Building a Solar Funnel

This afternoon I went to the library to read the recent issue of Sky and Telescope. Lo and behold, there is an article on how to build a solar funnel. 

Coincidentally, I happened to have built one earlier this morning!

First, you need to get a funnel from the auto supply store.  Most funnels won't work.  The neck needs to be wide enough to accomodate an eyepiece from your telescope.  A Blitz Super Funnel (#05034) works perfectly.  I couldn't find one at any of the auto shops, but found one at KMart.

You also need a couple of hose clamps - a small one (1.5 inch) and a large one (5 inch). 

The one thing you will need to order is the rear-surface projection screen.  I ordered a Da-Lite High-Contrast Da-Tex rear-surface screen #95774.  I bought two pieces, each one-square foot in size, but you only need one (I assume problems will happen, hence the duplication). 

Step one, saw the funnel neck -- about ten inches from the large end, and seven inches from the small end.

Sand the rough areas.

Cut into the small end, about an inch or two deep in two places - this will allow a hose clamp to sqeeze this end and secure the eyepiece.

Insert the eyepiece of your choice - I used a 12.5 mm.

Use the small hose clamp to secure the eyepiece in place.

Wrap the rear-projection screen fabric on the large end and secure it with the larger hose clamp.  Either side of the fabric is as good as the other and it doesn't matter which side faces in or out.

It is best to use the solar funnel with a refractor, but I don't have one - so I used a reflector.  The problem with using a reflector to look at the sun is that the mirrors can be damaged.  Therefore, one has to reduce the amount of light going into the scope.  I drilled a 1.5 inch hole into the end cap used in storing the telescope, but this seemed to reduce too much of the light.  I ended up lifting the cap and holding it slightly ajar to allow more light to enter.

I didn't read the instructions in Sky and Telescope, but I assume they are sufficient. 

It may not be visible in this image, but the projection does so sunspots. 

Is it worth building one of these?  It is not as good as a direct view I get with the Questar or the Coronado PST, but it is sufficient for public viewing where two or more are gathered together.


Review of the Solarscope

I purchased a Solarscope in preparation for the Venus Transit, but also to use with elementary students at my wife's school.

These products are sold at www.solarscope.com.  The devices project the image of a slightly magnified sun onto a screen within a box, shaded from excess interfering light.

There are four editions, with the price ranging from $89 to $249.  The one that I really wanted was the "traveler's edition" which can break down into a smaller package for transport - but I did not think I needed to spend the $249 on this edition.  I wanted something more durable than the less expensive ones, so I bought the "wooden edition" for $189. 

As expected, it came shipped in a flat box and assembly was required.

The instructions could have been written with greater clarity.  Instead of making separate assembly instructions for each product, they are combined so that the reader has to be attentive as to whether a particular step applies to the Traveler or the Wooden Edition.

The instructions are also incomplete.  On the last page, Step 14 refers the reader to Step 5 in the Instruction Manual, and Step 10 refers to Step 15 in the Instruction Manual.  What is missing is any reference to completing the project are references to Steps 16, 17 and 18 of the Instruction Manual. It is not difficult to figure out how to complete the project, but it was disconcerting since one of these steps says, "Caution, once the screw cap is fastened, the lens cannot be dismantled!"

The terminology in the instructions are also inconsistent.  The instructions refers the reader to "The Instruction Manual," but among the documents, there is no such document.  The document in question is actually entitled "User's Guide."    The parts are also inconsistently labeled.  In the parts list there is a "lens tube" but in the text it is simply referred to as "tube." 

The instructions are not specific and each step must be carefully thought out during construction.  One of the panels is white on one side and tan on the other.  The instructions do not state this, but the white needs to face in, not out, in the construction.

Extra care should be taken in placing the panels into the grooves on the sides.
You'll need a hammer to gently tap the panels into place.

Be sure to check the intersection of the panels and sides to be sure there are no gaps, as is the case above.  This is easily corrected if done before the glue dries.

