Zodiacal Light

Looking east on a clear night, just before sunrise, a glow extends upward from the horizon. This light lingers, coexisting with the stars, before a brighter band of sky appears along the horizon, the Sun itself not far behind. Long exposure photography shows the phenomenon clearly, such as in the left side of the image below (the glow of the Milky Way galaxy is also visible on the right).

Astronomers first noticed the subtle first light, known as zodiacal light, centuries ago. In fact, identifying this phenomenon has been important to the practice of Islam. The fajr, or dawn prayer, is required before sunrise every day, but how long before? Unlike noon and sunset, the time of dawn is harder to pin down precisely.

The phenomenon of zodiacal light was significant enough to be named in the teachings of the Islamic prophet Muhammad: it was called "the false dawn", al-fajr al-kazib, to be distinguished from the later "true dawn", al-fajr as-sadiq. The latter time is widely accepted to be the correct one for the dawn prayer.

But what causes this light? In some ways, the cause is mundane: astronomers have long known that the glow originates from sunlight reflecting off of small dust particles in space. The long-narrow shape of the glow occurs because dust is not distributed uniformly throughout interplanetary space. Nearly all objects orbiting the Sun, from the largest planets to the smallest dust particles, cluster near a single plane, the plane of the Solar System. In our night sky, this plane appears as a line known as the ecliptic, along which the planets, Sun, and Moon travel. In turn, the constellations on the ecliptic are known as the zodiac. Voilà! Zodiacal light! Though most pronounced near the Sun at dawn, dim zodiacal light can be observed on a moonless night to follow the entire ecliptic.

However, this explanation merely raises another question. Where does the dust come from? Some debris comes from comets and asteroids, but some more evidence recently surfaced on this subject from an unlikely source.

On August 5, 2011, the NASA spacecraft Juno launched from Earth, the beginning of its five-year journey to Jupiter. Elsewhere on this blog, I've written in depth about Juno's mission and its many discoveries orbiting the Solar System's largest planet. However, the probe began gathering important data long before reaching its destination. Along its trajectory (pictured above*), Juno returned to Earth for a gravity assist to give it a boost to Jupiter. During its journey, scientists on the Juno team noticed something alarming: thousands of tiny streaks of light appeared on images of what should have been empty space!

Further analysis revealed that the streaks were tiny bits of debris knocked from Juno's solar panels, dislodged by microscopic dust particles impacting at high velocities. Unintentionally, the large solar panels of Juno became a interplanetary dust collector! Fortunately, the impacts were not large enough to cause damage detrimental to the mission, but they did reveal a surprising story.

In all, over 15,000 dust impact events were recorded, enough to measure in unprecendented detail the distribution throughout the inner Solar System. The figure above* (click to enlarge) shows the data. The top panel shows events on Juno's inbound stage from the farthest point of its first orbit (on the trajectory image, the point marked DSM or "Deep Space Manuever") to Earth flyby. The second shows impacts recorded outbound from Earth flyby through the asteroid belt, on its way to Jupiter. The horizontal axis measures distance from the Sun, while the black line indicates frequency of imapct events. For context, various significant distances and the distribution of asteroids (gray) in the asteroid belt are also included.

As a bonus, the outbound portion of the trajectory shown above was tilted from the ecliptic plane, while the inbound one lay within it (see again the trajectory image). Hence, we can clearly see that less impacts occur away from the plane of the Solar System. It is also clear that the impacts are reduced near Earth, since our planet's gravitational influence "clears its orbit" of dust. Nevertheless, it is the dust closest to us that causes most of the zodiacal light we observe.

In contrast, the vicinity of Mars appears riddled with dust, even more so than some parts of the asteroid belt! This was a great surprise, for it was expected most of the dust was from asteroids and that Mars would clear its orbit, just like Earth does. However, further data analysis confirmed that Mars must in fact be a major source of the dust that ultimately causes zodiacal light! There is much more to be discovered about this story: what mechanisms cause Mars to lose so much dust to space? Currently, the answer is not definitively known, though further space missions could provide clues. But after thousands of years of mystery, at least we now know that when we see that before-dawn glow, we have the red planet to thank.

Sources: https://www.al-islam.org/articles/al-fajr-sadiq-new-perspective-sayyid-muhammad-rizvi, https://earthsky.org/astronomy-essentials/everything-you-need-to-know-zodiacal-light-or-false-dusk/, https://agupubs.onlinelibrary.wiley.com/doi/epdf/10.1029/2020JE006509, https://www.jpl.nasa.gov/news/serendipitous-juno-detections-shatter-ideas-about-origin-of-zodiacal-light

*The last few figures in this post are from the paper "Distribution of Interplanetary Dust Detected by the Juno Spacecraft and Its Contribution to the Zodiacal Light" by J. Jorgensen et al.

The Gravitational Assist Maneuver

On October 7, 1959, the Soviet space probe Luna 3 passed over Asia and transmitted a handful of blurry black-and-white photos back to Earth. These were humanity's first glimpse of the Moon's far side (see below). The probe was launched on a circumlunar trajectory three days prior and its initial orbit about the Earth did not take it back on a path from which it could successfully relay its valuable data. However, Luna did not propel itself onto the necessary path. This groundbreaking probe was also the first to accomplish another feat: the gravitational assist.

