Of Parallax and Paradox

  And the evening and the morning were the third day.

14  And God said, Let there be lights in the firmament of the heaven to divide the day from the night; and let them be for signs, and for seasons, and for days, and years;

15  And let them be for lights in the firmament of the heaven to give light upon the earth; it was so.

16  And God made two great lights; the greater light to rule the day and the lesser light to rule the night; he made the stars also.

17  And God set them in the firmament of the heaven to give light upon the earth,

18  And to rule over the day and over the night, and to divide the light from the darkness; and God saw that it was good.

19  And the evening and the morning were the fourth day.

Genesis, Chapter 1, verses 13-19

Last week, in part two of the current series, I told the story of how astronomer Ole Roemer first discovered that light does not move from one place to another instantaneously, and how he made his initial calculation of the actual speed that light travels.  In retrospect, I should perhaps have given more emphasis to the many additional experiments that have been conducted to measure the speed of light in the centuries since Roemer did it.  These measurements, involving ever-more accurate devices and improved experimental techniques, are the reason that we have such an exact value (299,792.458 kilometers per second) today.  Some discussion of these experiments would have established, beyond a shadow of a doubt, that 299,792.458 kilometers per second is not a “hypothesis” or a “theory” about the behavior of light that is subject to debate, or could be overturned in some future experiment.   299,792. 458 kilometers per second is a concrete fact, as real as the hand in front of your face.

The importance of the fact that light’s speed (physicists call it “c”) is a far cry from infinite will become clear a little later on.  Right now, I want to begin a different topic with a simple question:  In all the times in your life that you’ve been outside at night, and looking up at the planets and the stars, have you ever wondered how, and when, people began to figure out how far away they are?  Determining their distances certainly wasn’t easy.  For the vast majority of the time that we humans have been around, we lacked the right perspective to even frame the question correctly.   That’s because, just like the Sun appears to rotate around the earth each day (an illusion which made it devilishly difficult to understand that it is really the Earth that is rotating), the night sky looks like a two dimensional surface, at a fixed distance from the Earth, with little lights plastered across its surface.  Imprisoned, constrained, and completely fooled by this compelling illusion, the ancients proposed all sorts of colorful beliefs about the night sky, all of which were premised on the assumption that the heavenly lights were all the same fixed distance away.  One of my personal favorites held that a black curtain surrounds the earth, and the stars are holes in the cloth through which the dazzling brilliance of heaven is shining through.

It was the Greeks who started to part the curtain by employing a straightforward mathematical tool called trigonometric parallax.  To get a quick and dirty feeling for the tool without the messy mathematical details, all you need to do is carry out the following simple exercise.   Position yourself directly in front of your television at a comfortable distance away.  Close your left eye.  Raise your index finger of your right hand straight up in the air.  Position your index finger directly in front of, and about six inches away from, your nose.  Make sure your finger is located directly in front of the middle of your television screen. 

Next, without moving your finger, open your left eye and close your right eye simultaneously.  You’ll see your finger “jump” quite a ways to the right, maybe even all the way off your TV screen (if your screen is small enough, and you are far enough away).  Now, repeat the exercise, but extend your arm all the way so that your right index finger is as far as it can possibly get from your nose.  You will still see your finger “jump” when you switch eyes, but the distance covered by the jump will be noticeably reduced, small enough that your finger probably stays well inside the boundary of the TV screen.

The change in the position of your finger with respect to the background TV is simply due to the fact that you are looking at your finger (and the more distant TV screen) from slightly different positions when you switch eyes.  The closer your finger is to your eyes, the greater the difference those two positions will make, and the more your finger will appear to jump against the screen.  This is where the mathematics comes in.  If you know the exact distance between your right eye and your left eye (the two viewing points), and you know exactly how far your finger appeared to move against the TV screen in the background, you can use simple high school trigonometry, invented by the Greeks, to calculate exactly how far your finger is from your eyes.

What’s the take-home message from our little example?  As long as you can observe a foreground object (like your finger) from two separate locations (like your left and right eyes), and you have background objects much further away from you than the foreground object, then by measuring the amount that the foreground object appears to shift against the background, when observed from the two locations, you can recover the crucial third dimension, and determine exactly how far away the foreground object is from you.

