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Roger's Equations

This blog is all about science and technology (with occasional math thrown in for fun). The goal of this blog is to try and pass on the sense of excitement and wonder I feel when I read about these topics. I hope you enjoy the posts.

Moore's Not Enough: The Future of Computing by Roger Pink

Posted October 15, 2014 9:04 AM by Roger Pink

Moore's Law

Gordon E. Moore, in his 1965 paper entitled "Cramming More Components onto Integrated Circuits" made the observation that the number of components (such as transistors) in an integrated circuit doubles every two years. At the time Moore wrote his paper, integrated circuits had around 50 transistors per chip.

By 1972, the Intel 8008 had 3,500 transistors. The semiconductor industry had adopted "Moore's Law" as an industry standard and reinvested profits into research and development to meet the schedule, thus the law became a self fulfilling prophecy. In 1982 Intel introduced the 80186 which had 55,000 transistors. 1993 saw the release of the Pentium chip with its 3,100,000 transistors. By 2008 AMD had reached 758 million transistors in the K10 Quad-Core. This year Intel released the 62-core Xeon Phi with 5 billion transistors. Next year Oracle will release the 32-core Sparc M7, a chip with 10 billion transistors. Moore's law is alive and well....for now.

But there are clouds on the horizon. There is a fundamental limit on the number of transistors you can fit on a chip. The semiconductor industry is already using a 20 nm process to make these chips and are quickly approaching the atomic scale. by 2020 the industry is expected to be using a 5 nm process. As the industry edges closer and closer to that fundamental atomic limit, it is becoming increasingly difficult to maintain the hectic pace set by Moore in 1965.

That's not to say that improvements to chips can't be made, but the costs are becoming greater and greater. Today's desktop processing power dwarfs anything that existed 20 years ago, yet counter-intuitively we are increasingly confronted by computing problems that conventional computers couldn't hope to solve.

Different, Not Moore

More than 30 years ago, a group of physicists and computer scientists held a conference on the Physics of Computation at MIT. Among the points to come out of the meeting was that there were many problems in science that could not be calculated by classical computers in an efficient way. The broad outline of a computer based upon quantum mechanics was proposed.

In the decades since there has been a lot of research in the field. How would a quantum computer work? What would it physically consist of? What kind of problems could it solve? For years quantum computers were more science fiction than reality, with tantalizing promises of computing efficiency as demonstrated in the graph below.

Several weeks back Google announced that it had hired Dr. Martinis from the UC Santa Barbara to work on quantum computing. I detail the story in an article I wrote:

Google Leaps Into Quantum Computing

As the technology of computing has evolved, the limitations of "classical" computers have grown more apparent. Many problems are so unwieldy they would take several times the age of the universe to solve. It's becoming increasingly clear that more processing isn't enough. Fundamentally different approaches to computing also are needed.

For the past few decades, several types of computing have been proposed and investigated including DNA computing, chaos computing and, perhaps the closest to becoming reality, quantum computing. Last year Google, in a joint initiative with Universities Space Research Association and NASA, announced the creation of the Quantum Artificial Intelligence Lab (QuAIL). Its goal is to pioneer research into how quantum computing might help with difficult computer science problems.

Article Continues Here


Other Approaches

Quantum computers aren't the only alternative to classical computers. Mechanical computers existed in antiquity. DNA and other biomolecular computational methods have been proposed. Even Chaotic computers, which I personally find fascinating, have been suggested. There are all kinds of unconventional computer designs that may be better suited for certain problems.

It's not hard to imagine a not too far off future where a computer has multiple types of processors and software that chooses between them based upon the type of work being done. Need to factor a large number or have a program that uses machine learning? Use the Quantum Processor. Designing a new protein? Perhaps the DNA Processor is best. It's hard to say now what will be possible since unconventional computing is a nascent field. What is increasingly clear is that brute force computing isn't enough. If we want to continue to progress technologically as we have with the control and manipulation of information, we will need to develop new approaches.