Since 1959, spaceflight, especially interplanetary spaceflight, has relied upon gravity assists to reach destinations all over the Solar System. Apart from Luna 3, all other examples we will consider involve using gravity assists to change orbits around the Sun, rather than some other object (such as the Earth in the case of Luna 3). The basic principle is as follows: changing orbits around the Sun requires changing spacecraft velocity relative to the Sun, known as heliocentric velocity. Conventionally, this is done using thrusters aboard the craft itself (e.g. with chemical rockets; see ion propulsion for another example). However, onboard thrusters always require ejecting mass, and heavier rockets are much more difficult and costly to launch.

Gravity assists take advantage of planets' orbital velocity and gravitational influence to alter a spacecraft's heliocentric velocity. Take the diagram below, which shows a probe flying by the planet Jupiter.

Passing close to Jupiter puts our probe on a curved trajectory about the planet. Moreover, as it falls "downhill" into the gravity well of the giant planet, it picks up speed (as indicated by the longer arrows). This gain in speed is short-lived, however, because it loses kinetic energy climbing out of the well as it departs. As a result, though the velocity vector is pointed in a different direction than before, it seems we've made no progress in increasing our probe's speed.

But this is not true: all velocities in the above diagram are relative to Jupiter, i.e. measuring the rate at which an observer on Jupiter would see the spacecraft traveling. What matters for its orbit though, is heliocentric velocity.

Suppose that, with respect to the Sun, our planet has an initial orbital velocity toward the left. Then the total heliocentric speed can increase for our spacecraft if the velocity relative to the planet is rotated to line up more closely with the planetary velocity (as indicated by the addition of arrows in the above diagram). Two of the greatest outer Solar System missions in history relied on this principle: the Voyagers.

Both Voyager 1 and 2 made use of a gravity assist at Jupiter to accelerate them to Saturn, and Voyager 2 did the same to reach Uranus and Neptune. While a slight change in direction at each planet is visible in the above diagram, the following graph better captures Voyager 2's changes in speed.

The blue curve graphs the magnitude of Voyager 2's heliocentric velocity at various distances from the Sun along its journey. Note that at each flyby of a giant planet, the probe's speed sharply increased for a short time (as it plunged into the planet's gravity well) but also was higher after each flyby than before, with the exception of after its final encounter with Neptune. The other curve shown is the Solar System escape velocity, that is, the velocity required at a specified distance from the Sun to ultimately escape its gravitational influence. Remarkably, Voyager 2 did not even have sufficient velocity to escape the Solar System until after its first flyby with Jupiter! Without gravity assists, the spacecraft would not be headed toward interstellar space today.

As indicated by Voyager 2's encounter with Neptune, gravitational assists can also reduce a spacecraft's heliocentric velocity. This is necessary for certain missions to the inner Solar System; objects launched from the Earth do not simply fall toward the Sun - they have to lose the angular momentum they inherit from our own planet!

In October 2018, the European Space Agency spacecraft BepiColombo on a mission to orbit Mercury in 2025. See here for an animation of the probe's seven-year trajectory. If the probe had been launched directly toward Mercury, the additional velocity acquired from falling into the Sun's gravity well would have made orbit impossible. Instead, the mission trajectory incorporated two Venus flybys and six Mercury flybys, all to slow down the spacecraft without the use of too much thrust.

Finally, some space missions even use encounters with planets to leave the plane of the Solar System! The Ulysses spacecraft, launched in 1990, had the goal of studying the Sun. In particular, it aimed to measure the solar wind (the flow of charged particles) and magnetic field emanating from the Sun. Unlike previous missions, Ulysses had the opportunity to study the Sun from above its poles in an orbit that was inclined 80.2° to the plane of the Solar System. A vast majority of solar system missions remain in the nearly flat plane of the Sun's equator in which the planets lie.

To achieve this unusual orbit, the probe went all the way to Jupiter just to flyby the giant planet. Jupiter's large mass allowed for a more effective gravity assist and its distance from the Sun meant that the probe was traveling slower there and the maneuver required a smaller change in velocity. Ultimately, Ulysses made a great deal of new discoveries, including that the solar magnetic field "flips" every 11 years.

Faced with the difficulties of efficient Solar System navigation, numerous space missions have utilized creative solutions involving gravity assists to reach their targets, providing another example of the spectacular innovations necessary to explore worlds beyond our own.

Sources: https://solarsystem.nasa.gov/missions/luna-03/in-depth/, https://solarsystem.nasa.gov/basics/primer/, https://www.researchgate.net/publication/228803791_Design_of_Lunar_Gravity_Assist_for_the_BepiColombo_Mission_to_Mercury, https://medium.com/teamindus/daring-gravity-assist-maneuvers-of-past-space-missions-411643cd3d55, https://solarsystem.nasa.gov/missions/ulysses/in-depth/

GW170817 and Multi-Messenger Astronomy Part 2

This is the second part of a two-part post. For the first part, see here.

The previous post described the gravitational wave event GW170817 (which took place on August 17, 2017) and how it was ultimately identified as a binary neutron star merger. In addition, it was associated with a gamma ray burst (designated GW170817) and imaged across the electromagnetic spectrum, an unprecedented and landmark event in the field of multi-messenger astronomy. Though it is intrinsically of interest to be able to both "see" (EM waves) and "hear" (gravitational waves) an astrophysical event, what are some other conclusions to be drawn from the merger?