In the thousands of years since this “trigonometric parallax” method was discovered, it has been used routinely to solve all kinds of useful problems, like determining how far a ship is from the shore.  Military types used to need that information in order to figure out how to fire their cannons to hit enemy vessels.  Not to be outdone, both the ancient Greeks and the first generation of astronomers to have access to telescopes used trigonometric parallax to calculate of the distance to objects within our own solar system.  For example, at about the same time that Ole Roemer was making his first observations of Io, Jupiter’s moon, Italian astronomer Giovanni Cassini was making careful observations of where the planet Mars was located with respect to nearby background stars from his location in Paris.  Moreover, Cassini had a research assistant make the same measurements from Equatorial Guinea, several thousand kilometers away (see the figure below). Through trigonometric parallax, Cassini determined a distance to Mars that was only 7% off of the currently accepted value, which we get far more directly by bouncing radar signals off the planet and measuring how long they take to return.

Does trigonometric parallax even work as a tool to measure the distance to the stars? Certainly not by placing observers at a known distance from each other on the Earth’s surface, the way Cassini did for Mars.  The shift in the star’s location against a background of more distant stars would be far too tiny to measure.  Every six months, however, the Earth itself moves in its orbit from one side of the Sun to the other, covering about 186 million miles in the process.  Perhaps that was a displacement large enough for the trigonometric parallax method to work?  Starting around the beginning of the 18^th century, astronomers began to pick candidate stars and, with the help of telescopes, note their exact positions, relative to other stars in their vicinity on, say, Dec 21^st, and then again on June 21^st, six months later.  The method is illustrated in the figure below.  If one of the target stars was observed to move against the other stars in its vicinity, the movement had to be due to the fact that the foreground star was being observed from two different locations, like it was being observed from two eyes, except the two locations were separated by those 186 million miles!  If the size of the shift in position could be measured reliably, astronomers would have all the information needed to calculate the distance to the foreground object (the target star).

Simple, right?  Well, yeah, except that for the longest time, no matter what star they selected as the target, the poor astronomers couldn’t measure any shift.  Luckily for us all (all, that is, except those who cling to the literal truth of Genesis) failure was not an option, and by the early 19^th century, several astronomers were competing to be the first to measure stellar parallaxes and compute stellar distances.  Finally, in 1838, an anal German scientist (is there any other sort?) named Friedrich Bessel won the race, and reported a reliable parallax shift for 61 Cygni (a relatively unassuming star in the constellation Cygnus).  Bessel had had good reason to suspect that this particular star might be a relatively near neighbor to the Sun (how Bessel made that determination is interesting in its own right, but beyond the scope of this blog), and was therefore a good candidate to reveal a parallax.  That parallax was exceedingly tiny, though, so small that when Bessel computed the distance to 61 Cygni, it came out to a jaw-dropping 52 trillion miles.

Suddenly, everything clicked into place.  As more stars had their distances determined, it became clear that the trigonometric parallax method had failed for so long simply because the stars are so mind-numbingly distant, which means that the amount they appear to shift was exceedingly tiny.  Although other stars were discovered to be closer than 61 Cygni, none were found any closer than Alpha Centauri, at 26 trillion miles away.  

Time to connect some dots.  At a speed of almost 300,000 kilometers per second, how long does it take light to cross the space between the stars and reach our eyes and our telescopes?  In the case of even the closest star, Alpha Centauri, the answer is 4.2 years. In the case of 61 Cygni, the answer is closer to 10 light years.  For other familiar stars, like Vega, we’re talking more like 26 years.

According to the Genesis version of creation, these stars all popped into existence in the course of a single day, the fourth after creation, and were lighting up the night sky by the time the fourth day came to an end.  But if we take into account the speed of light, and the distance of these stars from the Earth, this is flatly impossible.  On the assumption that the stars were approximately the same distance from the Earth 6000 years ago as they were when Bessel and his colleagues first measured their parallaxes (and, to a first order of approximation, that is the case), then their light had just gotten started on its journey to Earth on the day they were created, and would not have reached the Earth for years.  At risk of belaboring this point, the night sky would have been completely bereft of stars for the first 4.2 years, and then one single, solidarity point of light, the star we now call Alpha Centauri, would have winked on.  It would have taken the entire lifetime of Adam and Eve, for instance, for all the familiar stars in our sky to gradually become visible.

All right, you’re saying.  God has a lot of tricks up His sleeve.  Maybe he got around the pesky little speed-of-light problem by pulling a fast one on us.  Maybe, when He created the stars that would be visible to Adam and Eve in the night sky, He initially placed them all well inside the confines of our own solar system, close enough that they would all be visible on the evening of the fourth day (after all, he had up to 24 hours of wiggle room, so he could put them as far as 16 billion miles out in space, way past the orbit of Pluto, and their light would still have reached the earth before His deadline).   Then, maybe God employed some rather adroit stellar dynamics to whisk these stars out of the solar system fast enough that they would reach their present gargantuan distances in time for Bessel and his colleagues to measure them, 6000 years later. 

