Conjunction Junction - Wait, what's conjunction?

The other night as we drove home late from softball, my wife started asking me a few questions about astronomy terms, and so I thought I might write down a few of them.

• Conjunction: A conjunction is when two (or rarely three or more) objects are close together in the sky.  This is typically spoken of in terms of the planets. For instance, just this week Mercury and Venus experienced conjunction, and were very close in the sky.  With so many moving objects in the sky, a conjunction of some sort occurs just about every month -- and certainly so if you include the moon as one of the objects 

Jupiter and it's moons
 "being occulted"?
(I don't think that's proper English)

• Occultation: A very special conjunction where objects appear so close together in the sky that one object actually passes behind another. The most common types are when the moon passes in front of some object, and for a short time, that object is hidden behind it. I have never had a chance to observe this. Here is a list of lunar occultations for this year and you can see that the moon passes in front of stars all the time (nearly every day) but in front of major planets only a few times. And during those times, you can only see the occultations from generally small locations on earth. 

• Transit: A transit is another type of conjunction, when a smaller object moves in front of another bigger object. The most famous transit is when Venus transits the sun, an event that occurs twice every 120 years or so. The most recent was June 5, 2012, so I'm sorry -- if you didn't see it then, you probably won't see it ever.  I made sure to watch it, and took this picture. The transits of Venus in 1639, 1761 and 1769 are of historical interest, because they helped scientists get an accurate measure of the distance from the earth to the sun.

• Syzygy: This is just too cool of a word to leave out, even though I've never seen it written anywhere except in a glossary of astronomical terms. It's a great Scrabble word, worth 25 points, for those rare (impossible actually) occasions when you have 3 y's.  Essentially, a syzygy is whenever three astronomical objects are all in a line.

• Eclipse: An eclipse is when the sun, moon, and earth are in syzygy -- and depending on the order of the three, and when the syzygy occurs, you might experience an eclipse.  Every 14.5 days the three are aligned in some way, but most of the time the moon is slightly above or below perfect alignment, and so only a handful of times each year does some kind of an eclipse occur.  Here's the next ten years of eclipses.  The next total solar eclipse that will be fully visible in the North America will be on August 21, 2017, an event I'm planning on driving down to see. 

• Opposition: When a planet is at opposition, that means it is on the opposite side of the earth from sun. This is for the planets further away from the sun then earth -- and is usually the best time to observe them.  The planet is usually the brightest then -- and highest in the sky (along the local meridian) at midnight.
  
• Elongation: Elongation occurs for inferior planets (Venus and Mercury) and is when appears the farthest away from the sun. This marks the best times to observe Venus and Mercury -- when they are their brightest, and furthest away from the sun's blinding glare. 

What time was this photo taken?

As I read through my facebook feed, I was struck with following picture:

Immediately -- shows how much of a dork I am -- I thought "I wonder what time this picture was taken?!"

You see, as the earth rotates around the sun, shadows rotate around the objects that form them. In the northern hemisphere, these shadows rotate clockwise -- which is why clockwise is clockwise. The first clocks ever made were sundials, made by people living in the North, and then clocks were built later.

I figured I should be able to figure out the angle of the shadow of the arch and use it to figure out what time of day the picture was taken.  I could also figure out the date the picture was taken by looking at the length of the shadow. You see, everyday the angle of the sun at a given time changes. Right now, during the spring, the sun is higher in the sky every day at a specific time, which makes shadows shorter. Measure your shadow at 11:00am today and measure it again tomorrow and it will be smaller!

So I found a map of St. Louis, and used Geogebra to figure out the angle of the shadow of the sun, and the length of the shadow.  After about five minutes, I had placed a point on the map that represented where I thought the top of the shadow was, and had drawn a vector from that point to the point that represented the top of the arch. I compared that with the scale of the map, and estimated the length of the shadow to be about 1,000 ft.  After looking on wikipedia, I knew the height of the arch, and a little trig revealed the altitude of the sun to be about 32 degrees.

In a few more minutes I had estimated the angle of the the vector and converted that into a compass heading, which gives me the azimuth of the sun of approximately 111 degrees.  