One simple conclusion requires nothing more than a quick calculation, but verifies a foundational principle of physics that while almost universally assumed, had never been directly proven. This principle states that both electromagnetic waves and gravitational waves travel at the speed of light in a vacuum, about 3*10⁸ m/s. Recall that the merger is estimated to have taken place about 130 million light-years away. This means that both the gravitational wave signal and the gamma ray burst both took about 130 million years to travel from the source to detectors on Earth. Despite their long journey, they arrived within a few seconds of each other. Now, we cannot be certain exactly when the gamma ray burst was emitted, due to our incomplete understanding of how a binary neutron star merger would work. However, it is likely that the neutron stars must first collide (marking the end of the gravitational wave signal) before emitting a burst of gamma radiation. Moreover, this initial high-energy burst was estimated by most models to occur no more than a few minutes after the merger. Therefore, dividing the amount by which the signals could have drifted apart over their travel time, we obtain bounds on the "speed of gravity" relative to the speed of light. Even with conservative assumptions, these observations prove that the two speeds very likely differ by no more than one part in a trillion (0.0000000001%) and probably several orders of magnitude less than this. Theoretically, they are equal, but never before has this been measured with such incredible precision.

In a similar vein, the merger allowed other tests of various aspects of general relativity and field theory, such as the influence of gravitational waves on the propagation of electromagnetic field. The data all confirmed the current understanding of general relativity and set very tight bounds on possible deviations, better than those ever achieved in the past.

The detection of the merger also taught us about the very structure of neutron stars. Unlike black holes, which (to our knowledge) are effectively points of mass, neutron stars are on the order of a few miles across. Considering their mass (usually 1-2 solar masses), they are exceedingly dense, but nevertheless their physical size affects how the gravitational wave event unfolds. When the two objects get very close to one another, their mutual gravitational attraction is expected to cause tidal deformations, i.e. warping of their shape and mass distribution. In theory, information concerning the deformation is encoded in the measured waveforms.

The figure above (click to enlarge), while rather technical, gives some idea as to how exactly the gravitational wave data constrain the structure of the neutron star. The statement |χ| < 0.05 in the diagram indicates that the entire figure is made presupposing that the neutron stars were not spinning too fast (which our knowledge of neutron star systems suggests is a very reasonable assumption). The two axes measure the magnitude of two parameters Λ₁ and Λ₂ that measure how much the larger and the smaller neutron stars, respectively respond to tidal deformation. In other words, smaller values of the parameters (toward the lower left) mean denser and more compact neutron stars, as indicated. More on what these parameters actually mean can be found in the original paper here.

Next, the darker shades of blue represent values considered more likely given the shape of the gravitational wave signal. This is a probability distribution, and lighter shaded areas were not ruled out with certainty, but simply deemed less likely. The uncertainty in the original masses contributes to the uncertainty in this diagram. Finally, the gray shaded "stripes" indicate the predictions of several different theoretical models of neutron stars. These are distinguished by their different equations of state, which specify how mass, pressure, density, and other properties of neutron stars relate to one another. The varying predictions of these models show just how little was definitively known about neutron stars. Analysis of the merger event suggested that the "SLy" and "APR4" models were more accurate than the rest (at 50% confidence) and that the "MS1" and "MS1b" models are unlikely to be correct (with more than 90% confidence). No model was ruled out for sure, but the data above suggest that neutron stars are more compact than most models predicted.

The gamma ray burst that followed the merger also contained some information concerning how these mergers actually occur and the physics of when and why high-energy radiation is released. Notably, the gamma ray burst was a single short pulse (lasting under a second) with no discernible substructure. It was difficult to draw conclusions from this limited sample, but explaining the nature of the pulse and the delay may require a dense layer of ejecta from each of the neutron stars to momentarily impede electromagnetic radiation from the merger. It would take some time for gamma rays to penetrate this cloud of debris until they finally burst through.

Moreover, among the known population of gamma ray bursts, GW1701817A was relatively dim. This may have been due to the main "jets" of energy not being along our line of sight; most of the burst is hypothesized to have been released along the original axis of rotation of the two bodies. The discrepancy may in part have been due to observational bias, since brighter events are more likely to be observed. In such cases, the Earth likely was directly facing the angle of peak gamma ray emission. Detecting an event "off-center" elucidates somewhat the structure and extent of the these jets.

The image above (click to enlarge) was originally from this paper. It demonstrates schematically some different theories explaining the relative dimness of the gamma ray burst event and the structure of the jets along the axis of rotation. Earlier theories postulated a relatively uniform jet, as shown in the first scenario. If this is the case, our line of sight may have been outside the jet, but relativistic effects allowed us to see a smaller amount of the radiation. Other explanations postulate that the jet has some internal structure and "fades" with increasing angle from the axis (ii) or that the interaction of the jet with surrounding matter produces a secondary cocoon of radiation (iii). A final scenario is simply that this event was a few orders of magnitude dimmer than other known gamma ray bursts for some intrinsic reason, although the authors deem this unlikely.

Without the background information provided by the gravitational wave signal (the component masses of the merger, the timing of the merger, etc.), little of the above could be gleaned from the gamma ray signal. Nor would it be possible with only one of the two to conduct the precision tests of fundamental physics described earlier. These are examples of the power of multi-messenger astronomy. Having both an eye and an ear to the cosmos will continue to yield fundamental insights into the nature of our universe.

