded. The rate of generation of this matter-energy was calculated and found to be below that which could be measured by present day techniques. Evidence Of The Big Bang After the Big Bang and just before the electron density became low enough so that electrons did not scatter all the photons, the universe would become transparent and the theoretical temperature would be about 3000o Kelvin. The sources of the light emitted at that time are now about 14 billion light years away. These parts of the universe are receding from us and when a black body recedes, it is observed as being cooler because its light is red shifted*. As a result, the calculated 3000o Kelvin should be observed as 3o Kelvin and what's more, this radiation should be red shifted into the radio spectrum. This was predicted by Alpher and Robert Herman in 1948. At that time, there was no way of measuring such a low radiation because it would be masked by the internal noise of the radio receivers. In 1960, this idea again came to light in the minds of Robert H. Dicke of Princeton and two engineers at Bell Telephone Laboratories in New Jersey, Arno A. Penzias and Robert W.. Wilson. This time the electronic equipment existed for the measurement. Using a microwave horn antenna connected to a maser amplifier of extremely low noise, Penzias and Wilson succeeded in measuring a background microwave noise of 2.8o K. This result did not come easily. First they had to subtract the noise from our galaxy, from the sun, the sky, and the ground itself. They even cleaned the horn antenna to remove some radiating pigeon debris. The background noise remained. It had to be coming from space. After talking to radio astronomer B. Burke, they were put in touch with Dicke and all agreed that the background radiation from the Big Bang had been detected. This was later confirmed by measurements with other radio telescopes, by balloon carried telescopes, and even from instruments carried by the United States' U2 spy plane. Finally instruments carried out in space confirmed the result. For their work, Penzias and Wilson received the Nobel Prize in physics in 1978. It seems almost certain that this background radiation is indeed the result of the Big Bang. Though the Big Bang theory is continually being revised and is probably as yet in its infancy, this measurement went a long way toward advancing the Big Bang concept over the continual creation theory. The Big Bang Model In More Detail We cannot go over every detail of the Big Bang theory in this paper, however, a chronology of the events as theorized is in order. The theory began with a paper issued in 1947 by Robert Wagoner, William Fowler, and Fred Hoyle. Three concepts are thought to control the universe as it expanded just after the explosion. They are: 1) the universe cools as it expands, 2) initially the universe was so hot that collision of electromagnetic energy (photons) could produce matter in accordance with the relativistic equation E = mc2 (11) where E = rest energy of a particle m = the particle mass c = the speed of light 3) energy of a photon depends upon temperature in the following manner E = kT (12) where k = the Boltzmann constant T = the temperature in o K Based upon these ideas, the modern chronology is in the table on page 14, A Short Modern Look At The Universe (continued) Age of Universe Situation (Time after the Big Bang) ----------------------- --------------------------------------------------------------------------- -----------Under 0.01 sec No theories exist. Density so high that relativistic theory not valid 0.01 seconds T = 1011 oK Neutrons are left over from earlier universe. Neutrons + Positrons <--> Protons + antineutrons Too hot to get atomic nuclei from protons + neutrons (Note: neutrons are about 1/7 heavier than protons} Neutron --> proton + electron As temp drops this reaction can no longer be reversed. 15 seconds T = 3x109 oK photons --> positron + electron positron + electron --> energy (annihilation) Slight excess of matter over antimatter 1 minute T = 109 oK Neutrinos no longer react with matter. 3 minutes T = 9x108 oK Protons + positrons --> atomic nuclei (The first step in building atoms.) Collision of neutron + proton --> deuterium (heavy H) (This uses up all free neutrons.) Deuterium by collision --> helium (Helium = 2 protons & 2 electrons) No heavier elements. Must wait for stars to form. Note: There are 2 neutrons for every 14 protons when helium occurs (the 1/7 ratio). 