Fair enough.  After all, God is omnipotent, so there is really nothing beyond his power to accomplish if He sets his mind to it.  But even this incredible kluge cannot save Genesis, because, embedded in the speed of light and the distances to celestial objects lurks a far more profound challenge to the story.   That challenge will be the subject of the next blog.  Until then, would anybody like to try and trump me and hazard a guess as to what it is?

Science and Religion at the Speed of Light

In the last blog, I promised to demolish the Genesis account of creation without referencing Darwin, evolution, or anything to do with Earth’s geology.  Instead, I’m going to build my case with ironclad facts from the fields of physics and astronomy, facts that have been established over the course of hundreds of years of painstaking inquiry into the nature of physical reality. 

Although no one knew it at the time, Genesis began to unravel the very first time somebody looked at the planet Jupiter through a telescope.  As most of you know, the person in question was Galileo, and the time was the beginning of the 17^th century.  To his great astonishment, Galileo observed four points of light surrounding the giant planet.  Observing them over time, he noted that the positions of the lights changed in ways that made it obvious that they were satellites, orbiting Jupiter in the same way that the planets orbit the Sun.

One of these lights, Jupiter’s moon Io, is so close to Jupiter that it completes a full orbit in only a couple of days, going behind Jupiter for a brief period each time (in astronomy-speak, Jupiter “occults” Io).  Later on in the 17th century, the prominent Danish astronomer Ole Roemer systematically recorded the timing of these occultations over an extended period stretching from 1671 to 1677.   Combining his observations with those of some of his contemporaries, Roemer discovered a remarkably systematic pattern: the time between occultations gets steadily shorter as the Earth’s own orbital motion brings us closer to Jupiter, and then lengthens again as the Earth moves farther away.  Reporting his results to the French Academy of Sciences, Roemer hypothesized that

This… appears to be due to light taking some time to reach us from the satellite; light seems to take about ten to eleven minutes [to cross] a distance equal to the half-diameter of the terrestrial orbit

Clever fellow that he was, Roemer combined this time difference with early estimates of the “half-diameter of the terrestrial orbit” (the distance from the Earth to the Sun, from which he could easily calculate the difference in distance between the Earth and Jupiter when they are closest together compared to when they are furthest apart) to compute the speed of light for the first time (prior to that point, many prominent scientists, Newton included, believed the speed of light was infinite). 

The value Roemer obtained, about 211, 000 kilometers per second, is considerably lower than the currently accepted value of 299,792.458 kilometers per second.  That’s because the radius of the Earth’s orbit wasn’t yet known with any precision in his time.  Still, Roemer’s calculation was in the right ballpark, and the realization that the speed of light had a fixed value, instead of being either immeasurably high or infinite, marked a major advance in the history of science and our understanding of the natural world.  For example, we’ve already seen how fundamental a role the finite speed of light plays in generating time dilation effects.  In subsequent blogs, we’ll discover just how big a nail the speed of light was to drive in the coffin of the biblical story of creation.  But first, we have to identify another important nail, in the form of the distance between the stars and us.  That is the topic of the next blog.

In the beginning was the Word

 

The Holy Bible was written by men divinely inspired and is God's revelation of Himself to man. It is a perfect treasure of divine instruction. It has God for its author, salvation for its end, and truth, without any mixture of error, for its matter. Therefore, all Scripture is totally true and trustworthy. – from the Basic Beliefs of the Southern Baptist Church, currently 16 million members strong

At the core of most major religions is the belief that the universe has not existed forever.  Instead, it was created by a higher power at some specific point in the past, usually to provide a backdrop or platform for humanity to inhabit. Interestingly, arguably the most profound scientific discovery of the 20^th century was that the Universe has, in fact, not been around forever.  About 13.7 billion years ago, by current best estimates, the whole enchilada started out as an almost infinitely hot and infinitely dense speck, so tiny that even our most powerful microscopes couldn’t have seen it.  From there, the speck started to expand and cool, a process that is still going on today.  This “big bang” account leaves the question of how (and, if you insist, why) the universe came into being completely open.  The Catholic Church, for example, sees in the big bang the undeniable handiwork of God the Creator.