This tube-like stopper secures the mirror in place.  The problem is - which direction to insert it?
On one side it is solid, and the other side it is hollow.  My suggestion is to have the solid end opposite from the mirror.  That way it is easier to press the stopper all the way against the mirror, as I did with a screwdriver head as seen below. 

Once constructed, the Solarscope does everything it advertises. It is very easy to align for viewing.  I did find that it is easier to manage when the sun is lower in the sky, rather than at "high noon." 

Focusing is easy, but I did find one problem here.  I found was that there was too much play in the lens tube to suit me.  Maintaining focus was not easy because the tube tended to slide on its own. To resolve this problem, I took some parts I found in my garage. I took a plastic ring that was wider than the tube, drilled a hole in the side, and used a wing screw to build a device to secure the lens tube in place.

Don't expect the image of the Sun to be very large.  There is not much magnification power in the Solarscope.  It is sufficient to see the sunspots, but not enough to see detail of the spots.  It is perfect for eclipse viewing.  I am confident that it will be sufficient to see a transit of Venus.  I am not sure that it would be sufficient for a transit of Mercury - but this statement is purely speculation. The solarscope's web page says it is good for viewing transits of the smaller planet, so I would assume that is true - but for me the jury will be out on this one until 2016, when I hope to next see a Mercury transit. 

It will be excellent for use with school groups, and I look forward to the next time I spend a day at my wife's school with her students.

All in all, I rate this product very highly.  I would like to see them work on securing the focusing system, and would definitely like to see them revise their assembly instructions.  All in all, well worth the money.


Dark Nebulae

These images were taken with the online telescope system, Slooh.  Each of these objects is a dark nebula.

Barnard 93

This object was discovered by E.E. Barnard in 1913.  The dark nebula appears like a dark comet and obscures parts of M24 (the Small Sagittarius Star Cloud).  It was one of the first dark nebulae to be discovered. 

Barnard 145

   Barnard 145 is the horizontal dark area slightly below center in the image below.

Barnard 161

 Barnard 168

Barnard-168 and Cocoon Nebula are found in the same area. The long dark nebula B168
is seen extending from it across above. 

The Cocoon is primarily a red emission nebula (Sharpless-125. Embedded in the nebula is open cluster IC 5146.


Annular Eclipse - May 20 2012

Today there was an annular eclipse of the Sun.  I was not in the path of visibility, but thanks to the Internet, I was able to watch via different viewing sites in China, Japan, California, New Mexico and Nevada. 

An eclipse of the Sun happens when the Earth, Moon and Sun are in a straight line, with the Moon in the middle.  If the orbit of the Moon was in a perfect circle and one the same plane as the orbit of the Earth and Sun, there would be an eclipse every month.  But that is not the case.  The Moon's orbit is a slightly different plane than that of the Earth's orbit around the Sun, so eclipses are unusual and worth getting excited about.

By far, the most interesting is the total eclipse of the Sun.  That happens when the Moon is just the right distance from the Sun so that the disk of the Moon completely covers the disk of the Sun, making the Corona of the Sun visible.  

Because of Kepler's First Law of Planetary Motion, the Moon orbits the Earth in an ellipse rather than a perfect circle.  This means that sometimes the Moon is closer to the Earth during an eclipse so that it doesn't cover the Sun's disk completely.  We call these "annular eclipses."  Annular, not "annual" -- which comes from the word "annulus."  This is a word that is sometimes used in math or geometry, but not often used in common English.  It comes from the Latin "annulus" meaning "little ring."  

When the solar eclipse occurs so that the Moon is too close to the Earth to completely cover the Sun's disk, what we see is a "little ring," or annulus of the Sun's disk.

Here are some pictures from Reno, Nevada, USA, that I snapped every ten minutes via USTREAM.com

8:20 PM Eastern Time

8:30 PM Eastern Time

8:40 PM Eastern Time

8:50 PM Eastern Time - and the clouds roll in!

9:00 PM Eastern Time - and the people on location are getting nervous with the cloud cover.

9:10 PM Eastern Time - the clouds are almost gone.

9:20 PM Eastern Time 

9:29 PM Eastern Time - just at the crucial moment, clouds threaten!