I knew there is only two times a year where the sun has that exact altitude and azimuth, once in spring and again sometime in the fall -- and I took a chance that this picture was taken on spring break (reasonable enough right?). So I looked up the altitude and azimuth for the sun on the days during spring break:

Since the photo was tagged as uploaded on April 1* I started with that date, and found the following data in the table:

The first column is the time (AM), the second column is the altitude of the sun, and the third column is the azimuth of the sun.  I was disappointed that I didn't see my exact values in the table -- but I didn't expect to either, for two reasons:
  1. I didn't know if this was the correct date -- the picture might have been uploaded that day but taken several days (or even a half a year?!) earlier.
  2. There is some degree of uncertainty in my measurements. As I moved around the point where I thought the top of the shadow was, the angles varied somewhat. To be specific, they varied less than a degree more or less than my values, but that's significant enough to make my answers have to be estimates.

Let me treat each of these reasons separately.  Assuming the picture was actually taken on April 1, and my measurements were slightly off, I would estimate that the picture was taken around 8:34 am local time (I could be off by an hour if the website doesn't account for daylight-savings time, but I'm going to assume they were smart enough for that).

If I don't assume to know the date the picture was taken, and trust my measurements, I would argue that the picture wasn't actually taken on the 1st.  Looking at similar tables for other days, I get much closer altitude/azimuth combinations for a few days later:

 If I had nothing else to go on, I would estimate the date/time of the picture was April 3, 8:33am.

Perhaps the photo takers will provide the true answer in the comments below?

*There was some discrepancy between my wife and I as to when the picture was actually uploaded onto Facebook. It was posted April 5th, "tagged" April 1, but I have reason to doubt the "tagged" date. Only time will tell who wins our little "argument" -- although regardless of who wins, I will probably lose -- right guys?  I love you honey!

The Constellation Leo

This post is the one of a series on constellations and posted throughout the year as each constellation comes into prominence.

Leo is one of my favorite constellations. It was one of the first after I fell in love with astronomy in 2008. It was the first one that I had never noticed before, but set out to find and add to my repertoire.

Leo is a lion, and one of the constellations that I feel actually looks like its supposed to:

Leo the Lion
Image by Backyard Stargazing

It reminds me of the sphinx:

What helped me to identify Leo was to find the sickle -- the curve of six or seven stars which I call the "backwards question mark".  The dot of this question mark is the brighest star in Leo, called Regulus, or Reggie for short. At #15, he is one of the brightest stars in the northern hemisphere. He lies almost exactly on the eclipitic.

Lying along the ecliptic, Leo is therefore a zodiacal constellation. This means the sun, moon, and the planets periodically pass through Leo. When I was first learning about it, in 2008, Saturn was moving around under Leo, though now it has moved on and is located in the relatively blank section of sky in Virgo and Lyra.

The sun passes through Leo from mid-August to mid-September, which makes Leo a nice constellation to look for in late winter and spring. I find it by locating the Big Dipper, and pretending it is dripping things. If it drips things down thru the cup, those drops would fall on Leo's head:

The Big Dripper and Leo

Image by Catawba Astronomy Club

Below is a more specific map of Leo.  With a telescope, Leo houses a few good Messier objects worth looking for, but none are good sights for binoculars.

Leo
Image from Wikipedia

Reflections on J-Term 2013

We just finished J-Term and I have so much to write about, but so little time to write, so let me just do quick summaries and if I have any time (this summer?) I'll come back and elaborate.

For those of you who don't know, at our school J-Term is a week-long opportunity for our students to take some unique classes and learn things their teachers don't normally get to do during the school year. For instance, many students took iPad video making, or an interesting Hunger Games exploration, knitting, chess class, etc. The teachers suggest offerings and the students sign up for three different classes they'd like to take.

This year I offered two classes: Astronomy (which I have taught before) and a new class which I called "Did You Get My Email?" but might more formally be called Digital Communications.

Star and Planet Locator
by Edmund Scientific

In Astronomy we learned a 15-20 constellations, discussed how to use a Planisphere, the idea of altitude and azimuth, how to find the planets along the ecliptic, and how the sun moves through different constellations (the zodiac) throughout the year. Next on the list would have been declination and right ascension, but we ran out of time.

The Star and Planet Locator made by Edmund Scientific is an great tool for teaching these concepts -- and at only $3.95 per unit it's one of the cheapest I could find.  I bought mine a few years ago and kind of remember a 25 for $50 deal so if you're interested in a classroom set, look around.