The church may be right.  In the absence of any evidence one way or the other, divine intervention has just much right to a seat at the table as any other conjecture.  Thus, in concert with those of a religious persuasion, I’m quite open to the possibility that the Universe had a creator.  However, there is one particular religious belief concerning creation that I could not disagree more violently with: the specific details of the creation account as described in the Old Testament. Actually, to say I “disagree with” the biblical version of creation doesn’t do my position justice.  The Genesis version of the Universe’s creation can’t possibly be correct.  It’s just flat-out wrong. It’s untrue.  The sooner that all religions and denominations embrace the Catholic notion that Genesis should be taken figuratively, not literally, the better off all of us will be, believers and non-believers alike. 

This embrace cannot come fast enough for me. As recently as 2008, a Gallup poll found that fully 44% of US adults agreed with the statement "God created human beings pretty much in their present form at one time within the last 10,000 years or so”.   We can assume that a similar percentage would have agreed with the statement “God created the heavens and the Earth sometime in the last 10,000 years” as well, had this question also been asked.

So what does Genesis actually say?  Very briefly, Chapter 1 asserts that the heavens, the earth, and all living creatures, including the first humans, were created in the space of six days.  Assuming that the subsequent course of human history, as laid out in the Bible, proceeded uninterrupted from that week, various Biblical scholars have computed the time that has elapsed since that monumental week as about 6000 years. 

In this latest series of blogs, I’m going to confront this Biblical account of creation head on.  But I’m not going to go about it the standard way, which is to champion Darwinian evolutionary theory over the Genesis story of how humans came to be, or to lob geological arguments at the Young Earth Creation (YEC) movement, whose members assert that most of the geological evidence for an old Earth is instead the product of a relatively recent event - Noah’s flood.  These conventional ways of framing the issue might well be futile anyway.  In the words of the YECs themselves,

“We further deny that scientific hypotheses about Earth history may properly be used to overturn the teaching of Scripture on creation and the flood”.

So what kind of argument am I going to mount instead? I’m afraid you’ll have to check out the next blog to begin to find out!

The Difference a Day Makes

 

Last time, I explained how the movement of the Earth around the Sun creates the illusion that the Sun is moving through the zodiacal constellations.  There’s just one loose end to tie up.  At sunset, which is, as we’ve discovered, a good time to visual local motions, the Earth is moving down and to the right of the Sun; that is, the Earth is moving in the direction of a point below the western horizon.  That Earthly motion is what pushes the Sun constantly up and to the left.  Below, I’ve included the first figure from the last blog just to reinforce this point.  See how the Earth’s movement pushes it continuously to the right of the Sun?   And how that motion shifts the Sun continuously leftward?

This “cause and effect” is something to be savored, partly because you can think of it happening at any time of the day or night.  For example, remember from the “Beatles” blog that after sunset, the Earth’s rotation “pulls” the Sun along that line below your feet towards the Eastern horizon, on a course that will culminate in sunrise?  The Earth doesn’t stop orbiting the Sun just because it’s nighttime, of course, so throughout the night the Earth’s movement is constantly pushing the Sun back and to the left.  This has the effect of slowing the Sun’s forward progress to the eastern horizon, slightly delaying sunrise.  In other words, the Earth’s movement makes the nights just a little bit longer than if the Earth was stationary.  Similarly, the constant forcing of the Sun to the left during the day works to slow down the Sun’s forward motion then too, stretching out the length of the day.  The impact is small, adding only about two minutes of length to both day and night.   Still, it’s interesting to sit back and consider that each 24-hour day would be about four minutes shorter than we measure it to be if the Earth wasn’t moving around the Sun.

Now, let’s get back to how the Earth’s movement impacts our view of the stars.  I’ll ask you to once again imagine you’re out and looking up right at sunset, when the sun is barely above the western horizon.  If, every day, the sun is drifting slowly leftward, then every successive day that the sun sets, the stars that, the night before, were just far enough left of the Sun to be visible for a brief period just after sundown, before they rotated out of view, will now be swallowed up in the Sun’s glare, and disappear completely from the evening sky.  Meanwhile, in the morning sky, prior to sunrise, just the opposite will happen.  Since the Sun is drifting leftward, there’s a little sliver of sky visible just before dawn that was swallowed up in the Sun’s glare the night before.  Thus, in the early morning hours, just before sunrise, the Earth’s movement giveth; in the early evening, it taketh away.

On the scale of a single day, these effects are miniscule.  Over time, though, the evening losses and the morning gains add up until, over the course of a month, an entirely new zodiacal constellation becomes visible in the pre-dawn sky, while another zodiacal constellation disappears from the sky after sunset.  In any six-month period, these effects are enough to completely alter the pattern of stars that are visible overnight.

And that’s really all there is to it.  We’re done with our treatment of local motion, and I will wish you a brief adieu while I work on the next topic.  Until next time, Whabbloggers!

