Posted by: SteveInCO | 13 May 2012

Venus Transit, 5/6 June 2012

UPDATE

Boy do I have egg on my face.  Not just a chicken egg either, it’s an elephant bird egg.  I am drowning in egg.

You see, this Venus transit is happening on the 6th of June all right… the morning of the 6th of June in Europe.  Which means it happens on the evening of the fifth here.

FIFTH OF JUNE.

I sincerely hope no one misses it because of this mistake I have made.

Another update

Pictures here.

A What?

This year the 6th of June is not just the anniversary of D-day–which is noteworthy enough.  It is also the date [edit–if you are in the eastern hemisphere!  Otherwise it’s on the 5th of June.] of one of the rarest predictable astronomical events.  And if you miss it the next one is in December of 2117, so you have plenty of time to get ready.  (The last one was in 2004–these events come in pairs about eight years apart–but the pairs themselves have 100+ year gaps between them.)  Many, many people like my grandfather (1899-1986) or other grandfather (1913-1995) live long lives and never get even the opportunity to see this event.

Venus transits the face of the Sun on 2004-06-...

Venus transits the face of the Sun on 2004-06-08. Here, the black drop effect is visible. (Photo credit: Wikipedia)

It’s a transit of Venus across the sun.  For six hours and forty minutes on this day, Venus will be directly between the earth and the sun.  If you can get a hold of some #14 welder’s plate or an equivalent, you can safely look at the sun, and you should be able to see a black dot moving across it over the course of several hours.  The picture above is from the 2004 transit.

Eclipse viewing glasses can be used to observe...

Eclipse viewing glasses can be used to observe the transit. (Photo credit: Wikipedia)

Here’s the info on where it will be visible, and when.  Some places on earth (large parts of South America and Africa) will have night time the entire time and will miss it but most land areas on earth will be able to see at least part of this.  The transit starts at 22:09 UTC [on the 5th] and ends at 4:49 UTC on the 7th [no, 6th], which works out to 16:09 and 22:49 Mountain Daylight Time.  (UTC is basically London time without daylight savings time, and is six hours ahead of MDT.  Those of you not fortunate enough to live in the Mountain Time Zone can calculate from here.)   So for people living in the “lower 48” of the United States, the transit will start sometime in the afternoon, and will still be progressing when the sun goes down.  People in Alaska and Northwestern Canada get to see the whole thing.

I’m going to talk here about why these events are so doggone rare, why they come in pairs, and then I will explain why Venus transits were so important to the history of science.

Why It’s So Rare

Why is it so rare?  Venus is closer to the sun than we are, and is orbiting just like we are, and quite a bit faster, too.  Earth orbits once every 365.256363 days and Venus does so 224.70069 days.   So, like long distance runners (or cars) on a race track, Venus will “lap” Earth periodically, passing between the earth and the sun when it does so.   That moment it is “lapping” the earth is known as an inferior conjunction.  (When Venus passes behind the sun, it’s a superior conjunction.)  In fact, if you do the math, inferior conjunctions should happen once ever 1.599 years or so, basically a smidge less than 1 year, 7.2 months.

(Some of these diagrams I did in MS Paint and they won’t be very precise.)

So why don’t these transits happen every 1.6 years?

Diagram showing how transits of Venus occur an...

The answer is, because Venus’s orbit isn’t quite on the same plane as ours.  In the figure above, the orbits are to scale but the sun, earth and Venus are drawn much larger than they “should” be.  With that in mind, the top figure shows the common situation as an almost edge on view; Venus is at “inferior conjunction” (between us and the sun as seen from “above” the solar system) but it’s at a point in its orbit where it’s “below” the plane of the Earth’s orbit.  The second figure shows the conjunction happening at some other time, when the earth is 90 degrees further along in its orbit (planets orbit counter-clockwise as seen from above their north poles, so the bottom diagram shows where the earth is three months or 1/4 year later in the year), and the two orbital planes intersect.  The (very hard to see) red dashed line shows where the planes intersect.  This point in the earth’s orbit is the “sweet spot” and if the earth is here when Venus “laps” it, Venus will appear to pass directly in front of the sun, as it climbs from “below” the earth’s orbit to “above” it.  Venus will spend that instant right smack on the center of the sun’s disk like a bullseye.

You’ll note that the same thing can happen when the earth is on the other side of the sun, with Venus dropping “below” the plane of the earth’s orbit as it goes through the inferior conjunction.