These worksheets I offered:

• Learning the Constellations: Identify the constellations you see in different maps
• Using a Star Finder:
• Using a Star Finder Part 2:
• Seasons: Questions regarding seasons and sun on star finder
• Angles Between Stars: measuring altitude and azimuth with hands, degrees, etc.
• Estimating Location of Stars: practicing altitude and azimuth with a star finder
• Celestial Coordinates: practice with declination and right ascension
• Stars and Heavens in Scripture: Bible passages referring to the stars and heavens
• The Star Clock: Using the big dipper to tell what time it is

The other class I taught was new to me -- Digital Communications. I'll admit I'm not proud of how this class turned out because I didn't put the time into it over Christmas break that I should have. In this class we learned about a ton of different technologies, leaning quite heavily on "How Stuff Works" descriptions of: the telegram, telephone, television, computers, hard drive, cd player, text messaging, email, radio, etc. We also studied binary numbers, and spent some time describing how computers convert all information into numbers, which are all converted into binary, which can mean everything can be stored ultimately as a handful of 1's and 0's somewhere.

I also did some hands on materials, though I had ambitions of doing way more. We played around with simple circuits, hooking up batteries and lights. We made a few electromagnets, and I showed them a homemade "byte" -- 8 bits -- which I made with just a piece of wood, 8 nails, and a about 40 ft of wire. I never used it in anyway besides holding it up occasionally when we discussed that 8-bits define a character in Ascii, or that three of these 8-bits define a color of an individual pixel in a picture, and so on.

I learned from this that I enjoy doing things hands-on and should take more time to make that happen in my classroom. I learned that radio shack has a lot of small circuit components for sale, such as LED's, solar panels, resistors, switches, etc and I have a lot of material now that I'll be able to use in our electricity unit in physics.  And I learned that classes will survive, even if you are fully prepped for them. Maybe that wasn't the lesson I should have learned -- but I did.

Magnitude of Stars

I remember one of the hardest things for me to understand when I first began studying astronomy was grasping the "magnitude" of stars. Magnitude -- or more properly -- apparent magnitude is a number that describes how bright a star or object in the sky appears. 

Star Magnitude Scale
Image by Astroplot

On printed star maps, you can't really show brightness very well, and so larger and smaller dots are made to try to trick your eye into seeing different magnitudes. Typically, a scale is provided like what is shown tot he right which you can use to identify the brightness of a star.

Star Magnitude Chart
Image by Royal Astronomical
Society of Canada

When astronomers first began describing the brightness of stars, they grouped all stars into six classes. The brightest stars were called first order stars, and the faintest visible stars were sixth order stars. Thus began the magnitude scale, a quite subjective process but useful none the less. Many of the stars that were first classified as 1's still have a magnitude of around 1 today, and the faintest visible stars are still given a magnitude of about 5 or 6 today.

As telescopes and binoculars were invented and turned to the skys, we realized that there were whole classes of stars we couldn't see. All of a sudden there were 7th order, and 8th order, and so on.  Now, with binoculars on a clear night, you might be able to see stars up to magnitude 9.  With a telescope and a clear night, perhaps even 10, 11 or 12. The earth's biggest telescopes can see stars of magnitude 22 (with a 24" lens) or magnitude 27 (with an 8m lens). And ones you are out of earth's atmosphere, the hubble space telescope can see magnitude 32.

Of course, all these numbers are pretty meaningless without some more precise way of defining them. As we developed ways of measuring how much light is visible instead of just eyeballing it, we could reclassify stars more exactly.  The earliest astromomer's estimated that 1st order stars were twice as bright as 2nd, and so on. Remarkably, without any tools to really measure light intake, they were pretty close. Turns out, to maintain the classifications of the early astronomers, a factor of about 2.5 is required instead. Though the whole system could have been scrapped and redone, astronomers chose a system that tries to mimic the original by using a logarithmic formula.

First, an arbitrary star had to be chosen to be a starting point for the scale. Astronomers chose the bright star Vega. This was set to be 0, and all other stars were compared in brightness relative to Vega. If Vega was 2.5 times brighter, that star was rated 1, and there are roughly a dozen that have magnitudes near one, which corresponded fairly consistently with the earliest classification of 1st order stars.

Stars that were 2.5^2 or around 6 times fainter than Vega were classified as 2's. There are roughly 50 stars with a magnitude of around 2.

The 175 or so stars that were 2.5^3 or 15 times fainter than Vega were classified as 3's.