Your Sign... or Mine?

All right. In yesterday’s blog, I promised to talk about astrology, so let’s start with the most common form of astrological knowledge: your “sign”. Literally everybody knows what their sign is, right? Mine happens to be Cancer; yours is most likely one of the others, perhaps Leo, Virgo, or Libra; maybe Scorpio, Sagittarius, or Capricorn; possibly Aquarius, Pisces, Aries, Taurus, or Gemini. It is also common knowledge that our signs are dictated by the date of our birth, with each of the 12 signs roughly aligned with one of the 12 months of the calendar year.

Astrological signs are so deeply embedded in popular culture that horoscopes run everyday in major newspapers, and knowledge of one’s sign is often considered an important form of personal information (“Hi! “I’m a Cancer. What’s your sign”)? But what are astrological signs, really? Where do they come from? Why are they called “Sun” signs”? To answer these answers, I’m going to ask you to look at some familiar “landmarks”, and some familiar locations, from a new and different perspective.

If you happen to look up at the stars tomorrow night, one of the first things that will strike your eye is the fact that the stars seem to form recognizable patterns, called constellations. Each astrological sign is named after a particular constellation. People born this month are Aries, because their astrological sign corresponds to the constellation of the same name. So, when you look at the sky in April, are you able to see Aries? The answer is a most emphatic “No”! Right now, Aries is as invisible as astronomical objects ever get!

The diagram below tells the story. It depicts where the Earth is in its orbit at roughly this time of year (the illustration says “The Earth in May” instead of "The Earth in April" because a slight discrepancy has emerged over the centuries between the real position of the sun against the stars, as shown in this figure, and the designation of where the sun is in astrological terms.  I'm deliberately glossing over this discrepancy for purposes of this blog). If you draw a straight line between the Earth, and Sun, and the sky beyond, the arrow points directly at Aries. That’s why you can’t see it. Right now, the Sun and Aries occupy the same location in the sky. They rise and set together, so Aries is not visible at night.

Once the sun sets, however, other astrological (or more precisely, zodiacal) constellations ARE visible. Near the Western horizon are the constellations Taurus and Gemini. Cancer is small and not very prominent, but the big spring winner of the zodiacal constellation sweepstakes, Leo, is very prominent; you can identify Leo by the stars that are arranged in the shape of a mirror-image question mark. The other zodiacal constellations visible early tonight, Virgo and Libra, are further to the east, and harder to spot because they are lower in the sky. But, if you wait until later on, and give the Earth a chance to rotate further east, the more familiar summer constellations of Scorpio and Sagittarius will rotate into view.

But wait, you may be saying. I’ve just named the astrological signs for birthdays that come later on this summer and fall. If astrological signs are defined by which constellation the sun is aligned with that month, and the sun is in Aries right now, it must have to be shift position to align with these other constellations over the course of the next few months. That is, the sun must be moving constantly along an imaginary line that connects these constellations.

Well, it is certainly the case that the sun appears to move along such a line. The figure above tells the real story, though. It is really the Earth that is moving along its orbital track. Every day, we shift position to the right along that imaginary line by some 1.6 million miles. This movement forces the line extending from the Earth to the Sun and beyond to pivot leftward. As you can see, the effect is to “push” the Sun through the constellations that happen to be lined up with the Sun’s position in the sky: that’s what defines a zodiacal constellation. By next month, May, the Earth will have moved far enough to co-locate the Sun with the stars that make up the constellation Taurus, the Bull, which is why May babies have Taurus as their Sun sign.

Simple, right? In the figure below, we’ve fast-forwarded exactly half the year, to early November.  In that amount of time, the Earth has shifted an enormous distance, enough to push the Sun all the way to the position in the sky that’s occupied by Libra. Then, the Sun “enters” Scorpio, the sign of you mid-November babies (again, the astrological dates for Libras and Scorpios are somewhat earlier than the dates would be if the astrological dates were aligned with the actual present-day position of the Sun in relation to the zodiacal constellations).

That’s pretty much the story, Whabbloggers, at least for astrology. In the third blog of this series, I’ll return to the issue of how the apparent movement of the Sun through the zodiacal constellations changes the stars we see in the night sky. Would you care to steal my thunder by speculating on that in the comments section?