1 comments; last comment on 10/16/2014
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Delicate Audacity: The Saturn V Rocket by Roger Pink

Posted September 25, 2014 5:40 PM by Roger Pink

"It was quite a monster to ride. It had a total of seven and a half million pounds of thrust, and the first stage burned four million pounds of propellant in two minutes. When you rode that monster up, you knew you had a real tiger by the tail. If felt like a train wreck when you staged off that first stage to the second stage; it was quite a machine to ride out!" -Astronaut John Young- In the Shadow of the Moon

Delicate Audacity

The Saturn V rocket was the most powerful rocket ever launched. It was used in the Apollo program in the 1960s and 1970s and also to launch the Skylab space station. It was the workhorse that made one small step and one giant leap possible. It redefined rocketry and changed the way a generation looked at space. It was a stunningly precise piece of powerful machinery that took every ounce of human ingenuity to exist. It was a milestone of rocketry.

The Saturn V was a 363 feet tall, 3 stage, 6.2 million pound monster. It generated 34.5 million newtons of thrust at launch. It could launch 260,000 lbs into Low Earth Orbit (LOE) and 100,000 lbs into Trans Lunar Injection (TLI).

Developed at NASA's Marshall Space Flight Center in Huntsville, Ala. The first Saturn V was launched without a crew. On November 9, 1967, the Apollo 4 mission to test the Saturn V rocket was a success. There would be many more successful missions over the next six years. The final Saturn V launched the space station Skylab into orbit on May 14, 1973. In all there were 13 Saturn V launches, 12 of which were successful and one (Apollo 6) that suffered a partial failure.

This Isn't Rocket Science

"It is difficult to say what is impossible, for the dream of yesterday is the hope of today and the reality of tomorrow" - Robert H. Goddard

Wernher von Braun was the man behind the team that designed the Saturn V rocket. The Saturn V rocket was based on von Braun's earlier Aggregate series of rockets developed in Germany in the 1930s and 40s. The Aggregate series of rockets had borrowed a great deal from American rocketry pioneer Robert H. Goddard (considered the father of rocketry). In 1963 von Braun, when speaking of the history of rocketry said of Goddard "His rockets...may have been rather crude by present day standards, but they blazed the trail and incorporated many features used in our most modern rockets and space vehicles".

Goddard never lived to hear those words, dying in 1945 only knowing that his rocketry dream, ignored in the U.S. for his entire life, had become a weapon in the hands of the Nazi's. In 1920, Goddard had suggested in a letter to the Smithsonian the idea of photographing the Moon and planets from rocket powered fly-by probes. This was picked up by the media at the time and universally panned. Goddard was ridiculed and mocked by the general public and the press. A New York Times editorial wrote, among other things "That Professor Goddard, with his "chair" in Clark College and the countenancing of the Smithsonian Institution, does not know the relation of action and reaction, and of the need to have something better than a vacuum against which to react-to say that would be absurd. Of course he only seems to lack the knowledge ladled out daily in high schools." Of course the New York Times and everyone else was wrong, thrust is indeed possible in a vacuum and this concept was well understood at the time in academic circles. Still, the unwarranted criticism forced Goddard to withdraw from public discussions of rocketry.

As a consequence, Goddard received very little public support for his research and development work. Germany became the leader in rocketry for the next two decades. A short 12 years after his death the U.S.S.R succeeded in launching the first artificial satellite into orbit. 12 years after that, a massive rocket incorporating many of Goddard's ideas would carry men to the moon. One can only imagine the pride Goddard would have felt, had he lived to see it.

Three Stages

The Saturn V was a three stage rocket. The first stage, the S-1C, was 138 feet tall and had a diameter of 33 feet. It provided 7,500,000 pounds-force (33,400 kN) of thrust using RP-1/LOX propellant. The stage had five Rocketdyne F-1 engines, the center one fixed and the surrounding 4 hydraulically gimballed to control the rocket. The burn time of the stage was 150 seconds. The S-1C was built by Boeing company and designed by the engineers at the Marshall Space Flight Center (MSFC).