Sources: https://journals.aps.org/prl/pdf/10.1103/PhysRevLett.119.161101, https://arxiv.org/pdf/1710.05834.pdf, http://iopscience.iop.org/article/10.3847/2041-8213/aa91c9/pdf

GW170817 and Multi-messenger Astronomy

The first astronomers had only their own eyes as tools, and visible light was their only source of information. Recent instruments have broadened our sight to include all types of electromagnetic radiation, from radio waves to X-rays and gamma rays. Each part of the spectrum is suited to different types of observations and gave us incredible new insight into the cosmos. However, the second decade of the 21st century saw the advent of a fundamentally new kind of astronomy: the detection of gravitational waves.

Gravitational waves, as discussed in a previous post, are the "ripples" in spacetime that propagate in response to the acceleration of massive objects (stars, black holes, and the like). All objects with mass produce these waves, but the vast majority are far too small to detect. It was only with the advent of extremely sensitive instruments that the first detection of gravitational waves was made by LIGO (the Laser Interferometer Gravitational-Wave Observatory) in 2015. This detection, and its immediate successors, were of binary black hole merger events, in which two black holes orbiting one another spiraled inwards and finally combined into a single, larger black hole. The last moments before merging brought exceptionally colossal objects (weighing perhaps dozens of solar masses) to great accelerations, the perfect recipe for producing strong gravitational waves detectible across the cosmos. However, these cataclysmic events were quite dark: little electromagnetic radiation was emitted, and no "visual" evidence for these events accompanied the wave signal. Something quite different occurred in 2017.

On August 17, 2017 at 12:41 UTC, the LIGO detectors at Hanford, Washington and Livingston, Louisiana and the Virgo gravitational wave detector in Italy simultaneously measured an event as shown above (click to enlarge). The two LIGO frequency-time diagrams clearly show a curve that increases in frequency before disappearing at time 0. This corresponds to two inspiraling objects orbiting one another faster and faster before merging finally occurs and the signal stops. In the Virgo diagram, the same line is not very visible, but further analysis of the data nevertheless expose the same signal from the noise. The gravitational wave event, designated GW170817, was genuine.

Having three detectors at different points on the Earth measure the event allowed a better triangulation of the location of the source than had occurred previously (when LIGO and Virgo were not simultaneously active).

The above figure shows a visualization of the celestial sphere (representing all possible directions in the sky from which the signal could have come) and locations from which the signal data suggest the signal originated. The green zone is the highest probability region taking all three instruments into account. This area is still 31 square degrees, quite large by astronomical standards. Fortunately, corroboration of the event came immediately from an entirely separate source.

The above figure (click to enlarge) shows at the bottom the same gravitational wave signal from before. The rest of the data come from the Fermi Gamma-ray Space Telescope and the International Gamma Ray Astrophysics Laboratory, both satellites in Earth orbit. As their names suggest, they search the cosmos for astrophysical sources of high-energy gamma rays. In particular, they monitor the cosmos for gamma-ray bursts (GRBs), especially intense flashes of radiation that typically accompany only the most explosive events, such as supernovae. As the figure shows, less than two seconds after the gravitational wave signal stopped (indicated the merger of two orbiting objects), there was an elevated count of gamma rays in each detector across the different photon energy levels. The source of this burst is indicated by a reticle in the celestial sphere figure above, lying right within the estimated location of the merger! It appeared that this merger had an electromagnetic counterpart! Further, analysis of the gravitational waves indicated that the masses of the two objects were around 1.36-2.26 and 0.86-1.36 solar masses (these were the uncertainty ranges), respectively, not heavy enough for black holes. What was going on?

The conclusion drawn from these events was that the merger was not of black holes, but of neutron stars, compact remnants of large stars that were yet not massive enough to collapse into black holes. An artist's conception of a binary neutron star black hole merger is shown above. Following the initial identification of the event, countless telescopes around the world trained on the event the very same day after a notice was released around 13:00 UTC, hoping to observe more following the merger.

And they were not disappointed. Less than a day after the initial gamma ray burst had faded, the source began to appear at other frequencies, and remained bright for several weeks before fading. The above figure shows the Hubble image of the merger's host galaxy, NGC 4993. This galaxy is at a distance of roughly 130 million light-years, and even at this distance, the collision of the neutron stars was clearly visible against the billions of other stars. Finally, the chart below demonstrates just how well documented the event was:

Many different instruments took images in X-rays as well as ultraviolet, visible, infrared, and radio waves. The horizontal axis indicates the rough timeline of events (on a logarithmic scale) in each part of the electromagnetic spectrum, stretching from less than a day to several weeks after the merger. Several representative images of NGC 4993 and the source within are shown at bottom.

Without extensive collaboration within the astronomical community, collecting this wealth of data on this binary neutron star merger would not have been possible. This marked the first time in history that a single event was measured in both gravitational waves and electromagnetic waves, not to mention how thoroughly the merger was photographed across the spectrum. This coordinated observation is known as multi-messenger astronomy, and may have profound implications on our future understanding of the universe. Some of what we learned from the binary neutron star merger is discussed in the next post.

Note: Most of the figures above are taken from the open access papers detailing the discovery and analysis of the binary neutron star merger. For further reading on the event, links to these papers may be found in the sources below.

Sources: https://journals.aps.org/prl/pdf/10.1103/PhysRevLett.119.161101, https://arxiv.org/pdf/1710.05834.pdf, http://iopscience.iop.org/article/10.3847/2041-8213/aa91c9/pdf

More Evidence for Planet Nine

For the first post in this series, which explains the motivation for the Planet Nine hypothesis, click here.

