Scanning the Skies

Last week, the LIGO-Virgo-Kagra Collaboration held a town hall with electromagnetic observers to discuss the status of the ongoing 4th observing run. Among the presenters were representatives of the Swift Burst Alert Telescope, or BAT, a satellite designed to detect gamma rays like the ones released by the binary neutron star collision LIGO picked up in 2017. They caught my attention with the name for their analysis tool for BAT: GUANO, and I'm a sucker for Dr. Strangelove references. What I started thinking about though, was what would be the best strategy for observing the whole sky, given that the satellite can only make detections in a small patch at any given time.

The theory is to use the same type of effect I discussed several years ago, where a spinning object tumbles in unexpected ways, thanks to Euler's equation:

According to this, if the angular velocity ω is not aligned with the symmetries of the object, represented by I, the velocity will change, even if the torque τ is zero. While it bears little resemblance to BAT, I decided to see what happens if I take a simple cylinder, and spin it off-axis. The plot below shows the cylinder in 3D, with a line marking a constant point on the outside to show rolling motion (though a plotting quirk makes it hard to see sometimes). Under that is a skymap of the parts of the sky the telescope has passed over.

You can see the color rescales to account for the telescope retracing areas it's seen before. I wondered though whether I could pick a particular rotational velocity that would allow the telescope to scan the whole sky without ever needing to apply a torque, which would require fuel. After failing to get an optimizer to figure out the best choice, I just tried a bunch of values, and settled on this one, which makes a nice latticework:

Of course, you can imagine the nauseating sort of view this pattern will give you! If this were actually the way the satellite operated, it would need a lot of post-processing, but the whole point of LIGO's public alerts is that detectors like this one can rapidly refocus on possible events, so I don't expect Swift to adopt this technique anytime soon.