The task sounded simple enough: develop
software to be used to direct an antenna, specifically the Algonquin
Radio Observatory, in tracking a GPS satellite. Observe the radio
frequency sent by said satellite to confirm successful tracking. Well,
however easy or difficult the task sounds to you, I can assure you that
it was quite a lot of work.
It was actually kind of nice working on this project because it was one that required planning, division of work, and development over a long period of time. Often, work catches up with me, and some of my best work comes through toward the end of a project. As difficult as it can be to work on something piece by piece, it was nice to work on this project in stages.
Using Matlab, a programming language frequently used by engineers and physicists for data analysis, algorithm development, and numerical computation, the class paired off, starting with the simple, but necessary functions, and working toward the final, complicated project.
After reviewing the specifications document, it seemed that a lot of the code to be developed was in simply converting things into the proper format. For example, dates and times, readily accessible on Matlab, had to be converted to Julian Dates, or epochs (Julian dates since a specific event). For anyone unfamiliar, Julian Dates represent the interval of time in days and fractions of a day since January 1st, 4713 B.C. For example, today's date, Friday, April 27th = 2456045 in the Julian date system.
Kind of sounds like star dates used in Star Trek, right? Yes, so we needed functions to compute that, and some to calculate specific things based on that. There was a lot of formatting involved with this project.
The real substance of this project was in determining a satellite's position, velocity, and the angles the antenna would need to use to look at a satellite for any given time. How do we determine a satellite's position, you ask?
Well, the first thing we need is an ephemeris file. Simply put, this is a list, or table, with the positions of the satellites in question at a specific time. The information concerning the whereabouts of GPS satellites isn't exactly secret, so we were able to get an ephemeris file of the satellites in question from not too long ago.
It is important to have a fairly recent ephemeris file because everything is in constant movement and nothing stays the same from one cycle to the next. The rotation and revolution of the Earth is not constant, the revolution of satellites is not constant, even the direction of axes, the directions we use to make measurements, changes over time, allow David Tennant, as Dr. Who, to partially explain: Timey Wimey. While he's talking about time, the same thing holds true for space. Simply put, the Earth doesn't stand still and so our measurements have to keep up.
So, ephemeris file gives us an idea of where satellites are at a specific time, say a couple of months ago. Then, we have to calculate where the satellites are now and where they will be in the future. This involves a lot of math. And I mean a lot.
First, we pick a time in which to observe the satellites. Say, a half hour interval, 1pm to 2pm on a specific day, say yesterday. Whatever. Now that you have that time frame in mind, you have to calculate the positions and velocities of the satellites as they travel in their orbit around Earth. The information from the ephemeris file helps us out, but from this we get the values in Keplerian coordinates.
Whoa...what? Alright, so most people imagine a satellite going around the Earth, and the Earth going around the Sun, to be in a circular orbit, as seen below where the black dot is Earth, and the red is the satellite. The distance between the two is the radius, R, and the speed of the satellite in its orbit is its velocity, v.
But, Johannes Kepler, German astronomer, observed and realized that orbits in space are more like the above right, where instead of the more massive object sitting at the centre, the orbit was more of an ellipse with the massive object off to the side (this position is known as a focus, or one of the foci, by the way). The model and way of understanding an object in a Keplerian orbit is to use Keplerian coordinates.
So, we determine the orbital characteristics of our satellites in Keplerian coordinates. Then we want to change to something called ECI, or Earth-Centred Inerial. This system, as you can gather from the name, places the Earth at the centre, and has the directional axes pointing in very specific directions.
Because I feel like showing off, here is a review of said directions. The z-zxis points along Earth's rotational axis, remember though it's changing all the time due to a wobbling, rotating Earth. But, more or less, north to south. The x axis points toward the vernal equinox.
Okay, so as the Earth goes around the Sun, the path it makes looks
similar to the above diagram. The vernal equinox, besides being the
longest day of the year, is the point where the Earth's path seems to
rise above the plane on which the Sun and most of the solar system sits.
So,
long side note. Basically, you have to determine the satellites
positions as they will be when you want to look at them, using the
ephemeris file. Then, you change it from Keplerian, with its crazy
ellipses, into ECI, Earth-Centred, to make it a little easier. But
you're not done!
Oh
no, you have to then determine the position of the station you're
viewing from in the ECI coordinate system AND it might be a good idea to
change from ECI to ECF, where the F stands for fixed. Basically, the
ECF coordinate frame fixes the x-axis at the Prime Meridian, 0° in
Longitude, that vertical line on maps running through Greenwich,
England. The reason you might want to switch is simply to make things a
little more straightforward.