The previous post touched on some ways in which the orbits of certain outer Solar System objects are similar. These may be quickly summarized in the following way: both the arguments and longitudes of the objects' perihelia are unusually clustered around certain values.

The above image shows numerous relevant parameters concerning the position of an orbit. In the case of orbits in the Solar System, the plane of reference is the plane of the Earth's orbit and the Sun, also known as the ecliptic. The reference direction often used for heliocentric objects is called the First Point of Aries, defined as the position of Earth's vernal equinox and so named for its location within the constellation Aries. The ones with which we are concerned here are the argument of periapsis ω (this is the general name for argument of perihelion to include non-heliocentric objects) and the longitude of the ascending node Ω. The sum of these two angles is called the longitude of perihelion because it measures the angle between the perihelion and the reference direction. In summary, the similarity in the arguments of perihelion indicates that the members of the relevant population of objects have similar orientations with respect to the plane of the Solar System, while the similarity in the longitudes indicates a clustering of these orbits in space.

A 2016 paper by Konstantin Batygin and Michael E. Brown ran a statistical analysis of these parameters for the six most extreme known trans-Neptunian (beyond Neptune) objects. Since they were discovered by a number of distinct observational surveys, the possibility of observational bias was dismissed. The analysis found that the clustering of the objects had only a 0.007% probability of occurring by chance. This suggested that another explanation was in fact required for the phenomenon. Further simulations suggested that a Planet Nine could account for the observations, provided that it have the required heft: at least around 10 Earth masses (or, equivalently, 5000 Pluto masses). In comparison, all the previously known trans-Neptunian objects put together weighed much less than a single Earth mass.

Shortly afterward, more evidence for Planet Nine was discovered, using data from a surprising source: the Cassini space probe. Launched in 1997, this Saturn orbiter allowed the calculation of the position of Saturn over time to unprecedented precision. These were compared to an extremely precise gravitational model of the Solar System known as INPOP, which accounts for the gravitational influence of the Sun, the planets, and many asteroids. The model then outputs planetary ephemerides, namely positions of the planets at given times. A paper published in February 2016 by Agnès Fienga et al. experimented with adding a Planet Nine at different positions to the INPOP. If the residuals (differences in Saturn's position between the predictions of INPOP and the real measurements from Cassini) are increased, this rules out the existence of Planet Nine in this position. However, if they are decreased, then this is evidence in support of Planet Nine, since it would partially explain the observed discrepancy.

The results of the paper are summarized in the diagram above. They showed that Planet Nine of 10 Earth masses and a semi-major axis of 700 AU was ruled out by Cassini's data to be in the red zones (this increased the residuals). The pink zones correspond to areas that would be ruled out by further inclusion of Cassini's data (the paper only used the measurements through 2014). The green zone, however, is where a Planet Nine would decrease residuals, making the INPOP model a more accurate picture of the Solar System. Therefore, the paper found this to be the most likely zone to find Planet Nine (with the single most likely position indicated). The addition of a Planet Nine in the farther regions of its orbit would not produce significant perturbations, and thus this is labeled "uncertainty zone".

Further analysis fine-tuned the estimates of mass, eccentricity, semi-major axis, and other parameters for the supposed Planet Nine. With an array of increasingly large telescopes at their disposal, astronomers will soon be able to settle the Planet Nine hypothesis one way or the other, bringing new insight into the current structure and the formation of our Solar System.

Sources: https://arxiv.org/pdf/1601.05438v1.pdf, https://en.wikipedia.org/wiki/Argument_of_periapsis, http://arxiv.org/pdf/1602.06116v3.pdf, http://arxiv.org/pdf/1603.05712.pdf

The Planet Nine Hypothesis

Beginning in the 1990s, advances in astronomy allowed the detection of many extrasolar planets, adding thousands of the number known within two decades. However, apart from the reclassification of Pluto as a dwarf planet in 2006, the population of true planets in our Solar System did not change. Many, many other smaller objects were discovered, though.

Many of these smaller objects lay within the asteroid belt between Mars and Jupiter, or in the Kuiper Belt, just beyond Neptune's orbit. Eris, Haumea, and Makemake are other dwarf planets whose perihelia (closest approaches to the Sun) bring them within the Kuiper Belt, 30 to 50 astronomical units (AU) from the Sun. However, an unusual object was discovered in 2003 whose orbital properties were quite different.

The object was later named Sedna and measures a little less than half the diameter of Pluto. Though the best images of it by telescopes are only a few pixels wide, it is clearly of a reddish color, nearly as red as Mars. The perihelion of this object was, at the time, the largest known in the Solar System, at 76 AU. However, it also has an extremely elongated orbit, bringing it to an aphelion (farthest point) of 936 AU! This orbit is shown in red above, compared to the orbits of the outer planets and Pluto (in pink). About a decade later, another object, provisionally designated 2012 VP113, was discovered with comparable orbital parameters, except with a slightly farther perihelion of 80 AU and an aphelion of 438 AU. The scarcity of known objects of this type is not only a consequence of their distance, however.