The 500 or so stars that were fourth magnitude are 2.5^4 or roughly 1/50th the brightness of Vega.

All stars apparent magnitude's then can be classified by:

b is the brightness of a star -- which is more sophisticated than I can explain or even fully comprehend myself. But the ratio bx / bvega is what's of importance for classification purposes.

Not all stars fit exactly into a classification, but with this new scaling system, one could define a stars brightness precisely in between magnitudes, and so stars could now be given magnitudes of 1.3, or 4.2. You can always compare a stars brightness to Vega by using the factor of 2.5^m.  For instance, the North Star has a magnitude of 1.98, and so Vega is 2.5^1.98 or about 6.1 times brighter.

There are some stars that are brighter than Vega -- for instance, the brightest star Sirius is 3.6 times brighter than Vega. To determine its magnitude then find -2.5 log (3.6) which is -1.4, and so there are some stars that  have negative magnitudes. In fact, some planets such as Venus can get even brighter and have a lower magnitude. Turned to the moon, the magnitude can get as low as -12.74, which means it is 2.5^-12.74 times fainter, or 2.5^12.74 times brighter than Vega. And shining more than 40 billion times brighter than Vega, our sun during the day chimes in at -2.5 log (40billion) =  -26.

To finish, here's a map of the Big and Little Dippers, to help you become a little more familiar with some of the numbers involved. Try to identify for yourself which stars are the brightest and faintest, and compare them with the numbers listed below.

Magnitude of stars in Ursa Major and Ursa Minor
Image by AstroBob

The Constellation Canis Major and Minor

This post is the one of a series on constellations and posted throughout the year as each constellation comes into prominence.

I came across this article on New Years Eve which inspired me to write a post about the star Sirius, and its constellation.

Canis Major and Canis Minor are two constellations near the famous Orion, and are worth knowing because they house two of the brightest stars in our sky.  Canis means Dog, and so these constellations are the Big Dog and the Little Dog. I see a bad stick figure and a pair of dots myself, but I suppose with a little imagination, it wouldn't be too much of a stretch to see them as Orion's hunting dog's, following him into the woods perhaps.

These constellations are only just starting to come out in the evening hours during winter -- so unless you're out relatively late, you might not see them. The inspiring article described Canis Major as reaching it's highest point in the sky at mid-night on New Years Eve, which means if you went out at a more "normal" star-watching time at least for parents such as myself -- say 7 or 8 pm -- it won't be up yet.

Fall Mornings
Winter Nights
Spring Evenings

The dog constellations serve to tell me about our progress through the school year.  At the beginning of the year, and through first semester, I tend to see them on my drive in in the mornings. As the year progresses through winter I won't see them as often, as they'll be out in the middle of the night. As the year reaches the end, these dogs are out and observable during family-friendly observing times of just before bedtime during the spring months -- March April or May.

Canis Major is a southern hemisphere constellation -- one that is approximately 20° below the celestial equator. At my latitude, that means it is not out for too long each day -- only about 8-9 hours a day. Canis Minor on the other hand is just barely a northern hemisphere constellation - approximately 5° above the celestial equator. That means we can see Canis Minor longer each day -- about 12-13 hours a day.

One of the reasons for observing the Dog's is because of the bright stars they contain. Sirius is the brightest star seen anywhere from earth, short of the sun. It's the bright one in Canis Major -- or the head of the stick figure in my  minds workings. Procyon in Canis Minor is another bright star - 6th brightest in the sky for Northern observers. I often confuse the pair of stars in Canis Minor with the pair in Gemini, as they are about the same width in the sky. You should be able to tell the difference two ways. First, in Gemini they are both bright stars, where as Procyon far outshines its partner in Canis Minor.  Second, Gemini is to the right of Orion and Canis Minor is above and to the left.

Many people describe these two bright stars, and the red giant Betelguese as forming a great Winter Triangle in the sky. While I could draw this triangle in the sky -- it doesn't really pop out at me.

Winter Triangle

Another feature of Canis Major, is that it contains one of the biggest known stars -- what Louie Giglio described as "The Big Dog Star" in one of my favorite sermons of all time: How Great is Our God. At this link you may begin watching the portion where he describes The Big Dog Star. In it he compares a series of increasingly large stars with the earth as the size of a golf ball. On that scale, VY Canis Majoris would be the size of Mount Everest. Somewhere in Canis Major is a star too faint for you to see that is larger than the orbit of Jupiter around our sun. Put another way, if this star was where our sun was, we would be IN it -- not looking at it, and so would Mars and so would Jupiter. 