Doing the Local Motion

Last month, we discussed how the appearance and behavior of the Sun, the Moon, and Venus can be explained through the combined effects of various forms of “local” motion: the Earth and Moon rotating about their axes; the Moon revolving around the Earth; and Venus revolving around the Sun.  As you know, our own planet is in constant motion too.  Every year, the Earth completes a 600 million-mile journey around the circumference of an enormous circle with the Sun at the center (to get some idea of how truly colossal 600 million miles is, if you were to drive that distance, you would be on the road for almost a thousand years).  This translates into a constant speed of 19 miles per second, which is far faster than any supersonic jetliner, or even the shuttle.  

With the exception of the Earth’s axial rotation, which is responsible for our day/night cycle, the orbital motion of the Earth is woven more deeply into the fabric of our lives than any other form of local motion.  Consider: Virtually every one of our major sporting events, every one of our major holidays, every one of our major religious observances, and even Halloween, occurs at virtually the same time every year.  The adherence to that rigid schedule means that these shared cultural events occupy a particular point in space as well as in time.  They each have a reserved location on the Earth’s orbital path. 

The connection between these all-too-familiar activities and this underlying astronomical truth is not widely appreciated.  In part, this is due to the nature of the events themselves.  Let’s face it, folks: Tennis tournaments, football games, horse races, and Fourth of July celebrations do little to promote astronomical awareness; to the contrary, they tend to focus our attention firmly on a small piece of terra firma.  Even if we turn our attention to the objects in the sky, the impact of our orbital motion remains subtle.  There is very little hint of that motion in the behavior of the Sun, the Moon, or Venus, for instance.  Indeed, you would be hard-pressed to notice changes of any sort on a day-to-day basis (contrast that with the Moon’s orbital motion, which places it in a noticeably different location in the sky every night).  However, if we observe the night sky over a longer period of time, such as the three or so months that make up each of our seasons, the changes wrought by the motion of “Spaceship Earth” finally become apparent; so apparent, in fact, that they blow the observable effects of the other local motions completely out of the water. For, given enough time, the Earth’s journey around the Sun completely alters the thousands of stars that are visible across the night sky.

Tomorrow night, suppose you were to go out about an hour and a half after sunset and assumed the standard viewing position for our visualization exercises, which is facing due south.   Your mission, should you decide to accept it, will be to note and memorize a select few of the star patterns that you see when you look up.  Then, once a month for the next twelve months, you go out and observe again, constantly comparing the star patterns you see then with the patterns you saw the month before.

With myriads of stars to choose from, which patterns should you to focus on?  Good question.  On the one hand, I’d like you to bite off enough patterns to appreciate the breathtaking scope of the changes that the Earth’s rotation brings to the night sky.  On the other hand, I don’t want to overload your powers of observation and memorization with too many patterns.   To help me out of this dilemma, let’s restrict the objects of interest to just those star patterns that figure in that most unscientific of astronomically related disciplines: Astrology!

Astrology?  Why would a hard-nosed scientist like me want to have anything to do with astrology? As you know, I love to push back the barriers of ignorance, and going with astrology allows me to kill two “birds of astronomical ignorance” with one stone.   For the vast majority of us, astrology has something in common with the highlights of our calendar year: Although astrological concepts are embedded quite deeply into our culture and our consciousness, the connection between astrology and the Earth’s orbital motion is not widely understood.  By illustrating the effects of the Earth’s orbital movement with reference to astrological star patterns, I can make explicit the common underlying connections between astrology, the Earth’s motion around the Sun, and the changing view of the stars in the night sky throughout the year.

Am I being too ambitious here?  Perhaps, so lets create some suspense, and save the nitty gritty until the next blog.  In the meantime, feel free to share your present understanding of these connections in the comments section!

Venus, if you Will!

It’s mid February, Whabbloggers, and very soon, the evening sky is going to be graced with a rather stunning addition. Yes, our closest planetary neighbor Venus, known since antiquity as the Goddess of Love, is about to assume her position as the dominant “Evening Star”, brightest of all celestial objects save the Moon.

Where has Venus been lately? And why isn’t she the “Evening Star” all the time? To begin to answer these questions, suppose, about a month ago, you headed out to your back yard (or equivalent) at our preferred visualization time, right around sunset. You had taken pains to pick a clear day, of course, so the Sun was clearly visible along the western horizon.  The rest of the sky was still bright blue, with no stars visible just yet. Now, where was Venus? Even though invisible, you could have easily visualized her location by imagining a straight line joining you to the Sun and extending out behind it. Venus was almost directly on that line, some 67 million miles past (beyond) the Sun!

