Orbital perturbations and PUNCH

By Dr. Craig DeForest ☀️ (@craig.deforest.org)
Published:

I'm winding down my day and trying my hand at long-form posting again. If you like this, please say so by replying -- I'm trying to decide if this is a good medium for occasional collects on topics of interest.

So we launched the PUNCH constellation this week, along with a singleton spacecraft called SPHEREx. (SPHEREx is pretty awesome in itself, of course -- but it's not a constellation and therefore doesn't care as much about orbital perturbations as we do). All five spacecraft (our four PUNCHes plus SPHEREx) are in Sun-synchronous orbit over the day/night terminator line, and all five appear to be healthy (approximately 50 hours into the mission as I type this).

They're gradually separating: all five launched together on a single Falcon 9 rocket. Once they got into orbit, they got ejected from the upper stage using springs. SPHEREx got launched mostly in the forward direction and partly laterally, then the four PUNCH satellites got ejected, in pairs, at slightly different angles to the orbital track. You can see it happen in NASA's live broadcast on YouTube. The result is that now, just over 50 hours from launch, the spacecraft have separated. Here's a recent track from N2YO, which uses the published orbital tracking data from NORAD.

orbital tracks from n2yo Orbital tracks of PUNCH and SPHEREx from around 11pm MDT on 13-Mar-2025, about 50 hours after launch, show separation of the four spacecraft.

NORAD is very good at orbital tracking -- they track every significant object in orbit around Earth (benign or not), as part of their mission to identify and react to incoming ICBMs. They publish pretty precise tracking data of all the not-an-incoming-ballistic-missile items to help prevent other folks, also, from getting jittery about orbital vehicles. Those tracking data are pretty darned interesting and useful, in much the same way that Messier's catalog of items that are not comets turned out to be a list of some of the most interesting objects in the night sky.

NORAD has not yet (as of Thursday night) identified these objects by proper name – they have catalog numbers (63178 through 63182) and nicknames ("Object A" through "Object E", respectively), in order from front to rear along their orbit. I snapped the orbital track figure while everyone was headed north over Africa, so the object nicknames are Object A through Object E, top to bottom.

(Incidentally, orbits are fast. In the time it's taken me to type this much of this blog post, the group have crossed over the north pole and are now headed southward on the sunset side of the planet. The quartet are over Alaska right now.)

If you watched that YouTube video, you'd see that SPHEREx was ejected in the mostly-forward direction from the upper stage of the Falcon. So why is it falling behind?

Because orbits are weird, that's why.

Notoriously, if you want to re-enter from orbit, you fire retro-rockets to slow down. That lowers your orbit on the opposite side of the planet, and if you lower it enough, you re-enter the atmosphere and aerobrake out of orbit, perhaps even lithobraking to a halt.

If you retro-thrust only a little bit, you lower your orbit on the opposite side of the planet – but not enough to re-enter. That does two things. First, it shortens the length of your orbit: you are now on the "inside track" compared to your old orbit, so you get around slightly faster than you would have. Even more, something called the Virial theorem ensures that you move even faster on the opposite side of the planet than you were moving to start with when you fired your retrorockets. That speeds up your average orbital period (time to return to where you are right now).

The result of those two things is that, if you slow down by one meter per second while orbiting Earth, you actually pull ahead of your old position by almost two meters per second.

Of course, if you speed up (or get spring ejected in the forward direction), the reverse logic applies, and you'll end up falling behind by about twice the speed of your ejection.

The PUNCH spacecraft were ejected in pairs, at an angle to the orbital track, so that their forward and reverse perturbations would be approximately equal. We've tentatively identified the objects as A=NFI, and B, C, and D as WFIs (1, 3, and 2 respectively). That was harder than it sounds: they're only now far enough apart that we can separate them with the directional antennas on ground stations.

For the first day or so, all of them were flying through each ground station's beam at about the same time, so we had to rely on the spacecraft themselves to tell us who was who. Each PUNCH spacecraft has a GPS receiver, so they know where they are all the time -- but we can only talk to one at a time, so it's difficult to sort them out from the real-time data. They couldn't tell us their ground track until we commissioned them enough to get high speed downlinks working, so we could dump their housekeeping logs to the ground. Now we can check where all four were at a particular time, by looking at the log files, and pick out their order along the orbital track.

The one spacecraft that was ejected at the highest forward rate (and is therefore farther behind the others) is SPHEREx, and the JPL team are commissioning that "bird" just as feverishly as we're working on our own quadruplets.

In a few more days we'll trim the orbital drift with the PUNCH on-board thrusters, and about 87 days from today we'll use those same thrusters to arrest their relative drift and set them up as a fixed constellation, 120° apart, in as close to the same orbit as we can achieve -- which turns out to be pretty close, since we can control the velocity to within a small fraction of a walking pace.

The distance around the world, 650km above it, is about 44,000 km. To separate by 120°, the PUNCH WFI Observatories have to drift nearly 15,000 km each. To do that in 90 days, they have to average 2 meters per second (approximately) of relative drift. That is why we ejected them at about 1 meter per second (a walking pace). from the launch vehicle. Its' surprising what even a small amount of directed action, sustained continuously, can achieve.