Geometry, Trigonometry, and Amateur Satellites

Back to Part III. I'm still playing around with building a satellite tracking application. I'm helping with a special event station to help raise awareness for the Friends of Science East's effort to restore Tesla's last lab, Wardenclyffe, in Shoreham, NY.

First, the good news, the satellite pass finder and viewer is up and running at

http://copaseticflows.appspot.com/findsat!

Just drag the yellow thumbtack to your location and click the 'Passes' button and all the radio visible satellite passes for your location will be listed. By clicking on the map checkbox for any pass, you can display it on the globe. You can see how visible a pass will be from a city building by positioning yourself near the building and looking up for the pass. The app is still very beta, so please let me know if you see anything that could be better.

One of the big steps in getting the application to work was determining if a satellite would be visible over the horizon. To do this took some geometry and a little bit of trigonometry. The very same rules that they tell you to memorize in high school, but you can't see where you would ever use them. This is where!

For the mathematically curious, here's what I had to do. It follows from the proof drawn up by the folks at the Northern Virginia Community College. If you think about where you can see a satellite from on earth, it's where the earth, (the horizon), isn't getting in the way. If you draw a line from the satellite that's tangent with the earth, then, where that line meets the earth, anyone to the left of it in the picture below won't be able to see the satellite, and anyone to the right will.



The question is, given the height of the satellite the radius of the Earth, and the location on the Earth directly below the satellite, how do you figure out where the line meets the earth? The queston framed another way is how do you draw a line from a point so that it is tangent to a circle? First, draw a line from the point, (the satelite), to the center of the circle. Then, draw a second circle that has the new line as its diameter.




Where the second circle meets the first circle is where the tangent line from the satellite will just meet the Earth. How do we know that? This is where a few geometry rules come in handy. First, we should know that to find the tangent line of a circle, we draw a radius from the center of the circle to the point where we want to find the tangent. The tangent will be a line that forms a right angle with the radius line. Second, any triangle drawn inside a circle so that one of it's sides is the diameter of the circle and all three of its points touch the circle is a right triangle.

To prove that we actually found the tangent location, first draw a line from the intersection of the two circles back to the center of the smaller circle, (the Earth). Since it touches the edge of the smaller circle, and its center, this is a radius line and the tangent will be perpendicular to it. Next, draw a line from the intersection of the two circles back to the far side of the diameter of the bigger circle, (the location of the satellite). This newest line, the radius line and the diameter form a triangle. The angle that is opposite the diameter is a right angle. Remember, the tangent line makes a right angle with the radius of the small circle. That same angle is the right angle between the radius of the circle and our line back to the satellite, that's our tangent line!




If we can find out the distance from the location directly below the satellite, (remember, that's one of our givens), to the horizon, we can compare that to the distance between our location and the location directly below the satellite. If we're closer to the satellite ground location than the horizon, then we can see the satellite. If we're not, we can't, (ignoring diffraction effects we're not going to talk about yet).




To figure out the distance to the horizon, we'll go back to trigonometry. If we know the angle from the location on the ground directly below the satellite, then we can figure out the distance. The distance along a circle is the angle swept out by the circumference of the circle times the radius of the circle. We're in luck because we still have our tangent right triangle and it will let us solve the problem.




The short side of the triangle is the radius of the earth which we know. The hypotenuse is the radius of the earth plus the altitude of the satellite which we also know. We can plug those two numbers into the formula for the cosine of an angle and solve. The cosine of the angle is equal to the short side divided by the hypotenuse. The value for the angle is the arccosine of the same quotient, the Earth's radius divided by the hypotenuse, (the Earth's radius plus the satellite's altitude). Finally, by multiplying the angle by the radius of the Earth, we get the distance from the point directly below the satellite to the horizon.

Amateur Satellite Tracking Part III

Part I, Part II. I'm still playing around with building a satellite tracking application. I'm helping with a special event station to help raise awareness for the Friends of Science East's effort to restore Tesla's last lab, Wardenclyffe, in Shoreham, NY.

When reading through the Google Earth API documenation on linestrings, I noticed that they could be 'extruded'. This means that a plane is drawn down from the line to the ground. This seemed like an odd option at the time, but now I see the use for it. It turns out that it's difficult to tilt the view back far enough on Google Earth to see the satellite above from ground level. A wall that extends from the satellite to the ground though? Well, that's a different matter! (See the video below).

There are two next steps. One is to identify the horizon for a satellite. With this information, we can make a sort of automated siting scope to determine if a satellite is worth investigating further. The other thing to finish is making all 61 amateur satellites visible instead of just the one.