The second stage, the S-II, was 82 feet high and 33 feet in diameter. It provided 1,000,000 pounds force (4,400 kN) of thrust using LH2/Lox propellant. The stage had five Rocketdyne J-2 engines in the same configuration as the S-1C stage. The burn time was 367 seconds. It was built by North American Aviation.

The third stage, the S-IVB was 58.4 ft in height and 21.7 ft in diameter. It provided 225,000 pounds force (1,001 kN) of thrust using LH2/LOX propellant. The stage had one Rocketdyne J-2 engine. The stage was capable of two burns, one for 165 seconds to establish LOE and a longer 335 second burn to obtain TLI. As each of the stages burned propellant they became less massive and the rocket's acceleration increased, thus the exponential curves for each stage on the chart.

A Reliable Rocket

The first Saturn V launched with a crew was Apollo 8. On this mission astronauts orbited the moon but didn't land. Apollo 9 tested the Apollo moon lander by flying it in Earth orbit without landing. Apollo 10 the lunar lander was tested in space. Apollo 11 was first mission to land astronauts on the moon. Apollo 12, 14, 15, 16, and 17 all successfully landed astronauts on the moon. Apollo 13 technical problems prevented a moon landing, but that problem wasn't related to the Saturn V.

In 1973 the last Saturn V was launched, without a crew, to launch the Skylab space station into Earth orbit.

The Skylab mission Saturn V had only two stages. The Apollo missions had three stages. The first stage lifted the rocket to an altitude of 42 miles. The second stage nearly into space. The third into Earth orbit and pushed toward the moon. First two stages fell into the ocean. Third stage either stayed in orbit or hit the moon.

The Saturn V was a multistage liquid-fueled launch vehicle. NASA launched 13 Saturn Vs from the Kennedy Space Center, Florida with no loss of crew or payload. It remains the tallest, heaviest, and most powerful rocket every brought to operational status and holds the record for the heaviest payload launched and heaviest payload capacity to Low Earth Orbit .

The Saturn V was designed under the direction of Wernher von Braun and Arthur Rudolph at the Marshal Space Flight Center in Huntsville, Alabama with Boeing, North American Aviation, Douglas Aircraft Company, and IBM as lead contractors. Von Braun's design was based in part on his work on the A-10, A-11, and A-12 in Germany during World War II.

Epilogue

Wernher von Braun was always quick to acknowledge his debt to Goddard. In 1926 Goddard successfully launched a liquid fueled rocket. In 1963, von Braun remarked "Goddard's experiments in liquid fuel saved us years of work and enabled us to perfect the V-2 years before it would have been possible." I'm certain Goddard wasn't thrilled by the fast completion of the V-2, but if he were alive today, he'd have more than the Saturn V to be proud of.

Last week, a private launch vehicle (rocket) company named SpaceX was named as one of two companies awarded by NASA to launch manned missions to the International Space Station. SpaceX, founded by Elon Musk, has stated its goal is to make man an interplanetary species and plans to construct rockets capable of traveling to Mars in the next decade. Only ten years ago such plans sounded like science fiction, but recent successes by SpaceX makes Mars a very achievable goal. It will mean a rocket on the scale of the the Saturn V. SpaceX has already utilized many design features from the Saturn V in their smaller rockets. Many of those features originated in Goddard's work almost 100 years ago. Goddard's innovations and vision continues to permeate modern rocketry; undeniable vindication for a man ahead of his time.


