rightAscensionOfAscendingNode property
Right Ascension of the Ascending Node (RAAN) In Degrees.
Two numbers orient the orbital plane in space. The first number was Inclination. This is the second. After we’ve specified inclination, there are still an infinite number of orbital planes possible. The line of nodes can poke out the anywhere along the equator. If we specify where along the equator the line of nodes pokes out, we will have the orbital plane fully specified. The line of nodes pokes out two places, of course. We only need to specify one of them. One is called the ascending node (where the satellite crosses the equator going from south to north). The other is called the descending node (where the satellite crosses the equator going from north to south). By convention, we specify the location of the ascending node.
Now, the earth is spinning.This means that we can’t use the common latitude/longitude coordinate system to specify where the line of nodes points.Instead, we use an astronomical coordinate system, known as the right ascension / declination coordinate system, which does not spin with the earth.Right ascension is another fancy word for an angle, in this case, an angle measured in the equatorial plane from a reference point in the sky where right ascension is defined to be zero.Astronomers call this point the vernal equinox..
Finally, “right ascension of ascending node” is an angle, measured at the center of the earth, from the vernal equinox to the ascending node.
I know this is getting complicated. Here’s an example.Draw a line from the center of the earth to the point where our satellite crosses the equator (going from south to north). If this line points directly at the vernal equinox, then RAAN = 0 degrees..
By convention, RAAN is a number in the range 0 to 360 degrees.
I used the term “vernal equinox” above without really defining it.If you can tolerate a minor digression, I’ll do that now. Teachers have told children for years that the vernal equinox is “the place in the sky where the sun rises on the first day of Spring”. This is a horrible definition.Most teachers, and students, have no idea what the first day of spring is (except a date on a calendar), and no idea why the sun should be in the same place in the sky on that date every year.
You now have enough astronomy vocabulary to get a better definition. Consider the orbit of the sun around the earth. I know in school they told you the earth orbits around the sun, but the math is equally valid either way, and it suits our needs at this instant to think of the sun orbiting the earth. The orbit of the sun has an inclination of about 23.5 degrees. (Astronomers don’t usually call this 23.5 degree angle an ‘inclination’, by the way.They use an infinitely more obscure name: The Obliquity of The Ecliptic.) The orbit of the sun is divided (by humans) into four equally sized portions called seasons.The one called Spring begins when the sun pops up past the equator. In other words, the first day of Spring is the day that the sun crosses through the equatorial plane going from South to North.We have a name for that! It’s the ascending node of the Sun’s orbit. So finally, the vernal equinox is nothing more than the ascending node of the Sun’s orbit. The Sun’s orbit has RAAN = 0 simply because we’ve defined the Sun’s ascending node as the place from which all ascending nodes are measured.The RAAN of your satellite’s orbit is just the angle (measured at the center of the earth) between the place the Sun’s orbit pops up past the equator, and the place your satellite’s orbit pops up past the equator.
Implementation
final double rightAscensionOfAscendingNode;