Since the Sun actually has some breadth in the sky, about a half degree’s worth, the earth does not have to be precisely at one of the two sweet spots at the time of an inferior conjunction in order for a transit to happen, but it’s got to be pretty doggone close.  We can call the places where Venus can appear to transit the sun “transit zones.”  They straddle the sweet spots on either side of the earth’s orbit.   The further away from the sweet spot you are when there is a transit, the further off center Venus’s path across the sun will appear to be.  If the earth is in the transit zone closest to us in the diagram above, but hasn’t reached the sweet spot yet, Venus will cross the sun’s disk below the center of the sun’s disk, but if the transit happens just after the earth passes through the sweet spot, it will appear to cross above the sun’s center.   (And vice versa, for the transit zone and sweet spot on far side of the earth’s orbit as seen in the diagram.)

The transit zones are on opposite sides of the earth’s orbit, and the calendar year is defined in terms of earth’s going around its orbit once.  (Well not quite, but that’s another long and complicated story.)  So that means that transits can only happen at two different times a year, and they are about six months apart.

And indeed if you look here (scroll down to three tables for three different 2000 year periods) you will see that it’s true: all of the transits of Venus between 2000 BCE and the 1600s happened either in late May or late November (six months apart).  1761 and later, through June 3 of 3956 CE, they are in early June and early December, and gradually shift to later and later days.  (That’s because the calendar year is not quite as long as the earth’s orbital period; like I said it’s another long and complicated story.)  There is a sudden shift in dates with the 1761 transit, and that is because we dropped 11 days going from the Julian to the Gregorian calendar in 1752.  When we did that our calendar year became slightly shorter (365.2425 versus 365.25 days), so after that point, the dates of the transits not only make an 11 day jump, but they start to shift more rapidly.

Why Transits Come In Pairs

Remember above, when I said that Venus “laps” the earth every 1.599 years?  Well, let’s follow this through.  Let’s say Earth is just barely past the June sweet spot, but still in the transit zone when there is an inferior conjunction (like happened on June 8, 2004).  You will see a transit.  Let’s call that inferior conjunction “Conjunction 0.”  A tiny bit less than 1.6 years later, there will be another inferior conjunction, but the earth will be 6/10ths of the way around its orbit then (January 14, 2006), a bit past the transit zone on the other side of the sun.  Call that “Conjunction 1.”  Another 1.6 years pass, and Conjunction 2 happens (August 18, 2007), a grand total of 3.2 years after Conjunction 0, so it’s 2/10ths of the way past the transit zone near us.  Conjunction 3 is at 4.8 years (March 27, 2009), with the earth 8/10ths of the way past the transit zone.  Conjunction 4 is at 6.4 years (October 29, 2010), and the earth is at 4/10ths of an orbit past the near transit zone.  Conjunction 5, though, is at 8.0 years, in the transit zone.


Well, actually it’s at about 7.996 years, which puts it on June 6 [no, 5th!], 2012.  Which means if Conjunction 0 was near the end of the transit zone, Conjunction 5 is near the beginning of the transit zone.   We’ll see Venus cross in front of the sun, but instead of crossing above the center of the disk, it will cross below the center of the disk.

You can see what’s going to happen now.  The next four conjunctions, 6-9, will be near where Conjunctions 1-4 were, but just a couple of days earlier.  Conjunction 10 on June 3, 2020 will be close to Conjunction 5, but it will fall just outside the transit zone, and the long over-a-century wait for another Venus transit is under way.

If you were to make a movie of where the conjunctions happened, you’d see five evenly spaced lines like spokes on a wheel, slowly turning clockwise.  Eventually Conjunction 66–which matches up with our original Conjunction 1–will end up happening on December 11, 2117, hitting the far transit zone, and you will see the first of a December transit pair.

What would happen if a transit actually happened very close to a “sweet spot”?  Well you’d only see one transit then, not a pair.  The conjunctions 8 years before and after that transit will be outside the transit zone.  If you look at the NASA table, you can see that this will happen by about 3089 CE with the December transit zone, and after 3713 CE with the June transit zone.  We are rather fortunate to be living in a time when transits do come in 8 year pairs.

The Importance of Venus Transits in History

Like any science this is interesting by itself but there’s a lot more story here.  Transits of Venus helped us figure out how large the solar system is–and by extension, how far away the nearest stars are.

We Can Make a Map to Scale, But We Don’t Know What the Scale Is

By the early 1700s, we understood the theory of gravitation, and Kepler’s laws.  Because of this we knew the shapes of the planetary orbits and their inclinations, and we knew the proportions between their sizes.  We knew these things because we could observe in which direction planets appeared to be on any night.  We could use this to figure out how long it took a planet to orbit the sun and then triangulate to locate a planet in space relative to the earth’s orbit.  Kepler’s third law told us that the cube of the distance from the sun was proportional to the planet’s period (its “year”).  So we could see that Jupiter took 11.86 times as long as the earth did to go around the sun, and know with some quick arithmetic (square 11.86 to get 140.7, take the cube root of that to get 5.201) that Jupiter’s orbit is 5.201 times the size as earth’s.  (By the way, the story of what Kepler had to do to figure out his three laws–without benefit of telescopes, the theory of gravitation, or calculators, or calculus [the mathematician’s power tool] for that matter, is a fascinating one, but it’s beyond the scope of this post.)

