Wednesday, April 30, 2014


MAVEN (Mars Atmosphere and Volatile EvolutioN) is a NASA space mission primarily focused on studying the Martian atmosphere. Previous Mars missions have already given us hints into Mars's past, including numerous signs of past liquid water and various geographical and chemical signatures of a planet that was habitable many, many years ago. MAVEN will approach the problem of elucidating Mars's past from a different angle, by examination of its upper atmosphere.

Before MAVEN, our hypothesis as to the demise of Mars's habitability was as follows: several billion years ago, when the Solar System and its planets were still young, Mars had, like Earth, a molten core.

Earth's molten core consists of metals such as iron that conduct electricity. The circulation of these metals throughout the core, induced by the rotation of the Earth, generates a magnetic field (as in the illustration above). This magnetic field, in turn, protects us from the charged solar wind by deflecting it towards the poles. Mars is theorized to have had a similar core and magnetic field. However, being farther from the Sun and smaller, Mars's core cooled over time, and eventually solidified. The planet's magnetic field then weakened, and solar wind blew away a majority of Mars's atmosphere, leaving it with a rarefied layer of mostly carbon dioxide. Such a thin atmosphere would have been inhospitable for liquid water, and thus any bodies of water dried up, likely killing any life, if it had developed there.

MAVEN's observations did not alter this basic understanding, but will provided much more detailed information. For example, by observing how solar wind interacts with Mars's current atmosphere, the spacecraft provided data concerning the exact mechanisms involved in atmospheric loss (see below). To this end, MAVEN carried several instruments that measure solar wind and its impact on Mars. Also, by observing the current rate of gas loss, the mission allowed scientists to extrapolate backward and infer a more precise timeline of Mars's climate evolution. In order to accomplish this goal, MAVEN included instruments that detect gaseous ions escaping from the Martian atmosphere. These are the "volatiles" to which the name refers. Finally, the probe also had a device known as a mass spectrometer, which can measure the abundance of different isotopes of certain chemical elements. Since heavier isotopes are less likely to be ejected from Mars simply due to their slightly greater mass, the ratio of isotope abundance in Mars's atmosphere versus that in Earth's, for example, can indicate exactly how much has been lost and thus how dense the atmosphere was in the past.

Artist's rendering of MAVEN

MAVEN launched on November 18, 2013. After about a ten month cruise, the probe entered orbit of Mars on September 21, 2014. A few weeks after, the spacecraft assumed its science orbit, a highly elliptical orbit. The low point of its orbit brings MAVEN within 100 miles of the surface, allowing it to easily sample the atmosphere, and the high point brings it to more than 3000 miles from Mars's surface, so that the spacecraft can also take global observations.

Late in 2014, MAVEN discovered a mechanism by which ions in the solar wind penetrated deeper into the atmosphere than previously thought possible. Also, to extend its range further, MAVEN periodically dipped its orbit even farther down toward the surface, reaching a minimum altitude of 78 miles instead of 93 miles. The first of these "deep-dip" campaigns took place in February 2015.

During March, MAVEN encountered multiple unexpected atmospheric phenomena. The first was the presence of an aurora in ultraviolet wavelengths at a relatively low altitude over Mars's northern hemisphere (the geographic locations are indicated in the image above). Also, the orbiter detected a dust cloud between 93 and 190 miles above the surface of Mars, which could not be explained by any atmospheric mechanism known at the time. On April 3, MAVEN completed its 1000th orbit of Mars.

MAVEN achieved one of the basic goals of its mission in November 2015; in that month, NASA announced that the solar wind rips gas away from the Martian atmosphere at a rate of about 100 grams per second. This rate varies significantly with solar activity and is believed to have been greater billions of years ago. This result, when combined with other Mars missions, finally allowed a comprehensive understanding of Mars's loss of carbon dioxide (the main component of the Martian atmosphere).

Mars used to have a great deal of carbon dioxide in a thick atmosphere, far more than in the rarefied blanket of gas surrounding the red planet today. Some of this carbon dioxide was trapped in mineral carbonates (as shown) or is cycled between the atmosphere and ice caps as they melt and refreeze. In addition, MAVEN's atmospheric loss measurement shows how a process called "sputtering" allows some gas to escape. However, orbital spacecraft indicate that the amount trapped in carbonates is not enough to explain the loss. Further, while the "sputtering" process favors the escape of the heavier isotope carbon 13 over carbon 12, the preference is only slight: this process alone cannot explain the higher isotope ratio measured on the ground by the Curiosity rover. Instead, the discoveries of MAVEN suggest that another mechanism is primarily responsible, namely the interaction of solar ultraviolet radiation (denoted "hv" in the image) with carbon dioxide molecules that causes dissociation. After this process, carbon 12 has a much higher chance of escaping the atmosphere than carbon 13, explaining the observations.