To read more about SpaceX and their rockets, please visit my editorial on IHS Engineering360:

SpaceX Innovates as It Aims for Mars


As always, thanks for reading. Look for more articles by me here on CR4 and also on IHS Engineering360. - Roger

16 comments; last comment on 09/30/2014
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Why LiFi? by Roger Pink

Posted May 08, 2014 12:00 AM by Roger Pink


The Coming Data Crunch

Everywhere you look nowadays, the world is becoming more mobile. Smart phones, phablets, tablets and laptops increasingly demand wireless bandwidth for applications, music, movies and other media. With the fast adoption of these devices in developing nations and the insatiable thirst for more bandwidth in mature markets, it is estimated that by 2017 more than 11 exabytes of data traffic will have to be transferred through mobile networks every month [1]. Considering that this estimate doesn't include the data traffic that will be generated by technologies that haven't become mainstream yet, but are likely to be increasingly adopted (streaming TVs, smart watches, smart appliances, etc.), it's not hard to anticipate a future wireless data capacity shortage.

An impending capacity calamity isn't the only issue facing today's wireless communications. There are also limits to its availability in hospitals, on aircraft, and wherever else radio frequency (RF) interference can cause problems. Wireless networks are also not very secure; RF can penetrate walls, which creates security risks. Wireless networks are also energy inefficient. There has been a movement toward microcells, picocells and femtocells that increase bandwidth in areas of high wireless data usage (train stations, airports, etc.) in a targeted way, but still, the amount of energy needed for wireless communications is growing very quickly and will ultimately be unsustainable.

LiFi to the Rescue!

Fortunately there is an emerging technology that is able to address the wireless data problems of capacity, availability, security and efficiency. The technology is called LiFi, short for "light fidelity," and it was on display at CES this year. A company called Oledcomm demonstrated a modified smartphone that used LiFi and was able to achieve wireless data rates of 1 Gbits/s.

LiFi devices are rare and the technology is still very much in the development stage. The concept of LiFi is simple enough. There already exists an extensive lighting infrastructure for illumination-from the light bulbs in your house, to the street lamps outside, to the personal lights you use to read on a plane or train. LiFi could take advantage of this existing infrastructure by modifying those illumination sources and turning them into LiFi transceivers. The idea is if you blink those light sources extremely fast, far faster than the human eye can detect, you could use that intensity modulation to transmit data.

For traditional sources of illumination, like incandescent lamps or fluorescent lamps, this wouldn't work. But LED light sources, quickly being adopted worldwide due to its energy efficiency and long life, can have their intensity modulated quickly and precisely enough to make LiFi a reality. Of course, the LED lamps commercially available today are not appropriate for LiFi. New lamps with embedded microchips and a photodetector (so it can receive data as well as transmit) will have to be created in order for what is being called visible light communication (VLC) to become reality.

LiFi and the Internet of Things

The development of visual light communication comes at an opportune time, as the internet of things is just starting to gain traction. The internet of things is a holistic term for the virtual representation of everyday objects, such as appliances, electronics, thermostats, vehicles and much more, on wireless networks. Connecting devices wirelessly to a network allows for remote operation, better tracking of usage and better inventory controls. A popular example of how this might be useful is receiving a notification from your refrigerator when you are out of milk, or being able to adjust your thermostat with your phone. This can only occur if your refrigerator or thermostat is connected to a network, and that's why LiFi is so well suited for the internet of things. LEDs and photodiodes are relatively cheap to manufacture and have a small form factor, so they are easily integrated into most household devices. Once integrated, the LED/photodiode is effectively a LiFi transceiver, communicating with the local LiFi hub.

Conclusions

If LiFi does become a reality, it certainly will solve some of the problems facing wireless data. For one thing, there is far more capacity available by using the visible light part of the spectrum rather than the radio wave part that is currently used by wireless networks. Already LiFi has demonstrated fast data rates with the potential for significant improvement. Since LiFi uses the visible spectrum, it won't interfere with electronic devices like WiFi would. This would mean no worries in hospitals and other WiFi-prohibited areas. Since walls are generally impenetrable to visible light security risks are reduced. Best of all, LEDs are efficient emitters, meaning that the integration of LiFi into micro, pico and femtocell networks will appreciably reduce the energy usage of wireless networks even as wireless data usage grows exponentially.