The annulus is almost complete

A perfect ring of fire!

And now we begin to watch the reverse process.

This was a view via Slooh.com from Mt Fuji

USTREAM.com had several channels, one of which showed a multitude of Asian sites.

Map of Visibility of Transit of Venus

The chart above shows the areas of visibility of the June 5/6 transit.  For North America, the transit will be visible on June 5 and will still be in progress as of Sunset.  In parts of Africa, Asia and Europe, the transit will be visible on June 6 and will be in progress at Sunrise.  For parts of Asia and Australia, the transit will be visible in whole or in part.


Understanding Kepler's Three Laws of Planetary Motion

Several years ago, Sky and Telescope published my work on "Pittendreigh's Law of Planetary Motion."  It was a joke, but there is truth to it.  Pittendreigh's Law states that the earth is moving faster and faster around the sun every year you age - and those of us who are getting older can certainly attest to this fact!  The older you get, the faster the years go by. We can also attest to Pittendreigh's Law of Gravity - because the earth is moving faster around the sun with every year we age, gravity is getting stronger.  Take my word for it - that 10 inch reflector telescope used to be so easy to move into the backyard.  But with gravity getting stronger every year, I struggle with it more and more.  By the time I'm 80, that thing will weigh a ton!

On a serious side, Kepler produced three laws of planetary motion.  I'm amazed that he was able to develop these at the dawn of modern astronomy.  He came up with two in 1609 and the other in 1619.  Keep in mind Galileo applied the telescope to astronomy for the first time in 1609. 

Kepler's laws are:

1.  The orbit of every planet is an ellipse with the Sun at one of the two foci.
2.  A line joining a planet and the Sun sweeps out equal areas during equal intervals of time.
3.  The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit.

So, what does all this mean?

Let's take Kepler's First Law.  In Kepler's mind, God created a perfect and orderly universe.  That meant that the planets orbiting the Sun must do so in a perfect circle.  Observations and calculations of Mars and other planets did not fit that theory of orbits being perfect circles.  God, it turns out, may have created a perfect and orderly universe, but as the Creator is more complex than Kepler expected, God's perfect universe was more complex.  And more interesting.

The planets do not orbit in a perfect circle, but rather in an ellipse.

Now a circle is an ellipse, but it is one specific type of an ellipse.  An ellipse can be thought of as "sort of a round thing."  Or more accurately, an ellipse is a circle or oval.  Or to be exact, an ellipse is a  plane curve, especially a conic section whose plane is not parallel to the axis, base, or generatrix of the intersected cone, or the locus of points for which the sum of the distances from each point to two fixed points is equal.

If the plane is parallel to the base, the ellipse is a circle.

If the plane cuts into the cone at an angle, the ellipse is not a circle but an oval.

In other words, an ellipse is a sort of round thing.

But more than that, an ellipse has two focal points, or two focuses -- or since "focuses" is not the grammatically correct plural of a focal point, we use the term "foci."

What are these foci?  Where do they come from? 

Keep in mind, Kepler's First Law says, "The orbit of every planet is an ellipse with the Sun at one of the two foci."  So if the Sun is at one foci, what is at the other foci and how do you know which of the two foci is the Sun?

The answer is simple, but first you have to understand a little more about the nature of an ellipse, which is about to get a little more complicated than just "a sort of round thing."  After all, the borders of the states of Colorado or Texas or "sort of round things" and no decent planetary orbit would ever look like Colorado or Texas (no disrespect to the residents of those states)

For a moment, let's start over in thinking about how to define an ellipse. Let's start with the two foci. 

Now let's connect the two foci with a string.
 Now let's tighten the string so that it does not hang lose:

 Now let's move the string around, keeping it tight, so that it moves from one place to another. 
Let's say I keep track of the extreme point of the string as I move it from place to place.  And then let's say I connect those dots where the string had been extended as I moved it around.

Hey!  I have just formed an ellipse.

Not only that, but I have two focal points in that ellipse.  One focal point has one end of the string, and the other focal point has the other end. 

The Sun goes on one of those two foci.

What goes on the other?

Nothing.  It is empty space.