In October 2016, after observing Mars for more than a total Martian year, MAVEN had a fairly fleshed out account of how water escapes Mars. More precisely, it measured escaping hydrogen in the upper atmosphere that resulted from disassociation of water vapor (H2O) in the lower atmosphere. Before MAVEN, it was believed that this loss of water vapor occurred at a relatively constant rate. However, the spacecraft found that the rate of hydrogen escape is larger by a factor of 10 between when Mars is closest to the Sun compared to when it is farthest. This suggested that the amount of water vapor in the Martian atmosphere varies significantly throughout its year and helped to elucidate the process of its escape.


Wednesday, April 23, 2014

Eclipses and Saros Cycles 3

This is the third part of a three part post. To begin viewing the first, click here.

The previous post revealed the primary astronomical tool for predicting eclipses, the saros cycle. According to this cycle, the Moon has the same apparent size, inclination to the Earth's orbit, and angle to the Earth-Sun line in the Earth's orbital plane every 6585.32 days. Therefore, if an eclipse occurs on a given date, another very similar eclipse will occur about 18 years later with respect to the above parameters. During an eclipse, the angle of the Earth-Sun line to the Earth-Moon line will either be 0° (for a solar eclipse) or 180° (for a lunar eclipse), and the Moon will be at the same angle after a saros cycle, so two eclipses separated by a saros cycle must either both be solar or both be lunar. Similarly, during an eclipse, the Moon is either passing through the Earth's orbital plane at the ascending node or the descending node, and the eclipse after a saros cycle has passed will involve the Moon at the same node. Finally, the apparent size of the Moon will be the same for eclipses separated by a saros cycle.

However, many other conditions are not invariant before and after the length of time of a saros cycle. For example, since the decimal part of the length of the saros cycle is .32 days, two eclipses separated by a saros cycle will not be at the same time of day on Earth. In fact, the second eclipse will occur about 8 hours later than the first (.32 days is approximately 8 hours). This also guarantees that the eclipse will not occur in the same place on the Earth's surface. Futhermore, since the saros cycle is about 18 years and 11 days, the Earth will also be in two different places on its orbit around the Sun when the two eclipses occur.

In addition, 6585.32 days is not exactly an integral multiple of each of the synodic, draconic, and anomalistic months. For instance, 242 draconic months is about 6585.35 days (using the more precise value of 27.21222 days for the draconic month), which, although very close to the length of 223 synodic months, 6585.32 days, is not equal to it. As a result, even as as 223 synodic months pass from one eclipse and the Moon returns to its position along the Earth-Sun axis, the period of 242 draconic months is not quite complete, so the Moon will not have quite reached its node. Thus, over time, the eclipses separated by saros cycles shift until, eventually, the necessary conditions no longer align, and eclipses cease. Any given saros series will therefore only have a certain number of eclipses before the alignment ends.

The above image illustrates the progress of a saros series of lunar eclipses, where the gray bullseye represents the Earth's shadow (recall that if the Moon passes through the light gray, or partial shadow, of the Earth, the eclipse is partial, and if it passes entirely into the dark gray area, the total shadow, the eclipse is total). This series of eclipses is also at the descending node. Therefore, we can see that, before the saros series begins, the Moon has already passed the descending node at the time of the correct angular alignment of the Moon, Earth, and Sun. Thus the Moon is "too low" to be hit by Earth's shadow (blue-gray Moon). However, after a saros cycle has passed, the angular alignment is once again correct, but a full draconic month has not yet passed, so the Moon is a little less past its descending node than before.

Eventually, the draconic month has drifted backward enough so that the passage through the descending node does coincide with the correct arrangement of the Moon, Earth, and Sun in the orbital plane, and the path of the Moon does take it through the Earth's shadow. At this point, partial and then total eclipses will occur. However, over time, the Moon's progress in the draconic month will again fall behind, and at the time of correct angular orientation, the Moon will have not yet reached the descending node. At this point (the pink Moon), eclipses will cease and the saros series ends.

A similar phenomenon occurs with solar eclipses. In the above diagram, a few total solar eclipse paths across the Earth are shown, all from the same saros series (though there are many others), and again at the Moon's descending node. Note that each eclipse is indicated by a path along the Earth's surface. The paths are the areas which experience totality some time during the eclipse. The path of the eclipse moves from west to east, even though the part of the Earth facing the Sun moves from east to west along the globe. This is because the Moon's velocity, and thus the velocity of its shadow, is greater from west to east then the area that of the point on the Earth's surface moving from east to west.