This scatterplot, published in a paper by astronomers Chadwick A. Trujillo and Scott S. Shephard, shows the perihelia and eccentricities (a measure of the "elongatedness" of an elliptical orbit; a perfect circle has an eccentricity of 0) of various objects outside Neptune's orbit. Curiously, there is a clear drop-off at around 50 AU, with only a few known objects beyond. Notably, there is also a gap between 55 and 75 AU. This gap is not only an artifact of our telescopes being insufficiently powerful: Sedna and 2012 VP113 were detected farther out, so if there were objects in this gap they should have been easier to find. The high eccentricity of Sedna and 2012 VP113, as well as the existence of this gap, aroused suspicion that a massive object may have gravitationally perturbed the trajectories of objects in this region, illustrated in the image below.

The same paper indicated another unusual feature of the population of these farthest known objects.

The horizontal direction indicates the semi-major axis of each object (yet another measure of the size of an orbit; however, it is closely related to the two discussed previously: it is simply the average of the perihelion and the aphelion). The vertical variable on the scatterplot is the argument of perihelion, which is simply the angular position around the orbit of the orbit's perihelion (relative to where it crosses the plane of the Solar System). All known objects whose semi-major axes exceed 150 AU have arguments of perihelion all clustered roughly around 0°. In the eight-planet Solar System model, this should not be the case: gravitational perturbations from the gas giants would randomize the arguments of perihelion over millions of years. However, a large planetary body orbiting well beyond the known planets could constrain the arguments of perihelion. This led to the hypothesis of a new planet, nicknamed Planet Nine.

The above image shows the orbits of many of the same objects represented by dots to the right of the black line in the scatterplot. Note how in addition to the clustering trend noted above, the perihelia are also all on the same side of the Sun. The figure also shows where Planet Nine would possibly orbit given the positioning of those objects. The story of the Planet Nine hypothesis continues in the next post.

Sources: http://home.dtm.ciw.edu/users/sheppard/pub/TrujilloSheppard2014.pdf, http://www.aoi.com.au/bcw1/Cosmic/Sedna-PIA05569-sml.jpg

Solar Sails

Solar sailing is a method of propulsion in space that utilizes solar radiation to accelerate a spacecraft, reducing the amount of fuel required for interplanetary missions.

The key to solar sailing is that light, though it has no mass, does have momentum! At first, this seems contradictory; the typical (Newtonian) definition of momentum that one first learns is that momentum equals mass times velocity, or p = mv (p denotes momentum). The mass m is simply a number indicating the quantity of matter in a given object, while p and v are vector quantities, having both magnitude and direction.

However, this definition of momentum is only approximate. Einstein's theory of special relativity holds that momentum, energy, and mass are all different aspects of a single quantity. The famous mass-energy equivalence E = mc² (c is the speed of light) captures part of this relation. However, this equation is actually a special form of a more general expression for energy:

where p is momentum and m₀ is the rest mass of an object (objects which are moving have additional mass and therefore additional energy by the mass energy relation). Photons, the particles of light, travel at the speed of light and are in fact never at rest. However, since objects with a nonzero rest mass can never reach the speed of light, it makes sense to classify photons as massless. Since m₀ = 0, the equation reduces to E = cp, or p = E/c. Furthermore, light has energy, so it must have momentum. Different frequencies of light have different energies so photons of greater frequencies (such as X-ray or gamma ray photons) have correspondingly greater momentum.

Considering ordinary molecules for a moment, the macroscopic phenomenon of pressure (for example air pressure) emerges from individual collisions of particles with a surface such as the surface of a balloon. The average force that air molecules colliding with a surface exert is the pressure on that surface. Moreover, each of these collisions involves a transfer of momentum: a particle bouncing from a surface reverses the direction of its momentum vector so by the conservation of momentum the deflecting object also experiences a change in momentum. A similar momentum transfer occurs when light impacts a surface, creating what it known as radiation pressure.

The reason we do not feel radiation pressure whenever we enter sunlight is simply because this pressure is minute relative to the other forces we feel, dwarfed even by the force of a single tissue resting on a surface. The atmospheric pressure at sea level, around 100 pascals (Pa), is over ten billion times greater than the radiation pressure on a perfectly reflecting surface in direct sunlight on Earth (around 10 μPa = 10^-5 Pa). Note that this phenomenon is distinct from what is called the solar wind, a term which refers to the stream of particles with mass constantly emanating from the Sun. These particles also exert a pressure when they collide with objects in space, but it is over a thousand times smaller than even the minute radiation pressure. Despite the apparent insignificance of radiation pressure, as in the case of ion propulsion, even small forces add to significant acceleration in space over time.

The concept of using radiation pressure as a means of propulsion is the foundation of the solar sail. Its design is simple: a large sheet of lightweight, reflective material surrounds the spacecraft payload (as in the artist's conception above). Notably, it is desirable for the sail material to reflect rather than absorb photons because this increases the acceleration of the sail.

The concept of a solar sail dates back to shortly after Maxwell's theory of electromagnetism was established in the 1860's in the works of Jules Verne. However, its first applications in spaceflight occurred almost 150 years later. Radiation pressure was used to save fuel in minor maneuvers on the MESSENGER mission and to compensate for a loss of maneuverability in the Kepler space telescope. However, the first true solar sail was IKAROS (Interplanetary Kite-craft Accelerated by Radiation of the Sun), a spacecraft launched by the Japanese Aerospace Exploration Agency (JAXA) in 2010 to demonstrate the technology.

IKAROS's solar sail measured 20 meters across the diagonal with a reflective film only 0.0075 mm thick that incorporated 0.025 mm thick solar cells to power the telemetry and steering instruments. The orange panels around the edges of the sail steered the craft by altering their reflectance with liquid crystal reflectors. For example, if one side of the sail were made more reflective then the opposite sides, the radiation forces would differ across the sail, causing it to rotate.