The Constellation Gemini

This post is the one of a series on constellations and posted throughout the year as each constellation comes into prominence.

Gemini is an important constellation to learn for a number of reasons. Known as the twins, it is home to two of the brightest stars in the sky -- Pollux and Castor. Pollux on the left is the 12th and Castor the 16th brightest stars in the Northern hemisphere. These stars are the heads of two twin brothers standing side by side. On a good night, you can see lines of stars outlining the bodies, as shown below:

Gemini
Image from Wikipedia

Gemini is one of the 12 zodiacal constellations, which means it lies along what's called the ecliptic. The ecliptic is a circle of constellations surrounding us which lies along the same plane as the planets and the solar system as a whole. Therefore, any planets you see are always somewhere along this plane. Gemini is therefore useful to know as planets are often located nearby.  For instance, the bright planet Jupiter will be approaching Gemini early 2013 and spend late 2013 and most of 2014 within the region.

Being along the ecliptic means that the moon will pass through the constellation once a month.

Being along the ecliptic also means that the sun will pass through the constellation (rendering it invisible of the brightness of the sun) once a year. The sun passes through Gemini from May 21 to June 20 each year. During the winter months, the sun is in the opposite side of the sky which makes Gemini an easy constellation to see.

Below is a map of the surrounding constellations for the evening hours in December.

2012 December skies ~ 7pm
2013 January skies ~ 6pm
Image by Skymaps

As you can see from this image, Gemini is pretty easy to spot -- being above and to the left of the familiar constellation Orion. Finding the bright head stars should be easy to do, but next time you have a clear night, see if you can identify some of the other stars making up the body. I have often seen them as forming the Greek letter Ω (Omega).

Of course, a description of Gemini would be incomplete without mentioning the Geminids, a meteor shower that is one of the best in the year. During the nights around December 13 and 14 each year, many bright meteors (sometimes around 100 per hour!) can be visible. They emanate from Gemini - which means they will go outwards away from Gemini. They don't always begin in that constellation, but their paths will tend to point away from Gemini more often than not. Most meteor showers are best observed in the wee morning hours.

A good binoculars object, M35 is a nice cluster of stars that will be my goal to find in the next month. It has the width of the moon, and contains well over 200 stars, but most are invisible to the naked eye. Castor is supposedly juggling it on his foot like a soccer ball.

The Coathanger

The last couple of nights have had some clear skies in Michigan, and since I can't sleep (thinking about the imminent second daughter coming any day now) I have been doing a lot of stargazing lately. I was reminded of the amazing creativity and power of God as I brought out a new simple tool to help me stargaze, a pair of binoculars.

The first time I saw in an astronomy book a picture of a family using binoculars to look at the stars, I thought "Wow -- how desperate!"  I had major skepticism on how well they could really help the view. But as I tried them this week (and my binoculars are by no means that spectacular -- they're small) I must admit being amazed at how much more I could see. Yes, it made things slightly bigger -- mine were 7x -- but more impressive to me was that you can see more stars!

The Coathanger

Nothing made that more evident then when I discovered a new constellation (new to me that is) called the Coathanger. I was just wandering around looking at the stars (actually, following one of satellites that I couldn't see with the naked eye) when I ran into a tight grouping of stars, technically an "open cluster" that I instantly recognized as "The Coathanger" that I had coincidentally read about that morning. Typically constellations don't look anything like they're supposed to for me, but this one most definitely did.

Technically, the recognizable shape of stars called the Coathanger is an asterism, as opposed to a constellation which is really just a chunk of the sky. As another example, the big dipper is another asterism, that is located in the constellation Ursa Major.  What made the Coathanger so impressive to me, was the fact that I cannot see it at all, without my binoculars. Click here for more information on Brocchi's Cluster, or Collinder 399, which is the catalog name for the cluster containing the asterism of the Coathanger.



If you'd like to find the Coathanger yourself, Here's a map of the stars that are visible in the evenings of midsummer in the Northern Hemisphere. If you need to look up different latitudes or months, try this more general link. 