12 protons remain after each helium formed Therefore, 1 He atom for every 12 H 25% of U should be He 75% of U should be H. Observation confirms above percentage 700,000 years T = 3000 oK Universe density = 1000 atomic nuclei/cc Electrons + Nuclei --> H and He scatter photons. Universe becomes transparent No great number of free electrons left to form atoms No further reaction of matter and energy 109 years Stars and galaxies form. Not sure about mechanism. Heavier elements fused in stars GENERAL MEETING January 18, 2008 "Symmetry: From Human Perception to the Laws of Physics" - Dr. Mario Livio, Senior Astrophysicist, Hubble Space Telescope Science Institute What do the fundamental laws of nature, human perception, the music of Johan Sebastian Bach and the selection of mates have in common? They are all characterized by certain symmetries. Symmetry is a concept that bridges the gap between the laws of nature and psychology; science and art. Yet the "language" of symmetry - group theory - emerged from a most unlikely source: an equation that couldn't be solved. Dr. Livio will tell the story of symmetry, of group theory, and their applications to everything from string theory to how we select our mates. He will also follow the sad lives of two mathematical prodigies who opened the door for these concepts. NOTE: The business portion of our General Meeting on Friday, January 18th, will be held immediately following the presentation by our featured speaker, Dr. Mario Livio. This is to accommodate Dr. Livio's itinerary. His talk will begin at 8pm sharp. As a courtesy to him, please arrive at the Roy Smith Theater and be settled in your seat a few minutes before 8pm. After the business meeting, we will adjourn to the observatory for refreshments and celestial viewing as usual. 8PM IN THE ROY SMITH THEATER MEMBERSHIP DUES Regular Membership: $21 Sustaining Membership: $31 Sponsoring Membership: $46 Family Membership: $5 First Time Application Fee: $3 Sky & Telescope: $32.95 Astronomy subscription: $34 (Subscription renewals to S&T can be done directly. See "Membrship-Dues" on website for details.) AAI Dues can be paid in person to Membership Chair or Treasurer, or by mail to: AAI, PO Box 111, Garwood, NJ 07027-0111 DR. LEW'S SEMINARS See Dr. Lew Thomas for possible upcoming seminar topics. (Choice of topic at Dr. Lew's seminars is determined by participants' interest) EMAIL CONTACTS president@asterism.org President of AAI editor@asterism.org Editor of The Asterism Ray Shapp, Editor Deadline for submissions to each month's newsletter is the first Friday of that month. membership@asterism.org AAI Membership Chair trustees@asterism.org All three Trustees of AAI ray@asterism.org Ray Shapp for the website exec@asterism.org Executive Committee plus Trustees QOs@asterism.org All Qualified Observers Info@asterism.org AAI president, corresp. secretary, and computer services chair DOME DUTY SCHEDULE January 25 Team A February 1 Team B February 8 Team C February 15 Team D FRIDAYS AT SPERRY January 25, 2008 What's Up: A Down-to-Earth Sky Guide (Advance view of February sky) Kathleen Quinn Vaccari February 1, 2008 Explorer 1 Al Witzgall February 8, 2008 A Tale of Two Moons Bonnie Witzgall All schedules above were accurate at time of publication. Please check www.asterism.org for latest information (click on "Club Activities") February 2008 presents us with what may be the rarest event that any of us will ever witness. Regulus, the heart of Leo the Lion, is about six degrees from Saturn, but that leaves just enough room for a total lunar eclipse to take place between them. A triple event like this will not happen again for over a thousand years. The next total lunar eclipse will not happen until December 2010. We also have a solar eclipse this month, but the Moon is too far away to cover the entire disk of the Sun, so this is an annular eclipse. Furthermore, it is visible only from Antarctica. This would not be worth a mention except for the fact that the path of annularity passes directly through the Russkaya Antarctic research station. If the Russians have reopened this station as planned, the scientists there will, weather permitting, see a blazing ring of sunlight surrounding a black Moon for 2 minutes and 8 seconds. Back in New Jersey, be sure to look to the east on the very first morning of the month to see Jupiter pass about half a degree below Venus. The two planets are moving in opposite directions, but we are in the best time zone to witness the exact conjunction. As Venus moves toward the Sun, Mercury comes out to meet it. Near the end of the month the two inner planets are just about a degree apart. Overall, 2008 is a bad year for Venus. From the end of February until the beginning of October, the brightest planet never leaves bright twilight. Venus always