We could, in essence, draw a scale diagram of the solar system since we knew the proportions.  But we didn’t know the actual size of any of it.  We did not know how far away the Sun is.  But we could call that distance, whatever it is, an Astronomical Unit (AU) and define everything in AUs.  So another way to state what we just figured out about Jupiter is that it is 5.2 astronomical units from the Sun.

There didn’t seem to be any direct way of figuring out these distances; it’s not as if we can stretch a tape measure all the way to some other planet.

The Moon Suggests a Way to Measure the Solar System

We did have a good idea about the distance to the moon.  In fact the first reasonably accurate measurement happened in the second century BCE, by a Greek named Hipparchus.  He was able to predict where the moon would be against the background of stars at any given time, and noticed that when the moon rose or set, it was off from the predicted location by some amount.  He realized this is because we, the observer, were off from the line between the center of the earth and the center of the moon by one earth radius, and that made the moon appear to shift against the background stars (a phenomenon called parallax), much as when you shift your head, nearby objects appear to move against distant ones.  Get a decent estimate of the size of the earth, do some trigonometry, and voila, we have the distance to the moon.  Due to inaccuracies in the measured size of the earth and this parallax, he was off by 26,000 km, but that is less than ten percent.  Not bad for 2200 years ago without a telescope or anything remotely resembling modern instruments!

Could this method be adapted to measure the distance to some planet?  Or the sun?  Hipparchus himself was able to set a minimum distance to the sun (of about 3 million miles) because he could not measure any parallax when observing it during solar eclipses.  He could figure out how small the parallax would have to be for him not to be able to measure it.  But “at least 3 million miles” was all he could say.

Measuring Venus transit times to determine sol...

Measuring Venus transit times to determine solar parallax (Photo credit: Wikipedia)

It turns out though, that Venus transits provided a relatively easy to measure parallax of Venus’s position against the solar disk.  If the transit could be carefully observed from two different locations on earth, we could see that Venus in each location crosses the sun at a slightly different place–Venus would draw two different lines across the sun, with the transits starting at various different times depending on how long the line across the sun was.  We could time the transits with great accuracy, and thus accurately determine how far apart the lines are in angular distance.  Once we determined the distance on the earth between the two observations, and note the ratio of distances to Venus and the Sun (the sun is about three times further), a bit of trigonometry would give us the distance to Venus.  And everything else in the whole solar system, including the actual distance represented by an AU, can be figured from there, because we know all the ratios of distances.

A transit of Venus was expected in 1761.  One of the first international scientific collaborations ensued, with observations taking place in Siberia, Norway, Newfoundland and Madagascar.   There turned out to be difficulties determining the precise time the transits started and stopped, including problems caused by Venus’s atmosphere (which was discovered in this manner) and also turbulence in our own atmosphere.   Another transit happened in 1769, and yet more data was collected from Hudson Bay, Baja California, Tahiti, Philadelphia, and all over Russia.

French astronomer Jerome Lalande gathered all this data together, and calculated that 1 AU was 153 million kilometers.  That’s about 3 million km too high, but was by far the best measurement ever made of this value.  The biggest measurement problem was the “black drop effect,” a distortion of the images caused by the earth’s atmosphere.

Another attempt was made with the two transits of 1874 and 1882, with expeditions sent to Kerguelen Island (truly one of the most remote places on earth), and data from these, combined with the data from the 1760s values by American astronomer Simon Newcomb, gave the value of an AU as 149.59 million kilometers (±0.31 million km), which is only about eight thousand kilometers off from the best number we have today.  Combined with the measured value of the gravitational constant from Cavendish’s experiments in the 1790s, we were also able to use the law of gravitation to figure out the mass of the sun.

We are now able to launch space probes and do radar ranging, and we know the value of an AU to within 30 meters.  The best value today is 149,597,870,700 meters.  With methods like these, triangulating off of Venus transits became superfluous and while the 2004 transit was certainly observed just like the one coming up will be, no one did so in order to calculate how large an AU is.

Bonus:  Distance to the Nearest Stars

Now that we knew the size of the earth’s orbit, we could use it as a base line for measuring the parallax of the nearest stars with respect to distant stars, do some trigonometry, and get the distance to them as well, and it turns out to be on the order of 39.74 trillion kilometers for Alpha Centauri, the nearest bright star other than (of course) the Sun itself.

And we were able to figure all of this out long before radar ranging and interplanetary probes existed, because Venus sometimes, very rarely, crosses in front of the Sun.

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Responses

  1. “1 AU was 153 million kilometers. That’s about 3 km too high, “… Should be “3 _million_ km too high”. Great article!


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