Before we find the Coathanger, let me set the stage for you. If you have the map in front of you, it might help as I describe what you can see. To the northwest you should see the Big Dipper. I recommend you start by looking at the Big Dipper through your binoculars, and practice moving from star to star to get a feel for how big the binoculars are, and how many more stars you can see than you're familiar with.  For my set, each major star in the 7-8 that make up the dipper required me to move about one field of view in my binoculars, and it took some time before I could confidently move from star to star, so don't be surprised if it's a little difficult at first.

To the right of the big dipper, in the northeast, you'll find the "W" which is in the constellation Cassiopeia.

Behind you, in the south along the horizon, you should be able to find Scorpius, which is in my opinion a fairly obvious constellation that looks like a scorpion. Just behind it, to the left, you might be able to spot "the teapot" in Sagittarius.

Sky Map provided by skymaps.com
Looking east, this snippet covers from
about 45 degrees up to directly overhead.

Now turn towards the east, and then look straight above you. The point directly above you is called the zenith and the bright star Vega is pretty close to the zenith during the summer evening hours. You should come back and look at the stars around Vega in Lyra, as there are some beautiful and obvious double stars there that pop out with a binoculars, but try to locate the other constellations as shown in the snippet of the map above.  Below and to the left you should see what I call the "Northern Cross" which is in the constellation Cygnus, a swan flying south over the Milkyway river.  Below and to the right is a less obvious constellation of stars called Aquila, an eagle who is also flying south.

I find the Coathanger most easily by finding the three right stars in Aquila's tail, (the middle one is the brightest, and is named Altair) and following that line up about two binoculars widths (10 or so degrees). You should be able to see CR399 labeled on the portion of the map above. CR 399 is actually a little wider than a full binocular width for me, and coat hanger is slightly left of the line. If you see it, you'll know, because the line of stars marking the hanger part is so perfectly straight that it jumps right out at you.

Let me know if you spot it!  Also, be sure to say high to Jolly Mon and the Dolphin, my favorite constellation (Delphinus) while your looking in his neighborhood, and have fun checking out the skies!

Perspective in astronomy pictures

One movie that had a profound effect on me was E.T. Besides opening my eyes to a much larger world besides the earth we live in, I remember being amazed at Spielberg's beautiful filmwork and storytelling. Especially striking however, an image that often pops in my head is the picture of Eliot and the alien riding their bike transiting the moon. I must admit being tricked by the picture for many years and longing to see a moon that was that big! I always loved seeing the moon on the horizon because of the optical illusion it provides, but the illusion was never THAT big!  I want the moon to fill up more than half the sky like that! 

Of course, I learned later the moon itself was zoomed in on, the biker superimposed on top, but still, what a great picture!  

The thought for today is to calculate how far away are Elliot and the alien, given what we know about the true size of the moon? And we'll look at another "true" photograph from yesterday to calculate how far away the fisherman were.

One important fact that we need to know is the angular width of the moon. If you've been following the Summer Math Series so far, you'll remember I told you the moon and sun both occupy approximately 1/2 degree in the sky. This coincidence is a gift of God allowing for eclipses and measuring the solar system, but more about that later.  

I "photoshopped" the image of E.T. to see how wide the bike and boy are. It looks like 4.25 "bikers" fit across the moon, so that means the angular size of a biker is:

Using some trigonometry we can calculate the distance away the biker is. First, a triangle picture.  I am assuming that the biker in the picture is pretty much perpendicular to me, and so I draw a right triangle as shown:

The angle, height, and distance are all related by the tangent function:

   

That means that if we know two out of those three things, we can calculate the third. Earlier we measured the angle, and if I assume the height of the biker to be approx 5 feet, we can calculate the distance by rearranging the equation:

   

 Notice, if you type this into your calculator, you might get a more precise number -- I actually got 2864.786067 feet. That amount of precision is misleading, because I made two pretty uncertain measurements in the height of the biker (how do i know he isn't 5' 2" or 4' because he's sitting down?) and in the angular width of the biker (maybe its more like 4.5 bikers per moon, or only 4?)  When this situation arises, one rule of thumb is to round to as many numbers as you had when you made your assumptions. Since 5' had only one digit, I'm going to round to the nearest 1st digit.

So, if this picture was real -- the bikers would have had to be about a half mile away, giving you some idea of the telephoto lens required to make the shot.