How do you know which of the two foci is the Sun's position?  Doesn't matter.  Either one will do.

Now back to Kepler's First Law of Planetary Motion:  "The orbit of every planet is an ellipse with the Sun at one of the two foci."


Now for the Kepler's Second Law of Planetary Motion: "A line joining a planet and the Sun sweeps out equal areas during equal intervals of time."

Let's look at the image below.  You have the Sun, represented in yellow.  A planet, represented as green, and the Sun is at one foci of the ellipse and the planet is orbiting along that elipse.  The planet is at a specific point in time, which we could call January 1st, but for our purposes, we will call "Point A."

Let's say a week goes by.  Now the planet is at "Point B."

Now let's say an EQUAL amount of time goes by - one more week.,
and now the planet is at "Point C."

Kepler's Second Law says that the area of the triangle formed by A, B and the Sun,
 is equal to the area of the triangle formed by B, C and the Sun. 

Let's give our imaginary planet a year of 8 months.  Take any of the two shaded areas, each representing a single month, would have equal areas.

One of the implications for this is that the planet moves slower when it is far from the Sun, but faster when the orbit takes that planet closer to the sun.

Now let's go to Kepler's Third Law of Planetary Motion:  "The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit."


What's a "semi-major axis" of a planet's orbit?

If we are going to understand what a semi-major axis is, it sounds logical to first understand what a major axis is.

The major axis of an ellipse is its longest diameter, a line that runs through the center and both foci of the ellipse.  In other words, the two ends of the line would each be at the widest point of the shape of the ellipse.

The semi-major axis is one half of the major axis, and thus runs from the center of the ellipse, through one of the two foci of the ellipse and to the edge of the ellipse.

Essentially, the semi-major axis is the measure of the radius of an orbit taken at the orbit's two most distant points.

Now that we cleared that up, what was Kepler's Third Law again?  "The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit."


Maybe it would help if we expressed it as a mathematical formula:


OK, each of these letters means something, so let's take a moment to interpret them.

The letter "T" represents the orbital period.  It can be a year, days, seconds, whatever.  But I have to have a way of telling the "T" or the orbital periods of the two planets apart, so I'll give each a little subscription.

The little subscriptions on both sides of the equations designate Planet A or Planet B, so that on the first side of the equation, you have the orbital period of Planet A divided by the orbital period of Planet B.

On the other side of the equation you have this lower case "r."  That equals the average orbital radius of the planets, or that "semi-major axis."

There is a little more to this equation.  If you look at the upper right corner of each equation, you will see that one side of the equation will be squared and the other side will be cubed.

So let's give it a try.

Since we are currently waiting for the Transit of Venus, let's play with Venus and see how far away it is from the Sun.  Since Kepler's Third Law of Planetary Motion compares two orbital bodies around a central object, we don't really need to know anything about that central body, the Sun, but we do need to know something of another planet with which we can compare Venus.  Let's take Earth.

We know that Earth has an orbital period of 365.245 days and that it's semi-major axis is 149,598,261 km.  How do I know these things? I looked it up online.  That's OK, because in order to use this formula, you have to have some known elements of the equation. 

As for Venus, we know its orbital period is 224.7 days.

So let's plug these figures into our equation.

Our next step is to have both sides speak the same language.  One side speaks the language of "days" and the other side speaks the language of "kilometers." We want the answer in terms of distance, so the "days" on the top and bottom of the left side of the equation cancel out, so let's take them out of our equation and just leave the numbers.

Next step, divide 224.7 by 365.245.

Next, let's square the result of that division problem.  To "square" a number is to multiply it by itself, so .6152 times .6152 gives us .3785.

Now we can make this equation look a lot simpler if we take the cube root of both sides.  The cube root of .3785 is .7233.  By taking the cube root of the other side, we just remove the parenthesis and that cube number in the upper right corner. 

Now the equation is looking much simpler.  Let's get the unknown factor, the radius of Venus' orbit, or the semi-maximum axis, all by itself.  To do that, let's multiply both sides by 149,598,261 km.

So, there is our answer 108 million kilometers.