Launched on May 21, 2010, the IKAROS payload weighed only 310 kg and its cylindrical body measured on 1.6 meters in diameter and 0.8 meters in height. After reaching space, it followed the above procedure to release the sail (click to enlarge). By taking advantage of the centrifugal forces on four "tip masses" at each corner of the sail, the continually rotating apparatus can expand to full diameter and remain there without any rigid structure supporting the sail. The mission was a full success, demonstrating telemetry, propulsion, navigation, and attitude control for a solar sail.

Over the following years, NASA and the Planetary Society launched their own solar sails into Earth orbit for further testing demonstration of the technology, but IKAROS remained more significant as the first interplanetary solar sail. Once in space, craft employing solar sails do not have to carry any additional fuel, greatly reducing the amount of weight necessary for interplanetary missions. These sails may soon realize their potential as an inexpensive and efficient means of exploring the Solar System.

Sources: http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/relmom.html, http://kaffee.50webs.com/Science/images/KTG.origin.of.pressure.gif, http://blazelabs.com/pics/reflabstrans.gif, http://global.jaxa.jp/activity/pr/brochure/files/sat28.pdf

Applications of Ion Propulsion

This is the second part of a two-part post. The first post, describing the function of ion propulsion engines, may be found here.

Ion thrusters have many advantages over other forms of propulsion. In comparison with traditional chemical propellent, they are roughly 10 times more efficient, lightening the load of space-traveling craft and saving massive amounts of fuel for launch. This efficiency originates in part from the higher exhaust velocity of the xenon propellant particles, which are ejected from the spacecraft at speeds of 20-50 km/s! In addition, the electric power required to run ion engines is relatively small, on the order of a few kilowatts. In comparison, a typical microwave oven consumes 1.1 kW, and the power consumption is significantly less than that of a typical automobile. Solar panels can meet this power demand during flight, allowing ion thrusters to create smooth and continuous acceleration over the entire duration of a mission.

However, this efficiency comes at a price: ion propulsion produces very small thrusts. The first model of ion engine actually used in spaceflight, the NSTAR engine, produced a thrust of around 90 millinewtons. This is the same force that your hand would experience from a single piece of paper on Earth by gravity, a barely detectable force! However, this minute force can operate continuously, adding up to a significant acceleration over time in the frictionless environment of space. In comparison, space probes which operate on chemical propellant may exert thrusts in the hundreds or thousands of newtons (the equivalent of a couple hundred pounds at Earth's surface), but only for very short times.

The small thrust of ion engines pales even more in comparison to that of rockets that launch payloads from Earth's surface. To escape Earth's gravity, such rockets must exert a force greater than the force of gravity on the often huge rockets. For example, the Saturn V rocket (shown above) that launched humans to the Moon generated an astounding 34,500,000 newtons of thrust at launch. For this reason, ion engines cannot be used to launch spacecraft.

The idea of electric rock propulsion dates to the 1930's and the first test of ion engines in space came during the 1960's. However, no operational mission utilized ion thrusters until NASA's Deep Space 1 probe, launched in 1998. This spacecraft performed a flyby of the asteroid 9989 Braille and the comet 19P/Borrelly. To meet the acceleration requirements of the mission extension to comet Borrelly, Deep Space 1 changed its velocity by 4.3 km/s using less than 74 kilograms of xenon. The Hayabusa probe, launched by the Japan Aerospace Exploration Agency (JAXA) in 2003, was another important demonstration of ion thruster technology. This probe used ion thrusters on its mission to land on the near-Earth asteroid 25143 Itokawa, collect samples, and return them to Earth for analysis. In 2010, the probe successfully returned the sample to Earth, completing the first ever asteroid sample return mission. Hayabusa 2, another asteroid sample return mission, launched in 2014 with similar objectives.

An even greater demonstration of ion propulsion technology began in 2007 with the launch of the Dawn spacecraft. This spacecraft carried three ion engines, operating alternately throughout the mission. Thrusting frequently throughout its eight-year journey, Dawn followed a spiral outward from the Earth, past Mars, into orbit of the asteroid Vesta, and subsequently into orbit of the asteroid Ceres.

The above image shows Dawn's outward spiral as well as the intervals during which one of its ion engines was in operation. With the exception of the gravitational assist at Mars, Dawn thrusted almost continuously, moving outward under its own power. Its total velocity change exceeded 10 km/s, the greatest yet for a spacecraft under its own power. When it successfully entered orbit around Ceres in April 2015, Dawn became the first spacecraft to orbit two different extraterrestrial targets. This feat would not have been possible using traditional methods of chemical propulsion.

Meanwhile, advances continued in ion thruster technology. NASA's Evolutionary Xenon Thruster (NEXT) performed a 48000 hour test in a vacuum chamber lasting from 2004 to 2009 to demonstrate its successful operation. Using power at a higher rate but also providing somewhat greater thrust, the NEXT engine (shown above) is at least 30% more efficient than its predecessors and can operate for a longer time. Continued development of ion propulsion technology promises to provide the foundation necessary for more ambitious interplanetary space missions.