Using similar analysis, we can return to the real picture that we looked at yesterday and calculate how far away the fisherman are:

The fisherman are approximately 2 suns tall, or 1 degree.  Assuming that they are adults of approximately 6 foot in height, I calculate:

To me that looks about normal for a foot ball field away, so this picture was probably taken with very little zoom. 

How much daylight is left?

In yesterday's post, we learned about the angle, the foundation measurement tool for observing things in the sky. Today you'll use those tools, and your hand, to get a quick estimate of the amount of daylight left.

First, we should figure out how quickly the sun moves across the sky. Because the earth rotates once every 24 hours, the sun appears to move across the sky once every 24 hours. To be more specific:


Since the width of your hand spans approximately 10-15 degrees (mine is relatively "fat" and covers 15), you can use it to approximate how far the sun will move in an hour. So, what I've done on many occasions is counted how many hands up from the horizon the sun is, and approximated how long till sunset. Since you have 4 fingers, they make decent 15 minute approximations.

A few notes -- first, the sun does not travel straight down, but at an angle towards its final resting place. In the Northern Hemisphere (specifically North of the Tropic of Cancer line) where I'm guessing any of you readers are from, the sun will move further north as it sets, so you might need to tilt your hand somewhat to accommodate.

Secondly, it doesn't become instantly dark once the sun sets, but there is plenty of twilight to help you. I typically figure on an additional hour of twilight before it gets too buggy or dark to want to be outside.

If we know the width of the sun, we can calculate how long sunset will take, from the moment the sun first touches the horizon till it dips behind the horizon. The "width" of the sun, and the moon for that matter, is about 1/2 degree. So once the edge of the sun touches the horizon, you'll have: to enjoy the sunset before its gone.

You can also use this fact if your clock on your camera ever goes bad to tell when a picture was taken. In photoshop (who am I kidding... i just used MsPaint, I can't afford photoshop) I projected where the sun was going to travel, and more importantly how many "suns" were left in the sky. Since five suns were left, this picture was taken approximately 10 minutes before "sunset" which you can look up for any particular place and day.

Astronomical Angle Measurement

As many of you know, I get excited about astronomy. So this post is the first in a series devoted to understanding the math behind the measurements of our solar system.

Next clear night, go take a look at the stars, and try to identify some of the constellations. If you want some help, sky maps for June and July are available that I like. For the sake of this post, try especially to identify the big dipper -- which will be visible in the Northwest, about halfway between the horizon and the "zenith" which is the point straight above you.

If you've never done it before, hold out your hand straight in front of you, about as far as you can reach, and see how much of the big dipper you can cover up. Don't worry about looking silly or foolish -- that just means you're doing something cool. I do it all the time and no one ever mocks me about it.

Every time you do this, you should notice that the dipper looks about the same size. What you have done is effectively measured the size of the constellation, in a repeatable way. Now you can try to find Cassiopeia (the W in the North) or the teapot (part of Sagittarius, low in the southeast) and compare the size of those constellations with something more familiar.

Maybe you'll be fortunate enough to see the moon on this night, it will be about half full. Hold up your pinky and I bet you can make it disappear? Try it when it looks "HUGE" near the horizon and you'll realize how it's just an illusion. Try the same thing with the sun today or the next day and see if you can compare how big they look.

Astronomers have tools a little more sophisticated than their hands by which to measure things, but you can estimate the same sorts of measurements they make.  What you are measuring specifically is an angle. Angles can be measured from lots of places, but usually they are measured up from the horizon, in which case they are called "altitudes."  Below I am demonstrating two altitudes approximately 20 degrees and 10 degrees respectively.

Approximately 20 degrees

Approximately 10 degrees

The outstretched hand represents approximately 20 degrees for most people -- and the closed hand width represents about 10 degrees. You can measure how accurate your hands measure angles by trying to measure how high it is from the horizon to the zenith -- straight above you. It is exactly 90 degrees, and so you should be able to measure 4-5 hand-spreads up, or about 9 hand widths.

Some other measurements I often use are the width of my thumb or pinky:

Approximately 2 degrees

Approximately 1/2 degree

So? How big is the big dipper? How many degrees is it from the big dipper to the North Star?

Notes from Case for a Creator

Notes from Chapter 6: Evidence from Physics

In this chapter, Strobel described the anthropic principle.  Anthropic is Greek for man, and this principle is the idea that the "settings" of the universe are just prefect for man to exist.  I was disappointed that the chapter did not go into as many details as I would have liked -- so maybe I will have to do so myself, but don't expect that in this article... :-).

