Issue 57

The term Launch Window is bantered about for just about every space launch. The Artemis window varies, but for the most recent launch campaign it was a 2-hr window. Some missions have really tight windows, for example, many Space Shuttle missions to ISS were 4-minute windows. This article will introduce and illustrate just what is going on regarding a Launch Window. A launch window is when the launch site is lined up to when the launch site passes under the desired orbit plane for the launching spacecraft. As you remember from your Orbital Elements articles, that means matching Inclination and RAAN. I’m going to illustrate how the launch site in its rotation around the Earth’s axis passes under the orbit plane sought. I am going to use the case where of the inclination or the orbit we’re launching into is greater than the launch site latitude. So we’ll use Cape Canaveral as the launch site (28 degrees north latitude) and the ISS orbit (51° inclined) as our destination. With these constraints we will see that we get two launch opportunities a day to launch into that orbit.

Below is an illustration to show you just what is happening as we approach our launch window. The Earth is rotating, the launch site is moving eastward at its latitude along with that rotation (red dashed line), and the orbit plane is fixed in space (the yellow line). We’re basically waiting for the launch site to pass under the orbit plane, and when that happens it is GO time…launch the rocket! In our case, we have Cape Canaveral at 28°N latitude and we have the ISS orbit which is 51° inclined. Here is the illustration and below it is a paragraph talking you through what’s happening, it’s all about the “fixed” orbit (you’ll see why I added quotes around “fixed”) and Earth rotation and what latitude the launch site is at.

Let’s work left to right. You know the Earth rotates 15.04° per hour. So that red dotted line is the pathway of the Cape. It is moving eastward. Makes a one lap per day just like all the points on Earth. The ISS orbit is in yellow. The part of the orbit we can see is in the northern hemisphere and the southern hemisphere part is behind the Earth. It is tilted 51°. So, every time the Cape passes under the “fixed” orbit plane and we have a launch opportunity for an ascending azimuth. I’ll call this launch opportunity #1 of 2. I’ll show you a nifty equation to calculate what azimuth to program your rocket to fly later. So, there’s launch opportunity #1. Now, based on Cape being in the north hemisphere and the earth rotating 15 ° per hour, we move eastward and then about 7-hrs later the Cape again passes under the orbit plane, only this time it is a

descending pass, so we’ll fly out on a southwest azimuth or bearing. I call this launch opportunity #2 of 2. I mentioned sometimes the launch window is really wide, they may not be trying to enter a precise orbit, just a range or they may be able to execute orbital maneuvers to correct back to what they need. In the case of missions to ISS, the window may be 4 minutes long, wow, that’s a short amount of time. There is some steering the rocket can do to account for the width of the window, the Shuttle sure did have the ability to steer to precisely the orbit needed. Now, the Earth keeps rotating and 17-hrs later this pattern repeats. That’s the loop back line you see. So, now for the “why the quotes?’ around “fixed.”

If the earth was a perfect sphere and the atmosphere didn’t create a drag force on the ISS, this would be essentially a repeating pattern. Maybe a slight drift in time due to earth orbiting the Sun. BUT, the earth is not a sphere and has some interesting gravitational forces due to its shape that create a torque on the orbit and thus its twist, or RAAN, drifts. It is well modelled and thus the ISS orbit, which I said was fixed” is actually moving westward 5 degrees/day. That’s significant, so, this makes the repeat pattern shift. There are really smart astro experts always working the launch window calculations, and now that you are now armed with what you learned in this article you can chat with them and be most awesome and impressive!

One more item to know about. Which way do you launch? There is a simple equation that helps us know that. Reach back to your high school geometry because we are going to take the Cosine of 2 angles and then the arcsine of a number to get the northeast azimuth for our Cape-ISS example. Oh yes, (get ready for this, I know you remember it!) we will find that when we take the ArcSine of a number (must be less than 1) it has TWO answers. Finding that is easy, right? Its 180° minus the first answer we got. Let’s run the numbers folks, we got to understand which way to send the rocket when the launch window is open and we are GO to launch.

Here’s the equation that accounts for the launch site latitude and the orbit inclination and will give us the launch azimuth (true heading) needed to “hit” the orbit plane:

Launch Azimuth #1 = ArcSine [Cosine(Inclination)/Cosine(Latitude Launch Site)]

So for ISS we have 51° inclined orbit and the Cape is at 28° north latitude (that’s makes 28 a positive number). We run the numbers and get 45.5 degrees azimuth for the ascending launch opportunity. That looks about right! We’re heading northeast. So, what if we want to launch on the descending launch opportunity?No problem, know that ArcSine’s other solution is 180° minus the first azimuth. We get 134.5° for this launch azimuth for the descending opportunity.

Launch Azimuth #2 = 180 degrees — Launch Azimuth #1

The launch azimuth helps us “hit” the right inclination and the timing of when to launch helps us “hit” the right RAAN. Eureka, we get into the correct orbit plane and can subsequently maneuver to link up with the station. That aspect of launch window planning adds some complications to account for where ISS is in its orbit at launch time. That is a more advanced topic, but what you have learned in this article is pretty much the bulk of how launch windows work! Pretty cool stuff, now you know and can dazzle your friends and co-workers by explaining this.