Making all 61 satellites visible requires pulling the data from the Amsat site and parsing it correctly. This step is all done and you can see the map with all the satellites at
http://copaseticflows.appspot.com/sattrack

Satellite Tracking: Initial Succeess

New Tracking App	N2YO site

As I mentioned yesterday, I'm playing around with building a satellite tracking application. I'm helping with a special event station to help raise awareness for the Friends of Science East's effort to restore Tesla's last lab, Wardenclyffe, in Shoreham, NY. After a few very minor issues, the first satellite is being tracked! First, the satellites in the AMSAT Keplerian data are named in a different fashion than they are on N2YO's site, (the site I'm using to verify my results). So, LO-19 in Amsats Keplerian data table:

LO-19
1 20442U 90005G 11187.94329143 -.00000024 00000-0 64087-5 0 01550
2 20442 098.3466 141.1781 0012855 097.5464 262.7179 14.32152423120621

is designated as Oscar19 (LUSAT) on the N2Y0 site.

At first, I thought there just weren't actually any amateur satellites in the Amsat data, but soon realized the different naming after performing a 'Search By Satellite Name' on N2YO's site. I'll try to get a table that lists the associated names into one of these blog posts.

After looking into the naming issue, it only took a few minutes to disect the baseline code, (because it is very clear and well written as mentioned before), and feed it the Keplerian data for Oscar19.

And a few seconds later, there was Oscar19 on my screen just tracking along! Using N2YO's site as a reference, Oscar19 is showing up in about the right place as can be seen in the pictures above.

Now, I'm off to understand the time progression code and to add buildings to the map.

Buildings were no problem. Using the Google Earth API docs for layers, it took one line of code to add the buildings of Manhattan!

I ran into what I thought might be the first problem while perusing buildings. It's difficult to know where to look for the satellite without a good old 2D representation of it's position, (or by zooming way out), and it would be handy to have a 2D inlay of where the horizon is at the current position to know if the satellite was behind the horizon.

The time progression code for the satellite animation has an ingenious member called g_speed. By setting this to 1, you can see the satellite move in real time. By setting it to more than one, you speed up time and watch the satellite track for the entire day in just a few seconds.

Each satellite has a Icon member which is responsible for drawing the satellite on the screen. I'll be adding a LineString geometry member to the satellite that will store the locations on the satellite track and draw the line corresponding to the track as it progresses.

And it worked! As of this writing, one satellite is being tracked with it's trail streaming out behind it. I've sped time up 20 using the g_speed variable. You can see the current demo at:

http://copaseticflows.appspot.com/examhelp/sattrack.html

You'll probably need to rotate the earth a bit to find the satellite at first, but it's there!

Or watch a brief movie of it here.

Getting Started with Amateur Satellites and Satellite Mapping

Progress! See Part II.
I'm helping to plan an amateur radio special event on November 5th to raise awareness of the effort by The Friends of Science East to save Tesla's last lab, Wardenclyffe, in Shoreham, NY. One idea for the event is to operate from some of the buildings that Tesla occupied either as labs or as homes in Manhattan. I'm thinking an easy means of operation from there might be satellite. This brings up the interesting question of "which satellites are visible from which rooftops?" I've perused the net a bit and haven't found a program that will display amateur satellite orbits in relation to the NYC skyline, so I decided to plunk around and see if I could come up with my own. So far, I have a list of references I intend to start with and I know what technology I'm going to try to use.

Google Earth is now avaiable on web pages as a JavaScript plugin. I'll be using that as the programming framework. The docs for the portion of the API I plan on using can be found at:
http://code.google.com/apis/earth/documentation/geometries.html


Satellite trajectories are described by Keplerian data. The Keplarian data for amateur satellites is availabe at:
http://www.amsat.org/amsat/ftp/keps/current/nasa.all

Amsat also has an fb explanation of the Keplerian data elements at:
http://www.amsat.org/amsat/keps/kepmodel.html


The author of the site http://www.barnabu.co.uk has already written a great satellite debris tracking framework I'll be using as a code basis. To see more about it, go to:
http://www.barnabu.co.uk/satellite-collision-debris-tracking-in-the-google-earth-plug-in/

For an in-depth description of the algorithms used in the code, check out Wikipedia at:
http://en.wikipedia.org/wiki/Simplified_Perturbations_models

Finally, if you just absolutely positively have to find an amateur satellite right now, then the site you want is the excellent one by N2Y0.

Hiam Percy Maxim's Dad in Mecanno Magazine

Prior to reading all about Hiram Percy Maxim on Dashtoons, I'd never heard of the original OM of ham radio. So, while perusing the December, 1927 issue of Meccano Magazine, I was surprised to find an article extolling the inventive brilliance of Sir Hiram Stevens Maxim, Hiram Percy's dad! In addition to highlighting Sir Maxim's childhood work ethic, the article points out that he was almost the inventor of Cordite except for one flawed sentence in his application that was filed fourteen days before the ultimately accepted application of Sir Dewar, (inventor of the Dewar flask), and Sir Abel. The article further details Maxim's invention of the machine gun, (an early model is shown below), and includes a quote from the Lord of Salisbury to the Prince of Wales:
"I have just been telling Mr. Maxim that he has prevented more men from dying of old age then any other person that ever lived!"