One of the settings mentioned was

 the gravitational constant: G = 6.67300 × 10^-11 m³ kg^-1 s^-2  

This determines the strenght of the attraction force between objects with mass.  If this were much bigger, you would find yourself uncontrollably attracted to the desk, your laptop, your cat, and, you know -- things like the sun, and the center of the galaxy.  In short, the universe would collapse upon itself in the big crunch -- or at the very least, the size of the universe would be smaller.  If this value were much smaller, the stars and planets would not have formed as science suggests they would, nor would they hold together.

The other settings described went above my head, and I cannot begin to explain them here. But the overall argument is that there is too much "coincidences" in the universe for it to mathematically happen by chance.  The anthropic principle is one of the most convincing and powerful suggests that a designer is at work.  Imagine I propose to you a $1000 bet that I can flip a coin 25 times and it get heads every time. If you accept that bet, and then I actually perform the feat -- would you pay me $1000 -- or would you assume that I some how cheated?  Imagine now, the universe is the product of a coin flipped billions of times -- and it worked out as remarkably as it has.  Which requires more faith -- that it occurred by chance, or that something fishy is going on.

Science's best attempt at eliminating God from the coincidence is the multiverse (many universe) theory.  They suggest that many universes exist, and we happen to be living in the one that is suitable for life. This is the idea behind the lottery.  Winning the lottery is next to impossible -- but there are so many tickets bought and so many people playing, that its inevitable that SOMEONE will have the winning ticket, sometimes. Even if this is the case, though there is no evidence yet that another universe exists anywhere, let alone enough universes to cover the chances required to bring life -- science then has to explain how all those universes came to be. And, if we are truly "fortunate" to be living where we do, what does that mean for life?

I believe the hypothesis of a creator and a super mind controlling the laws of the universe is not only the simplest explanation, but He answers the "so what" question too, describing how we should live being as fortunate as we are.

Additional resources:
  Large number coincidences and the anthropic principle
  Evidence of Fine Tuning - contains a list of 34 measurements and explains why slight increases or decreases would make the universe impossible or inhabitable.

Notes from Case for a Creator

Just some notes from "The Case for a Creator" by Lee Strobel

Chapter 4: Where Science Meets Faith

Strobel interviews Stephen C. Meyer PHD

Meyer objects to the belief that Science and Religion cover completely different realms, which he calls NOMA (non-overlapping magisteria).  He argues that Christianity makes many factual claims, that are going to intersect with science and history, and must either be supported or denied.  Meyer suggests science shouldn't necessarily be anti-God.  He prescribes a philsophy of "inference to the best explanation" or abduction. His findings suggest that "Science, done right, points to God."

He provided six examples that are best explained by theism.
   1. The Big Bang requires a cause
   2. Antrhopic Fine-tuning: The universe has finely tuned constants (e.g. Gravitational constant, expansion  rate, etc.) that if any different would make life impossible
   3. Information required for origin of life
   4. Irreducibly complex objects in microbiology
   5. Cambrian Explosion, or the biological "big bang" where dozens of new life forms seemed to appear without transitional intermediates
   6. The consciousness of man.

Strobel asked about supposed bad design (a topic called disteleology) and whether that points to a flawed designer.  Meyer suggested most bad design examples can be explained in three ways:
   1. We don't know enough yet
   2. The design was optimized and constrained -- a laptop user can complain that the screen is too small, but if it were bigger they would complain that it was too heavy, or too expensive.
   3. Theism also posits that the curse of sin is causing a decay of creation.

Articles by Stephen Meyer:
   Evidence for Design in Physics and Biology
   Modern Science and the Return of the God Hypothesis

Other Articles Mentioned:
   Dembski, William.  The Design Revolution: Answering the Toughest Questions about Intelligent Design

Blue Marble

Moon Video

Got the telescope and the camera out tonight -- it was a beautiful night for stargazing.  The moon was out at first quarter, and Jupiter and its moons were out and shining brightly too.  We saw four moons at 8:00 when we first spotted it through the telescope, and when I came back at 10:40 I saw only 3, so I think one is in transit behind or before the planet.  But our moon made for some good viewing.  Below is a video clip of what it looks like through the telescope.