As mentioned above, successive eclipses in a saros cycle are separated (in time of day) by about 8 hours, approximately a third of a day. Thus the second eclipse takes place about 120° west of the first. Thus two eclipses in a saros series three saros cycles apart will be at about the same longitude. But for the above series, which take place at the Moon's descending node, eclipses later in the series are not as far along with respect to the draconic month as those at the beginning. Thus, just as for lunar eclipses, the eclipses in a series at the descending node shift "upward", and in the solar case, this has the effect of shifting the totality path north for each successive saros cycle. Thus the first eclipses in the same saros series as above, are only partial, and can only be seen near the south pole. Eventually, as the series progresses, the Moon's shadow intersects the Earth, again beginning at low latitudes. As in the figure, the path shifts north until the eclipses can only be seen near the north pole, and then not at all. The down-to-up or south-to-north pattern for saros series reverses for series at the ascending node.

Saros series are numbered, with separate numberings for lunar and solar eclipse series. For lunar eclipses, those at the descending node are given odd numbers and those at the ascending node even numbers. The situation is reversed for solar eclipses. The saros series, further, are ordered in number by starting date. Contemporary series which are currently producing total eclipses are in the low to mid 100's. For example, the solar eclipse on August 21, 2017 belongs to solar saros 145. Solar and lunar saros series each include around 70 eclipse events, spanning a period of roughly 1200 years. Of course, these series overlap, so any given year, eclipses occur from different saros series. For example, the year 2012 had solar eclipses from series 128 and 133, while it had lunar eclipses from series 140 and 145.

In conclusion, saros series are the most important tool in the categorization of eclipses, and have allowed us to identify when eclipses have occurred thousands of years into the past, and to predict when the will occur thousands of years into the future.


Tuesday, April 15, 2014

Eclipses and Saros Cycles 2

This is the second part of a post concerning eclipses and saros cycles. For the first, see here.

To understand how solar eclipses are predicted, we first must define some terminology relating to various types of "months". These months are not calendar months, but rather are time intervals related to the moon's orbit.

Synodic Month (29.53 days): This is the most common period referenced in the context of the moon. It measures the time it takes for the Moon to complete a revolution with respect to the line between the Earth and the Sun, or the time between two full moons or two new moons. However, this month is not equal to the period of the Moon's orbit, because the line between the Earth and the Sun shifts, as the Earth itself revolves.

The above image shows the position of the Earth and the Moon relative to the Sun at two successive new moons. Note the angle between the line connecting the Earth and Sun and the line marking the point at which the Moon has completed exactly one orbit around the Earth. Such an orbit takes 27.32 days.

Draconic Month (27.21 days): This "month" is the average time between successive crossings of the ascending node by the Moon on its orbit. The nodes of an orbit are the orbit's intersection with some plane of reference. In the context of eclipses, we are concerned with the intersection of the Moon's orbit around the Earth with the plane containing the Earth's orbit and the Sun. Since the Moon's orbit is inclined to this plane, there are only two points of intersection (see diagram below).

The two nodes of the Moon's orbit are the ascending node, at which point the Moon crosses from below the plane of the Earth's orbit to above (where the area "above" the plane is the space beyond the Earth's north pole), and the descending node, where the opposite occurs. Since, due to the effect of the Sun's gravity, the nodes of the Moon's orbit shift with time against the Moon's direction of orbit, the draconic month (time between crossing ascending node twice) is slightly shorter than the orbital period of the Moon (27.32 days). The draconic month is important for the prediction of eclipses because eclipses can only occur when the Moon is in the plane of the Earth's orbit and the Sun, i.e., when the Moon is at an ascending or descending node.

Anomalistic Month (27.55 days): The Moon's orbit, just like the Earth's and that of other celestial bodies, is not a perfect circle. Thus the Moon's distance from Earth varies. The farthest point of the Moon's orbit from the Earth is known as the apogee (deriving from Ancient Greek "from" and "earth", the second of which also gives us geography, geocentric, etc.), and the closest point the perigee (with "peri" meaning "around").

Diagram of the Moon's orbit (elongation exaggerated)

The anomalistic month measures the time it takes for the Moon to travel from one apogee (or perigee) to the next. Note that this length of time is slightly longer than a lunar orbital period, because the apogee and perigee move along the lunar orbit in the same direction as the Moon's motion, so it takes longer for the Moon to "catch up" to its apogee than for the Moon to simply complete an orbit. The anomalistic month is important for eclipse prediction, because although it does not affect the apparent position of the Moon in the sky, whether the Moon is closer to apogee or perigee does affect its apparent size, and thus can affect the type and duration of an eclipse.

Apparent size of the Moon at apogee and perigee.

Note that the apparent size of the Sun varies too, as the Earth's orbit is also elliptical, but the variation occurs at only a fraction of the magnitude (about 3% variation versus the Moon's 12%). Therefore, we focus on the Moon's apparent angular diameter as the determining factor.

