Can dust be in orbit around a spacecraft which orbits the Earth or Moon?

Question

In the title above, Can dust be in orbit around a spacecraft which orbits the Earth or Moon? let's define "in orbit" to mean gravitationally bound to the spacecraft long enough to go around it a few times. There may be strong perturbing forces so the orbit would not have to be nicely closed or even long lived.

This question is inspired by this answer to Satellite of a satellite of a satellite which explores the large end more than the small end of the scale.

"bonus points" for a known example of dust, debris or detritus gravitationally bound to a spacecraft.

---

As a factoid, a close orbit around a spherical body of the same average density will have the same period as worked out in this answer and discussed further here, so dust around a spacecraft will likely have a period of a several hours, not minutes.

Answer 1

A starting point for checking orbital stability is the Sphere of Influence for short term stability (or rather, to select a suitable frame a reference in the patched conic approximation), and the Hill sphere for more long term stability (satellites).

$$r_{SOI} \approx a\left(\frac{m_{satellite}}{m_{parent}}\right)^{2/5}$$

For a reference spacecraft, I'm going to pick a bulky one at 60 metric tons, because that's conveniently $10^{22}$ times lighter than the Earth.

• LEO: $r_{SOI} \approx 7cm$
• GEO: $r_{SOI} \approx 40cm$
• At Moon distance: $r_{SOI} \approx 4m$
• 500km above the Moon: $r_{SOI} \approx 3cm$

As the SOI will mostly be well within the spacecraft, it should be certain that any orbiting dust will have very non-Keplerian and unstable orbits, even before taking into the account the irregular shape of most spacecraft.

---

Radiation pressure is significant for dust. As a relatively large particle, let's take a cubic millimetre block of aluminium. $2.7 \cdot 10^{-6}kg$, each face $10^{-6}m^2$. The solar radiation pressure is $9\cdot 10^{-6} N/m²$ for a reflective surface, so over say five hours, it has been accelerated to about 5cm/s (comparable to what the gravity of the spacecraft has done over the same time span, turning the velocity vector of the orbiting dust around). That's a change in position in the order of dozens of meters over the same time, blowing it out of reach for the pull of the spacecraft.

---

I'm tempted to conclude that "no", due to the radiation pressure (even this alone) and weak influence of the spacecraft, dust can not orbit a spacecraft around the Moon or Earth, even only for a couple of orbits (the radiation pressure is blowing the particle away at the same magnitude as the spacecraft is pulling it around, so what is to bring it back to complete an orbit?). There may be some exceptions when in a very high orbit and the dust is in perpetual shadow.