Of course, we know from the earlier Sun blog that the Sun is a stationary object, so there’s nothing special about having gone out near sunset as far as imagining the location of Venus was concerned; you could have just as easily imagined the line connecting the Earth, the Sun, and Venus when the Sun was halfway across the sky at noon, or just clearing the eastern horizon at sunrise, or even when the Sun was below your feet at night. To make this point more concretely, take a look at Figure 1 below, which depicts the green/blue Earth, the yellow Sun, and four half-black circles. These circles represent the position of Venus at four points in her orbit around the Sun. Last month, at the time you made your hypothetical trip to your back yard, Venus was in the position corresponding to the circle on the far right of the figure, on the other side of the Sun from the Earth.

In the Figure, you’re looking straight down on the Solar System from directly above the Sun. Another very useful perspective from which to visualize the relative positions of the Sun, Venus, and the Earth is from a vantage point just behind and slightly above Earth, as in Figure 2 below. A month ago, Venus was in the position labeled “Superior Conjunction”. The Sun occupies the middle position, so the side of Venus that was turned toward the Earth was fully illuminated. We couldn’t see it, though, due to a combination of two factors. First, Venus was fully 160 million miles away, so its disk was quite small. Second, and more important, since Venus rose and set at almost exactly the same time as the Sun, it was never in the sky at night, and during the day, it was completely washed out by the Sun’s glare.

It is interesting to compare the source of Venus’ invisibility last month to the invisibility of the New Moon. As we found out in the lunar blogs, the Moon is located between the Sun and the Earth when it is New, so the side facing us is completely dark. Venus is invisible for entirely different reasons.

Like every other body in the solar system, Venus is never stationary. Day by day, our sister planet travels in the standard leftward (counterclockwise) direction all inner solar system objects travel as they orbit the Sun. The closer the object to the Sun, the faster it moves, and Venus actually whips along at over 75,000 miles per hour. You read that right: Venus covers 21 miles every second! You can see from Figure 2 that over the past month, this movement has been taking Venus gradually away from, and to the left of, the sun.

As Venus moves leftward, the distance she is putting between herself and the Sun (as viewed from our perspective here on Earth) is about to pay dividends for sky watchers. Fast forward in your visualization exercise to about three weeks from now, towards the middle of March. Take some time to settle down in your back yard just after sunset, maybe with a cocktail to keep you company. Sipping slowly, you enjoy the gathering dusk while waiting for the first star to appear. Presto: I guarantee that a bright object will pop into view over near the western horizon, and you will be the first on your block to welcome the Evening Star!

Every day thereafter, Venus will slip a little further to the left along its orbital path, taking her ever further away from the Sun. As she climbs higher in the sky, she will hang around for a longer period after sunset before descending down to the western horizon and disappearing from view (this rapid movement of Venus towards the western horizon is entirely due to the Earth’s leftward rotation; it has nothing to do with Venus’s own movement at all).

Let’s continue to follow Venus around in her orbit. As she travels ever further “up, up and away” from the Sun, eventually she reaches the half-way point, equivalent to the Moon’s “half full” position, the point of maximum displacement from the Sun (again, that statement pertains only to our perspective; from her own perspective, Venus stays remarkably close to 67 million miles from the Sun throughout her orbit). The period of maximum displacement will happen over this summer. The black and white ball at the top of Figure 1, and the extreme left of Figure 2, illustrates what position she will take.   By then, Venus has swung far enough from the Sun that she is quite a ways from the Western horizon at sunset, and remains visible for several hours after sunset.

Let’s pause for just a moment, consider Venus at this point in her orbit, and visualize her behavior in our sky over a 24-hour period beginning at sunset (i.e., through a full rotation of the Earth). Once it has disappeared, the Sun commences following the standard path below your feet (the path we visualized in the Sun blog) due to the Earth’s eastward rotation. Meanwhile, that same earthly rotation is driving Venus ever rightward, down to and eventually below the western horizon. By the time the Sun pops back into view along the eastern horizon in the morning, where is Venus? Still below your feet, of course, tracing out pretty much the same path as the Sun, just several hours behind. Since Venus doesn’t rise for several hours after the Sun, the event goes completely unnoticed because the planet rises into full daylight.

When the Moon swings into view at the half full point in it’s cycle, our satellite is clearly visible in the daytime sky.  Believe it or not, Venus is, too, if you know exactly where to look. The best opportunity comes when the half moon and Venus rise at almost exactly the same time, very close together, and then move in unison as the Earth’s rotation carries them up and across the daytime sky. I’ll be sure to point this opportunity out when it happens this summer. If you can spot Venus, you’ll be one of the few human beings on the planet who’ve ever seen it in broad daylight!