Help Index for Ham Radio Practice Exams at Copasetic Flows

You can now look up the available study material for the Copasetic Flows ham radio practice exams by subelement and group. The study material index can be found at:

http://copaseticflows.appspot.com/helpindex

Just click on the exam you're studying for using the tabs on the left-hand side of the screen. Then, you can select the subelement and group you're interested in using the buttons in the application window.

Subelement Progress Reports

Thanks to Dave, W4YDY, who remembered that the ham radio practice tests used to have a feature that created tests containing all the questions from a single test subelement.

For folks new to ham radio license tests, each of the three United States amateur license exam question pools, (technician, general, and extra), is organized into 10 subelements. Each of the subelements covers a particular subject area in amateur radio. For example, subelement 2 of the technician class exam covers 'Operating Procedures'.

Dave pointed out that his grandson used the subelement feature to practice the questions corresponding to a subelement as he was reviewing the same subelement in his study guide. When he took his exam he: "Only missed 3 questions and is now W4DWA."

The subelement focus feature and subelement progress charting has been added back to the U.S. ham radio practice exams at http://copaseticflows.appspot.com/hamtest. Now, in addition to tracking your practice test scores over time, you can also scroll down the scores tab to see your scores broken out per subelement. Each subelement score graph has a button directly below it that will setup a practice test of only questions from that subelement. You can also start a test for a particular subelement on the 'Test' tab by clicking one of the subelement buttons below the question and answer area.

Subelement Study Focus Added to Practice Exams

Subelement specific practice tests have been added to the free ham radio practice exams at http://copaseticflows.appspot.com/hamtest for the United States amateur exams. To study a specific subelement press the button, (look below the question area), that corresponds to that subelement. A new test will start specific to that subelement. The questions that appear in the exam will be only the questions for that subelement in numerical order. The exam header will have a message reminding you that you are studying for that subelement and not practicing a full exam.

As always with new features, if you see anything new or old that looks broken, please contact me at hcarter333@gmail.com. Have fun!

Dr. H.T. Barnes of Mecanno Magazine Fame

The September, 1929 issue of Mecanno Magazine briefly outlined Dr. H.T. Barnes efforts to destroy icebergs with thermite. Thermite is a mixture of aluminum powder and iron oxide, (rust), that burns at temperatures up to 5000 F, but does not normally explode. Dr. Barnes discovered that thermite embedded in ice would in fact explode. He patented the process as a method to destroy ice jams and icebergs. Decades later, the guys at Mythbusters would explore exploding thermite as urban myth, (see the video below), apprently unaware of Dr. Barnes' research. Here’s an excerpt from the Mecanno magazine article detailing Dr. Barnes' research:

"From ice jams to icebergs is a very natural step, and the inventor of the thermit method, Professor H.T. Barnes of Montreal, decided to try to blow up an iceberg by this means. For his first trial, he chose one that was nearly 100 ft. in height. Into a hole bored just above the waterline he placed 160 lb. of thermit and fired the mixture with a slow-burning fuse. Flames shot 125 ft. into the air and the berg was so badly cracked that one-third of it broke away completely a few hours later"

In addition to exploding icebergs, Dr. Barnes worked with Ernest Rutherford at McGill University in Montreal on the radio-chemistry experiments




that would eventually earn Rutherford the 1908 Nobel Prize in Chemistry "for his investigations into the disintegration of the elements, and the chemistry of radioactive substances". Dr. Barnes became Macdonald Professor of physics at McGill University in Montreal after Rutherford left the post to relocate to England.

Professor Barnes most publicized work however was his work on detecting and destroying icebergs. In addition to being featured in Mecanno Magazine, it was also featured in "Popular Mechanics" and "Popular Science" at the time.













Thermite is a mixture of powdered aluminum and iron oxide, (rust), that burns at temperatures up to 5000 degrees F. It doesn't normally explode, but when put in contact with ice as in Dr. Barnes' experiment, it will. As it turns out, the guys from the Mythbusters show unknowingly replicated Dr. Barnes experiment recently. You can watch the resulting explosion below:



Dr. H. T. Barnes Reading List:
Experiments with wireless telegraphy on trains

Engineering News Volume 67, 1912 Iceberg Detection

Ice Breaking Patent

Map for H. T. Barnes

View HT Barnes in a larger map

General Class Practice Exam Gadget Update to New Question Pool

The General class practice exam gadget has been updated to the new general question pool that took effect today.