takes a long time to move from the morning sky to the evening sky, but this is the longest trip in its eight- year cycle. The reverse trip usually takes just a week or two. Saturn, on the other hand, is at its best, reaching opposition from the Sun on the 24th and visible all night. It's not as bright as in previous oppositions since the rings are flattening out from our viewpoint, but they are still lovely in a telescope. Mars does not set until long after midnight but it is rapidly fading as the Earth races away from it in our smaller orbit. Science Outreach and Exploration Update Ken Kremer In honor of the 4th anniversary of the robots Spirit and Opportunity roving on Mars, the editors of Spaceflight magazine (British Interplanetary Society) celebrated by selecting a panoramic image created by Marco Di Lorenzo and myself for publication on the cover of the new January 2008 monthly issue (see below). The cover image is a cropped portion of a mosaic we originally published in the 3 September 2007 issue of Aviation Week & Space Technology magazine (p. 6 and 42). Look closely and perhaps you'll recognize this image. The complete panorama was reprinted in the October 2007 AAI Asterism Newsletter and was taken by Opportunity while perched at the rim of Victoria crater. I presented this image during my lecture at the AAI general meeting on October 19, 2007. It is also viewable at the Nasawatch webpage headlined "Stunning Image" : http://www.nasawatch.com/archives/2007/09/stunning_image.html#more Opportunity with robot arm at the rim of Victoria Crater on 28 August 2007. All four science instruments are visible on robot arm. Rover later entered the crater at roughly the center of the cover image and just to the right side of the robot arm. Cover reprinted by permission of Spaceflight magazine, January 2008 issue. Photo Credit: Marco Di Lorenzo and Ken Kremer. Meanwhile, Spirit has reached her third winter resting place and is safely sitting at a sun-facing 14 degree slope at the feature named Home Plate which is an eroded over volcano. Home Plate is the first volcano ever visited by a man-made robot sent beyond Earth. Spirit touched down on Mars on 3 January 2004, while Opportunity arrived three weeks later on 24 January 2004. Mars Rover website: http://marsrovers.jpl.nasa.gov What's ahead for the new year on Mars? Briefly, the top scientists and engineers in charge of Earth's invasion fleet at Mars told me the following: Opportunity is likely to remain inside Victoria crater for several more months of science operations during the approaching Martian southern hemisphere winter season. Spirit will collect hundreds more images as she takes another giant panorama from her winter resting spot. And all is A-OK on board the Phoenix lander currently cruising thru interplanetary space and set to touch down near the Martian north pole in May 2008. Stunning Beauties of Our Solar System by Ken Kremer Opportunity "on the brink" Opportunity takes a 'toe dip' to descend several feet inside Victoria for this first dramatic camera view from the crater interior on 11 September 2007 (Sol 1291) which points towards its first science targets. For context, note that Opportunity was perched at the crater rim visible on the far left side of this image when she took the image which appears on the January 2008 Spaceflight cover. Dust is noticeable on the camera lens and leftover from the near fatal global Martian dust storm of summer 2007. Reprinted by permission of Spaceflight magazine, January 2008 issue, p. 22/23. Photo Credit: Marco Di Lorenzo and Ken Kremer DAWN Asteroid Orbiter Update: The initial check-out phase of all spacecraft systems following launch was successfully completed. On 18 December 2007 the probe was transitioned to the interplanetary cruise phase with nearly continuous ion thrusting. For a beautiful new starfield image which includes the Eta Carina nebula, Check out the Dawn homepage: http://dawn.jpl.nasa.gov Please contact me for further information or science outreach presentations. My upcoming talks include: Rittenhouse Astronomical Society (RAS) at the Franklin Institute: Philadelphia, PA, Wed, Feb 20, 8 PM. "Lunar, Solar and Martian Eclipses". Website: http://www.rittenhouseastronomicalsociety.org Raritan Valley Community College Planetarium: Somerville, NJ, Wed, Apr 2, 7:30 PM. "Launching DAWN (and Phoenix): From Behind the Scenes at Kennedy Space Center". Website: http://www.raritanval.edu/planetarium Washington Crossing Nature Center: Titusville, NJ, April 12, 1 PM. "Mars, Saturn, Asteroids and Beyond" Dr. Ken Kremer Email: kremerken@yahoo.com NASA JPL Solar System Ambassador