Now, let’s return to the main event, the changes in Venus’ appearance that accompany its orbit around the Sun. You can see from the highly informative Figure 2 that, at the time of greatest elongation, Venus is actually “rounding the curve” and about to start swinging back to the right along our line of sight: A path that will bring it back into alignment with the Sun. Venus is still drawing closer to Earth during this time, so it continues to grow larger. However, as late summer gives way to autumn, each night the distance between our brilliant Evening Star and the Sun will shrink steadily, and the interval between when the Sun sets and Venus sets will shrink as well.

By Halloween, Venus’s orbital motion will have brought it right back into alignment with the Earth and the Sun, but between the two, rather than on the far side of the Sun as it is now.   Once again, rising and setting in tandem with the sun, Venus will fade into invisibility in our night sky. This time, her invisibility is caused both by the fact that Venus and the Sun will rise and set together, and also because our point of view is now aligned with the dark side.   In that sense, the Halloween “New Venus” and the New Moon of November 6th will have a lot in common!

And what then? Once again, Figure 2 tells the story: Venus’s incessant movement will cause it to move past the sun and off to the Sun’s right. Remember from our Moon blogs what happens to celestial objects that are located to the right of the Sun? When the Sun sets, objects to the right are already below the western horizon, and have a head start when it comes to being whisked around by the Earth’s rotation toward their appointment with the Eastern horizon. So it is that Venus will start to rise before the Sun, and take her appointed place as the blazing Morning Star. Over the course of next winter, the planet will swing further and further to the right, giving her more and more of a head start on the Sun. Consequently, Venus will rise earlier and earlier than the Sun, and stay visible for a longer period of time before dawn arrives and she fades into the morning twilight.

To really imagine this Morning Star behavior, let’s go back to Figure 1 and its “God’s Eye perspective” above the Sun. Pretend you are a specific location along the Earth’s equator (along the very edge of the disk), and the entire green ball representing the Earth is spinning in a counterclockwise direction. Venus is at the bottom of the figure. Now imagine spinning throughout the night. As you pass midnight, which is when you are exactly opposite the Sun on the Earth’s far side, you can see from the geometry in the Figure that Venus is soon going to swing into your view along the Eastern horizon. The Earth will have to complete almost another quarter turn before the Sun does its own appearance act, also to the East.

And that’s pretty much it! When Venus is located to the right of the Sun (from our perspective) she forms the Morning Star. When she is located to the left of the Sun, she forms the Evening Star. Over the course of this year, I encourage you to follow the progress of Venus, starting about three weeks from now along the western horizon. Check out how high she gets in the sky over the summer. In the autumn, track her movement back in the direction of the Sun, before she disappears completely. And then, next winter, if you find yourself with insomnia some night, or happen to get up unusually early, check out the Morning Star!

Figure 2 illustrates one more notable change in Venus brought on by her orbital motion, although you need a telescope or good pair of binoculars to see it. Right now, in the middle of February, the side of Venus that faces Earth is almost fully illuminated. As the planet swings in our direction, the proportion of the lit side that is visible from our vantage point shrinks steadily. When Venus is at her maximum elongation from the Sun, she is exactly “half full”, just like the Moon. Then, as Venus swings back into alignment with the Sun, late next summer and into fall, the proportion of her disk that is illuminated from our vantage point shrinks to a thin crescent (again, these phases are just like the Moon). You will see these phases of Venus clearly if you ever examine the planet in a good pair of binoculars or a small telescope.

Before leaving Venus completely, I’d like to take this opportunity to talk about the place for just a little bit. Virtually a twin of the Earth in terms of size, Venus has always been my favorite planet. I don’t really know why. She certainly isn’t more likely to harbor life than Mars; the surface temperature is about 800 degrees Fahrenheit, 300 degrees hotter than the highest setting on your oven. That temperature is pretty constant across the entire surface, too, despite Earth-like variations in latitude and altitude, and despite the fact that nights on Venus are longer than 100 Earth nights. The long nights are because Venus spins on its axis very slowly, a lot more slowly than the Moon even (you do remember from earlier blogs how slowly the Moon spins, right)? As with many other features, the slow rotation rate of Venus is still a mystery. As for how Venus maintains such a constant temperature, the answer is that Venus’s atmosphere is 90 times as dense as ours. The air pressure at the surface is equivalent to the pressure 3000 feet down in our oceans! Just as there isn’t a lot of variation in water temperatures at that depth, so too is there little temperature variation on Venus.

There is a great deal more that is fascinating about our sister planet, such as the current thinking about why she has such a thick atmosphere, but I will save that discussion for another blog.

Until next time, then, Whabbloggers… when I think I’ll tackle a little astrology!