LiFi is many years away from becoming a reality. Standards are being developed and technologies improved. Still, the promise of LiFi combined with the incredible demand for more wireless bandwidth make this emerging technology a leading candidate for the future of wireless networks.

Resources

[1] Cisco Visual Networking Index, "Global Mobile Data Traffic Forecast Update, 2012-2017," White Paper, CISCO (Feb. 2013).]

2 comments; last comment on 05/09/2014
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New Dwarf Planet And Other Solar System News by Roger Pink

Posted March 26, 2014 3:00 PM by Roger Pink

New Dwarf Planet Discovered

Astronomers have increased the size of the observable solar system after spotting a 450-km wide object orbiting the sun. The lump of ice and rock circles the sun at a greater distance than any known object, and never gets closer than 12bn kilometers - 80 times the distance from Earth to the sun.

If its size is confirmed it could qualify as a dwarf planet in the same category as Pluto. Researchers said the discovery proves the existence of the inner Oort cloud, a region of icy bodies that lies far beyond the orbit of Neptune - which at 4.5bn kilometers from the sun is the most remote planet in the solar system. Until a proper name is decided upon, the body is known only as 2012 VP113. Its pink tinge comes from radiation damage that alters the make-up of frozen water, methane and carbon dioxide on the surface.

Though exciting in its own right, the discovery raises a more tantalizing prospect for many astronomers: that a "Super Earth" up to 10 times the mass of our planet orbits the sun at such a great distance that it has never been seen.

Three images of the newly discovered dwarf planet 2012 VP113 taken about two hours apart on 5 November 2012. Photograph: Scott S Sheppard/Carnegie Institution for Science

Astronomers found 2012 VP113 by taking snapshots of the night sky an hour or so apart with an instrument called the Dark Energy Camera on the US National Optical Astronomy Observatory telescope in Chile. When they turned the images into a time-lapse movie of the sky, they could see the new body moving against the background of stationary stars.

"This object has the most distant orbit known," Scott Sheppard at the Carnegie Institution of Washington told the Guardian. "It extends the known boundary of the observable solar system."

Article Continued Here




Astronomers Discover Asteroid With Rings

For the first time ever, astronomers have discovered a ring system surrounding an asteroid. The finding is a complete surprise to planetary scientists, who are yet unsure exactly how such rings could have formed.

The cosmic bling was found around an object named Chariklo, which orbits in a region between Saturn and Uranus. At 155 miles across, or about the length of Massachusetts, Chariklo is the largest known asteroid in its neighborhood. Looking to get a better idea of its exact size and shape, astronomers trained their telescopes on the giant space rock as it passed in front on a distant star in June 2013. As Chariklo performed its eclipse, researchers noticed something odd: The star's light flickered just a bit immediately before and after Chariklo's pass.

The reason for this darkening was the asteroid's two dense rings, which had briefly blocked the starlight. The thicker inner ring is about four miles wide, while the thinner outer ring is a little less than two miles. Spectroscopic analysis of the starlight also revealed that the rings are composed partially of water ice.

The ice rings reflect light like a mirror, a property that helps explain an earlier anomalous finding regarding Chariklo. After the asteroid was discovered in 1997, its brightness mysteriously dropped off and only came back again in 2008. What apparently happened was that, as Chariklo moved through its orbit, its ring system turned edge-on when viewed from Earth. As they turned back to face us with their flat side, they reflected light toward our planet and Chariklo's brightness grew by 40 percent.

There are only four other known ring systems in our solar system - around Jupiter, Uranus, Neptune and, most dramatically, Saturn - and all the other ones have formed around planets. Astronomers aren't yet sure if Chariklo's ring system makes it unique among asteroids. In recent decades, more than 10 other objects in its neighborhood have been searched using a technique similar to Chariklo's stellar eclipse but have not shown any rings.