Sure
it is, you're thinking, but really, once you do the above steps,
switching from ECI to ECF is actually as easy as subtracting one number
from another.
Okay...so,
we finally have a list of the satellites we want to look at, and where
they'll be and when. Now, we need to determine how to point the antenna
in order to look at one of them. We first have to convert the station's
position (more math!?) into something called topocentric. Basically, it
means the antenna is at the centre of the system, makes pointing easier.
So, once we've done that, we determine the azimuth and elevation
angles.
As
might be discerned from the above diagram (I looked for a better one,
but didn't feel like drawing it myself), the azimuth angle is the
"horizontal" angle, rotated from due north, eastward to the object. And
the elevation is from the horizon straight up to the satellite.
Basically, say you're facing north, but you want to face the Moon. The
amount you turn on the spot is your azimuth, the amount you have to look
up is your elevation.
Once
you've done that, there's one little step left to do. Because of the
limits of the scope, namely that it cannot look through the horizon, you
cannot simply track all satellites at a given time. So, once you know
where the satellites are, you determine which ones might be easier to
track based on which ones will be visible for the longest portion of
time during the time you've chosen to track them.
Now
that you know where they'll be, this is easy, and once you see which
satellites are visible, you simply choose the one visible the most and
track it by telling the computer to rotate the antenna according to the
angles and positions you have calculated.
Well...that
was a lot of work just explaining that. Trust me, it was a lot of work
in general, and everyone one of us lost a lot of sleep making sure
things worked perfectly. To make this post a little more exciting, let
me tell you more about the Algonquin Radio Observatory, to be referred
to as here as the ARO.
Weighing over 1200 tons, with a diameter of 150 ft, or 46 m, it is the largest antenna in Canada.
Weighing over 1200 tons, with a diameter of 150 ft, or 46 m, it is the largest antenna in Canada.
Built
in 1966, the ARO has been used for countless scientific experiments
over the years. In the world of science, it was famous for the first
very long baseline interferometry experiment in the world. Basically,
using this antenna, and a smaller one in British Columbia, scientists
were able to focus on the same very distant objects and use that data to
actually establish the distance between the two antennas very
accurately. It was a breakthrough which is still used to this day and is
one of the ways we are able to determine our position on Earth with
such a high degree of accuracy. Additionally, the facility features an
atomic clock, hydrogen maser for anyone interested, and due to the
precise readings taken over the years, the facility is actually the most
accurately known position on the entire planet. In fact, surveyors used
this location, branching out, in order to update and increase the
accuracy of maps used all over Canada. It's an amazing facility, and
while I have some pictures of it, none could quite capture the sheer
size and impressive nature of it.
One
thing that was really cool was that we were allowed to go up and walk
on the dish! Moving the dish to an upright position, we climbed the
spiral staircase in the centre of the base, leading all the way to the
top.
Once
there, we were allowed to walk around, and see the dish for ourselves.
As you can see from the photos below, half of the dish is painted white
and the other half is not. The unpainted side will be finished this
summer, and the white paint helps make the antenna more accurate.
Sadly,
we were unable to see the horizon, due to the fact that the antenna had
to be pointed upright, but I managed to get a couple of nice photos in.
The mesh on the outside is because the antenna's dimensions were
expanded some time after it was built. It all works the same way, just
looks different.
This
is what we used to track the GPS satellites. Our code, its working
components described above, was fed to the facility and instructed the
antenna as to where to point and when. It was amazing to watch the
antenna swivel and point, while watching the controls light up as it
worked.
The
control panel, seen below, is old, and is not what they use currently,
but was part of the original design. I thought it looked pretty neat.
In
the end, it was an amazing project, and an amazing opportunity. I was
looking forward to this trip for some time, and it was really a nice way
to culminate this year. It brought so many ideas and techniques
together and really gave me a sense that I had learned something, and
that what I had learned could be exciting and truly applicable. I deal
in the theoretical so much that sometimes I need to be reminded of the
applications of my knowledge. Additionally, the facility was in the
middle of Algonquin park, so when I wasn't stressing over my work, I was
enjoying the serene wilderness.
Another year over, this one better than the rest, in terms of what I've learned. I now strike out to get ready for the summer, and to get ready to move and live in Edmonton for awhile. I hope to find employment quickly, and I look forward to keeping you up to date on my adventures.
Thanks for reading!
Another year over, this one better than the rest, in terms of what I've learned. I now strike out to get ready for the summer, and to get ready to move and live in Edmonton for awhile. I hope to find employment quickly, and I look forward to keeping you up to date on my adventures.
Thanks for reading!
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