Sources: http://www.extremetech.com/extreme/144296-nasas-next-ion-drive-breaks-world-record-will-eventually-power-interplanetary-missions, http://www.nasa.gov/centers/glenn/about/fs08grc.html, https://www.nasa.gov/audience/foreducators/rocketry/home/what-was-the-saturn-v-58.html#.VV8XomCprzI, http://darts.isas.jaxa.jp/planet/project/hayabusa/index.htmlhttp://science.nasa.gov/science-news/science-at-nasa/1999/prop06apr99_2/, http://alfven.princeton.edu/papers/sciam2009.pdf, http://dawn.jpl.nasa.gov/mission/

Introduction to Ion Propulsion

In physics, ion propulsion is a type of electric propulsion used by spacecraft. As with any traditional method of rocket propulsion, ion propulsion depends on Newton's Third Law: for every action, there is an equal and opposite reaction.

A typical rocket engine uses internal mechanisms to accelerate some type of exhaust away from the rocket. Since this constitutes a force on the exhaust, the engine experiences a force in the opposite direction. Crucially, propulsion requires that mass be lost from the rocket to exhaust. Other vehicles, such as cars, use friction between wheels and road to provide a force and therefore do not need to expel mass. Operating in space or the atmosphere in which friction is minimal (there is nothing to "push off" of), rockets instead carry extra mass to accelerate. As the name suggests, ion propulsion works by accelerating ions.

The above schematic illustrates the function of a gridded electrostatic ion thruster (which is usually what is meant by "ion propulsion"). On the left side, neutral atoms of the propellant move from storage tanks (not shown) into the ionization chamber. Simultaneously, an electrode fires electrons into the chamber with high velocity. These electrons knock other electrons out of the neutral propellant atoms to create ions. As a result, the ionization chamber becomes filled with electrons and positive ions.

At the other end of the chamber are two grids. They are connected to a voltage source that maintains a static positive charge on the inner grid and an equal and opposite negative charge on the outer one. Two effects combine to remove many of the free electrons from the ionization chamber. First, the positively charged plate attracts electrons, conducting them out of the chamber. Second, the contents of the chamber are very hot. Since electrons are much lighter than the positive ions, they move faster with the same amount of thermal energy and have a greater chance of collecting on the grid. Soon, positively ionized gas (plasma) builds up in the chamber.

This closeup on a gap in the positive grid shows how positive ions eventually escape the chamber. Eventually, so many ions accumulate in the plasma layer that the repulsive force between ions exceeds the force pushing this ions away from the positive grid. Ions then pass through gaps in the grid. Once they reach the other side, the repulsive forces from both the grid and the other plasma accelerate them outward. Returning to the larger diagram, the negative grid focuses the beam of ions so that they all proceed in roughly the same direction. Finally, another electrode fires electrons at the escaping ions, preventing them from losing velocity due to the influence of the negative grid and preventing a buildup of net charge in the engine.

Typically, the type of propellant used for ion propulsion is xenon gas. The use of xenon, which is element 54 on the periodic table, has several advantages. First, it is a noble gas so it is inert and does not react chemically with other parts of the engine. Further, it is the heaviest (non-radioactive) noble gas, so the thermal effect removing electrons from the gaseous plasma is enhanced.

NASA tested the ion thruster shown above in the early 1990's. The blue glow originates from charged xenon particles.

The next post describes the applications of the ion thruster and its impact on space travel.

Sources: http://www.space.com/22735-new-nasa-ion-thruster-to-propel-spacecraft-to-90-000-mph-video.html, http://ccar.colorado.edu/asen5050/projects/projects_2008/nowakowski_sep/sep_files/image006.jpg, http://www.researchgate.net/publication/259367890_On_the_microscopic_mechanism_of_ion-extraction_of_a_gridded_ion_propulsion_thruster, http://www.extremetech.com/wp-content/uploads/2012/12/1000px-Electrostatic_ion_thruster-en.svg_.png, http://www.nature.com/scientificamerican/journal/v300/n2/box/scientificamerican0209-58_BX2.html

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.

Sources: http://en.wikipedia.org/wiki/Saros_(astronomy), http://www.cropcircleconnector.com/inter2012/italy/bracciano-earthquake7.jpg, http://www.math.nus.edu.sg/aslaksen/gem-projects/hm/0304-1-08-eclipse/Path%20of%20Totality.htm, http://eclipse.gsfc.nasa.gov/SEsaros/SEperiodicity.html#section106

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.

Sources: http://www.hermit.org/eclipse/Graphics/diagrams/Rotations3.png, http://en.wikipedia.org/wiki/Saros_(astronomy), http://www.hermit.org/eclipse/Graphics/diagrams/Draconic.png, http://www.metahistory.org/images/moonorbit.gif, http://www.astro.virginia.edu/class/whittle/astr1230/im/moon_sidereal.gif

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.

Sources: http://eclipse.gsfc.nasa.gov/eclipse.html, http://image.gsfc.nasa.gov/poetry/ask/a11846.html, http://kids.britannica.com/elementary/art-87433/During-a-solar-eclipse-the-Moon-passes-between-the-sun, http://indiancountrytodaymedianetwork.com/sites/default/files/uploads/2012/11/solar-eclipse.jpg, http://www.topnews.in/files/SolarEclipse.jpg, http://upload.wikimedia.org/wikipedia/commons/thumb/3/37/Annular_Eclipse._Taken_from_Middlegate,_Nevada_on_May_20,_2012.jpg/320px-Annular_Eclipse._Taken_from_Middlegate,_Nevada_on_May_20,_2012.jpg, http://en.wikipedia.org/wiki/Saros_(astronomy),