By Duncan Steel 02/04/2019

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Last Friday Rocket Lab successfully launched another satellite from the Mahia Peninsula. In this post I describe the satellite’s orbital path, and how it will slowly vary in time over the next week. 

Rocket Lab successfully launched another satellite into orbit from the Mahia Peninsula soon after midday last Friday (March 29th), a wonderful achievement. Well done to all who contributed.

This satellite, with the appellation R3D2 (Radio-frequency Risk Reduction Deployment Demonstration, producing an acronym to delight fans of Star Wars), is a product of the U.S. Defense Advanced Research Projects Agency, or DARPA. Information about the satellite is available here (DARPA website), and also on various independent websites, such as here, and here, and here.

Many people will be interested in the intent of the satellite: to trial a new type of thin-membrane antenna that is tightly-folded before launch in a small, low-mass payload but is then deployed or expanded once in orbit, with the aim of making high-bandwidth communications feasible using mini-satellites and therefore giving much-improved internet connectivity to the whole globe (and in particular Third World countries with no possible fibre infrastructure). For myself, though, I am interested in orbits… and so this blog post is all about R3D2’s path around the Earth.

There are several websites that will quickly tell you R3D2’s approximate orbital parameters, and even show where it is (in terms of the point on the globe that it is passing over, right now). This is my favourite. If you don’t believe that such websites are telling the truth, you can go to an internet service such as Heavens-Above and with a few clicks get information about when R3D2 should be visible passing over your own location — and then go outside at the appropriate times to check!

Whilst many might think that such things would be kept secret, in fact the orbit of R3D2 is publicly-available, with precision. The source that I normally use is Celestrak, whilst others might prefer Spacetrack or the list of the Union of Concerned Scientists. The essential source of the data is the same: the U.S. military’s network of space surveillance radars and optical telescopes, which detect and track all orbiting objects that are large enough to be picked up by their sensors. All these have their orbital parameters freely available, except for various security-classified satellites (such as the X-37B space plane, and various reconnaissance satellites).

It was a simple thing, then, to look up the orbit of R3D2 without needing to ask Rocket Lab, and then plug it into the STK orbit integrator in order to see how the path of the satellite will alter over the next few days or weeks. The orbit I used for R3D2 was that determined by USSPACECOM over the first 60 hours post-launch. I just looked at how the orbit will alter over the next week, starting from the beginning of April 2nd UTC (which was 1pm NZDT).

R3D2 flies about 430 km above Earth’s surface. Its orbit is close to being circular, and is tilted by about 39.5 degrees to the equator. The reason for this tilt, which space scientists call the inclination, is that the Mahia Peninsula launch site is at about that latitude, and the rocket/satellite were directed very close to due east from there.

Orbits are funny things, in that they change all the time due to various well-understood physical effects. For a satellite in low-Earth orbit, like R3D2 which passes not far above our heads, the major effect is due to the fact that our planet is not spherically symmetric, but rather is slightly flattened (Earth’s polar radius is more than 21km less than the equatorial radius, which is why the top of the inactive volcano Chimborazo is the point on Earth’s surface furthest from its centre, rather than the summit of Mount Everest, as you might have imagined). This non-sphericity affects the gravitational field and therefore the paths of satellites, causing their orbital planes to swivel around or precess.

The graphic at right shows the location of R3D2 in its orbit at the start of April 2nd (again, UTC); the position and the path it took over the next 90 minutes, as it was coming up to completing its first orbit of the day; and at the bottom, the paths to be traced out by R3D2 over the three days through to the start of April 5th UTC. As you can see, in the final frame there is a ‘fan’ of paths taken by R3D2, and that is due to precession.





Another way of looking at R3D2’s orbit is to examine the ground track: the path it took over the surface more than 400 km below. The next graphic shows just this, on a map of the planet.





First, you will note that the furthest north and south positions are at latitude 39.5 degrees, due to that tilt of the orbital plane. Second, there are apparent groups of three paths, and about 15 such groups going northwards and 15 going southwards if one counts across from west to east. Why? Three is the number of days completed (April 2–4 inclusive) and 15 is the approximate number of orbits completed in a day, each lasting about 93 minutes. (Actually R3D2 does about one half-an-orbit more than 15 in a day, which is why a couple of those groups have more than three tracks.)

Perhaps you’d like to see the slowly-varying path to be taken by R3D2 over the next few days. A movie (172 seconds long, 56MB) showing this  for the three days starting from the beginning of April 2nd (UTC) can be seen by clicking here.

And for now, I am out of space.