Issue 50

Over the summer, Jack Anthony will break down each of the six orbital elements required to uniquely identify a specific orbit and satellite in that orbit. This week we start with semi-major axis. For those who can’t wait the entire summer, please visit Jack’s “Orbit Element Dance” on YouTube” and you’ll find a 1:02 video featuring Jack in his driveway demonstrating this highly effective way to learn about the 6 classical orbital elements (COE). Each movement ties to an important astrodynamics principle. Below is a screen grab from this video. As you can see, Jack uses the STP method of remembering the 6 COEs. Size, Shape, Tilt, Twist, Position of Perigee and Position of the Satellite at a particular time. Boogie Down.

Semi-major axis “a” is the only COE that is a distance, s in km, feet, nautical miles, you can use furlongs if you want…km is the most popular and you’ll see we use a Gravitational Constant number that uses km. Here’s an illustration showing you that “2a” is the measure of the major axis or long axis of the orbit. Now, while semi-major axis is a nifty number to know, let’s see what insight it provides into the orbit’s characteristics.

Semi-major axis is the “orbit energy” parameter, if you add or subtract velocity in-track, you change the semi major axis, you also change eccentricity, more on that next time. Thus by changing “a”, you change the energy of the orbit. Let’s do an example, Let’s say the semi major axis of a circular orbit is 7,000 KM (mean altitude 622 Km), what can we tell about the orbit? Let’s see how we can use a simple equation to find how long an orbit takes, that’s called the Orbit Period. OK, we’re going to do a little math here, relax, it’s easy. First, let me introduce the Earth’s Gravitational Parameter denoted Greek “µ.” It’s value is 398,600.4 km^3/sec^2. It’s a constant and it’s in the equation for determining the Orbit Period, how long it takes to orbit the Earth once. Here’s the equation:

The a^3 is semi-major axis raised to the 3rd power, or “a times a time a.” There’s a square root involved. Math is so much fun! So, with “a” equal to 7,000 KM, let’s see how long a lap of the Earth takes. Pi is 3.14159 (good enough for our use, it continues out really far). Got a calculator or Excel? Crank it out, what do you get? I get 5,828 seconds. Hummm, what’s that in minutes? I get 97.1 minutes.

OK, one more nifty thing to know. The Space Force and other organizations like Celestrak publish orbit elements for you to use. If you look at a Two-Line Element Set (TLE) you will not see semi major axis listed. Oh my, what’s with that? Well, they list the Mean Motion or how many orbits per 24-hr day. This is related to semi major axis. There are 1440 mins in a 24-hr solar day, so we can divide our 97.1 minute orbit period into 1440 and see we orbit the Earth 14.82 orbits per day.

So, the semi major axis is the COE that describes SIZE.

It can help us determine the Mean Motion and also the Orbit Period. Pretty cool! In reality, the equations, calculations and software does all the awesome astrodynamics for Space Force is far more exact.

They get into the nitty gritty details of a lot of parameters so we can precisely detect, track, identify and characterize a space objects pathway…its orbit. Now for a thinking problem. Let’s say you are in an orbit where you cross over the equator heading south to north (we call that ascending) at 105° West Longitude. The next time you whiz by going south to north over the equator, what longitude will you cross at? Hint, the Earth rotates 15.04° per hour eastward. Your satellite will come back around in 97.1 minutes or 1.62 hours.

What’s the Earth doing while you are completing that orbit? Who knows the answer? “Bueller, Bueller, Bueller?” (editor’s note: For everyone born after 2000 this is a movie reference…look it up, it will change your life 😎) I bet you can figure it out! You can call me at 719-205-1741 if you get stuck, or ask a fellow Guardian.

How are you doing learning and showing your friends and family the Orbit Element Dance? Let’s all learn it, you’ll be the talk of the ops center, neighborhood or your living room. I can do a Zoom for a large group and teach it. We can together master the moves and effectively demonstrate the dance and the COEs. Maybe then we can add “BeatBoxing” sounds…really make learning Astro fun and memorable.