In summary, progress through the synodic month indicates the Moon's position relative to the Earth-Sun line (in the Earth-Sun orbital plane), progress through the draconic month indicates how far the Moon is from the Earth-Sun orbital plane, and progress through the anomalistic month indicates the Moon's apparent size. It so happens that the length of time equal to 223 synodic months is about the same as that of 242 draconic months and 239 anomalistic months, all of which equal approximately 6585.32 days. The reason this is significant is that after this period of time passes, a whole number multiple of each of the three "months" will have passed, and the Moon will be in almost exactly the same position relative to the Sun, the same apparent size, and the same inclination from the Earth-Sun orbital plane. Thus if an eclipse occurs at a given date, a nearly identical eclipse will occur again 6585.32 days later! A period of 6585.32 days, about 18 years, is known as a saros cycle.

The sequence of eclipses produced beginning at a given date and including all the eclipses separated from the first by some number of saros cycles is known as a saros series. Eclipses, both lunar and solar, are classified by saros series. The next post explores the details and applications of saros cycles and series.


Monday, April 7, 2014

Eclipses and Saros Cycles 1

Solar and lunar eclipses are among the most spectacular of celestial phenomena. One of the great triumphs of astronomy was the accurate prediction of solar eclipses, beginning with Ancient Greek and Chinese astronomers. These predictions depend on a study of the cycles of the Earth, the Moon, and the Sun, known as Saros Cycles.

First, however, an explanation for the mechanism of eclipses is in order. A eclipse occurs when the Sun, the Moon, and the Earth are in a straight line, so that the Moon casts a shadow on the Earth, or vice versa. When the Earth casts a shadow on the Moon, the eclipse is lunar. When the Moon casts a shadow on the Earth, the eclipse is solar. An illustration of both of these eclipse types is shown below (not to scale).

In a solar eclipse, only a very small portion of the Earth's surface receives the shadow of the Moon, and this shadow moves across the Earth's surface as the Moon moves along its orbit. Furthermore, from the viewpoint of the observer on Earth, a solar eclipse is total when one is within the shadow of the Moon, and partial when one is in the partial shadow of the Moon (see above figure). The dark gray area is the shadow of the Moon, where both sides of the Sun are invisible. Thus in a total solar eclipse, none of the Sun is visible.

Total Solar Eclipse

The light gray area in the above diagram is the partial shadow, or penumbra. In this region, one side of the Sun is visible, but the other is blocked from view. In a partial solar eclipse, the Sun is never completely covered by the Moon, but the Moon rather skirts the Sun, covering only one of its edges.

Partial Solar Eclipse

Note that, on the diagram, since the Sun is larger than the Moon, the rays of the Sun on either side of the Moon converge with distance, and the shadow of the Moon on the Earth is a great deal smaller than the Moon itself. In fact, since the distance between the Earth and the Moon varies, when the Moon is farthest from the Earth and an eclipse occurs, the shadow of the Moon no longer reaches the Earth. In other words, from the perspective of the Earth viewer, the size of the Moon's disc is smaller than the size of the Sun's disc, and the Moon cannot cover the Sun. This leads to a phenomenon known as a annular solar eclipse.

Annular Solar Eclipse

Conversely, a lunar eclipse occurs when the Earth is between the Sun and the Moon. There are partial and total lunar eclipses as well, although the definitions differ slightly, as they are geocentric; in other words, the definitions are not based on an observer on the Moon, rather one on the Earth. Since the Earth's shadow is large, it can completely cover the Moon, as opposed to a solar eclipse, which is a localized event. A partial lunar eclipse is one in which the Earth's shadow does not completely cover the Moon, and a total lunar eclipse is one in which the Earth's shadow completely covers the Moon. During a total lunar eclipse, the Moon takes on a characteristic red color.

Total Lunar Eclipse

The Moon appears red during a lunar eclipse due to the fact that the only light reaching the Moon passes through a good deal of the Earth's atmosphere. Most short wavelengths of light are scattered by the time the Sun's rays have passed all the way through, so only long-wavelength light remains, causing the Moon to appear red in the visible spectrum. The same effect makes sunrises and sunsets appear red.

Though these types of solar and lunar eclipses differ in appearance, they are all manifestations of the same phenomenon: the alignment of the Sun and the Moon with respect to the Earth. Looking only at the diagram of a solar eclipse, one would believe that such events would be quite common, and would occur every time the Moon orbits around the Earth to come in line with the Sun. This would be true if the orbits of the Sun and the Moon lay in the same plane. However, the plane of the Moon's orbit around the Earth is inclined relative to the plane of the Earth's orbit around the Sun, and to make matters worse, the orbit is constantly shifting.

The next post discusses how eclipses can be predicted by understanding the various cycles of the Moon, Earth, and Sun.