Article Continued Here




Scale Model of the Solar System (Moon=1 Pixel)

http://joshworth.com/dev/pixelspace/pixelspace_solarsystem.html

Visit the website and scroll to get a sense of the vastness of our Solar System.

That's it for now. A pretty exciting day in Solar System News. Till next time - Roger




7 comments; last comment on 05/01/2014
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Oceans by Roger Pink

Posted March 20, 2014 9:04 AM by Roger Pink

The Great Unknown...Right Next To Us

Although oceans and other bodies of water cover 70% of the Earth's surface, we are only just now beginning to explore their depths in detail. I came across some neat topographical, sea floor age, depth, etc. maps of the oceans. Thought I'd share what I found. I've posted some below, but due to resolution constraints I have posted better images on my website, found here.


Ocean Facts!

The deepest part of the world's oceans is the Mariana Trench. The trench is about 1,580 miles long and about 43 miles wide. The maximum known depth of the trench is 6.8 miles at Challenger Deep. At the bottom of the trench, the pressure exceeds 1000 atmospheres. Remarkably, life has adapted and thrives in these extreme conditions at the bottom of the trench.

The deepest part of the Atlantic Ocean is Milwaukee Deep, part of the Puerto Rico Trench. It has a maximum depth of 5.2 miles.

The deepest part of the Indian Ocean is Diamantina Deep, part of the Diamantina Trench. It has a maximum depth of 5.0 miles.

The average depth of the Atlantic Ocean is 2.4 miles. The Pacific Ocean average depth is 2.7 miles. The Indian Ocean average depth is 2.4 miles. The average depth of the Arctic Ocean is 0.6 miles. The Arafura Sea north of Australia has an average depth of 250 ft (0.05 miles).

Ocean Depth and Age

Here is a map of ocean floor age

Here is a map of ocean depths

Ocean Currents

Here is a map of ocean currents

Conclusions

I hope you enjoyed the maps and got a chance to see the additional images and higher res images found on my website. I am very impressed with the work the NOAA has done and has made available online. Till next time -Roger

6 comments; last comment on 03/21/2014
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Vernal Equinox (Spring Is Here!)

Posted March 19, 2014 9:04 AM by Roger Pink

***Warning- The following blog entry contains a distinct Northern Hemisphere bias. If you are from the Southern Hemisphere...I'm sorry***

"O, wind, if winter comes, can spring be far behind?" - Percy Bysshe Shelley

It's been a long winter for most of us and there were times when it felt like spring may never come. With spring right around the corner, I thought I'd science it up a little with some interesting facts about the Vernal Equinox.

The Sun's Path Through the Sky

Over the course of a year, the Sun takes a slightly different path across the sky every day. Ancient astronomers noticed that these daily changes in the Sun's arc across the sky were periodic. The arc of the Sun moved higher and higher every day, producing longer and longer days, till a certain date. Then the arc of the Sun's path in the sky gradually moved lower and lower, the days shortening, till a certain date. Then the pattern repeated. The varying length of days due to this phenomenon clearly were responsible for the seasons and thus were of supreme importance for agrarian societies. As a result, the days when the Sun took its highest arc and lowest arc, as well as the days when the Sun's arc was halfway in between these extremes, were noted as important and named.

We know now that this peculiar periodic behavior of the Sun is a result of the Earth's axial tilt (23.4ยบ) as the Earth moves around the Sun. As the Earth orbits the Sun, the axial tilt points toward the Sun, perpendicular to the Sun, away from the Sun, and perpendicular to the Sun again. These orbital configurations correspond to the highest arc, halfway, lowest arc, and halfway respectively. Today we use the terms Summer Solstice, Autumnal Equinox, Winter Solstice, and Vernal Equinox to denote when these events take place.

The term Solstice comes from the Latin solstitium meaning "sun stands still", which makes sense since it corresponds to the dates when the arc of the Sun in the sky stops heading North (or South) and reverses course. As this reversal is happening, the Sun's arc seems to stay where it is for a couple of days (thus the name). The term Equinox comes from the Latin aequus (equal) and nox (night). Ver is the Latin word for spring and Autumnus is the Latin word for Autumn.This name makes sense as well, since the halfway point between the extremes of the Sun's arc correspond to days when the night and day are (nearly) equal in length for all latitudes.

Vernal Equinox

So here we are, approaching the Vernal Equinox (March 20th) after a brutal winter. The days have gotten longer and longer since the Winter Solstice on December 21st. You may be wondering why then the coldest days tend to be in January in the Northern Hemisphere when the shortest day is in December. We have the moderating effects of the oceans to thank for that. 70% of the Earth is covered in water and water is harder than dirt and rocks to heat up and cool down. The stored heat of the ocean delays the effects of the shorter days, thus the hysteresis.

So after the Vernal Equinox we will start having longer days then nights and temperatures will continue to rise. The snow will melt and the migrating birds will return. Plants will start budding, flowers blooming, and Spring will take hold in the North (I can only hope).

A Few More Details

As I described the solstices and equinoxes above, you might be forgiven for thinking that they were equally separated in time over the course of a year. So each season would be 365/4=91.25 days. Certainly from the orbital picture this appears to makes sense. However, here are the actually lengths of each season:

Winter: 88 days (Winter Solstice-December 21)
Spring: 92 days (Vernal Equinox-March 20)
Summer: 93 days (Summer Solstice-June 21)
Autumn: 89 days (Autumnal Equinox-September 21)

So what's going on? The reason some seasons are longer than others is because the Earth's orbit around the Sun is not perfectly circular, but rather slightly elliptical. A feature of elliptical orbits is the orbital speed will vary. In the Earth's case, at aphelion the Earth is orbiting the Sun more slowly than at perihelion. Since aphelion occurs during the Summer in the northern hemisphere, that season is stretched out by a couple of days (Thanks Kepler! (law two)).

It's also understandable if you are under the impression that the the Vernal Equinox always has fallen in March. That too is not true. In fact, around 4000 BC it fell sometime in June. This is due to something known as the precession of the equinoxes. Remember when I said that the four important points in the orbits corresponding to the equinoxes and solstices were when the Earth's axis was pointed towards, perpendicular to, away from, and perpendicular to the sun? Well the problem is that the direction the Earth's axis points changes over time. Thus the locations in the Earth's orbit (which corresponds to the month) when the axis is pointing towards, away, or is perpendicular are different as the direction the axis points changes. Think of it this way. If you've ever seen a spinning top, you know the handle that you use to spin will trace little circles as the top is spinning. The axis of the top is rotating (precessing). The Earth does the same thing, except it takes about 26,000 years for the Earth's axis to trace out one circle.

So 13,000 years ago we'd be approaching the Autumnal Equinox, not the Vernal Equinox. Every year the equinoxes and solstices shift roughly 10 minutes, so whereas this year the Vernal Equinox will occur March 20th at 4:57 pm, in 2018 it will occur on March 20th at 4:15 pm. You may have heard the term "Age of Aquarius". This term comes from the fact that as the Earth precesses, the constellation from which the Sun appears to rise on the Vernal Equinox changes. Since there are 12 zodiac constellations, and precession lasts about 26,000 years for one cycle, each sign is said to represent a 2150 year long "age".

Conclusions

So there you have it. The Vernal Equinox will come and go and Spring officially will begin! I know there are articles about the Equinoxes everywhere this time of year. I hope I provided a some extra tidbits to make this one worth reading.

Also, my Alma mater, UAlbany Great Danes, will get destroyed by play the Florida Gators tomorrow in the first round of the NCAA Basketball Tournament, so I just wanted to say "Go Purple!".

3 comments; last comment on 03/20/2014
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