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I'm reading about the 30-or-so USSR RORSAT missions that had unshielded, fast spectrum, highly enriched Uranium nuclear reactors powering a satellite, which was later moved up to a higher "disposal" orbit.

Apparently one of the biggest debris issues is the liquid NaK (former) coolant leaking.

But these are just liquid droplets. I can easily see how the number of drops would multiply much faster than solid metal breaking up... but how do the impact risks compare? Will a liquid drop do the same impact damage as a solid chunk of metal of the same mass?

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    $\begingroup$ I'm not sure it even matters, but wouldn't coolant even freeze/crystallize? I know even paint flakes are a significant hazard at orbital speeds as well. $\endgroup$
    – Erik
    Commented Jul 27, 2013 at 18:19
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    $\begingroup$ A bit of observational humor: Standing under the rain hurts a lot less than under a hail storm. The physics behind it is however a tad over my head (gazillion of forces to consider with liquids), but according to Wiki, sodium-potassium freezes at only -11°C (12°F), so it might not matter, like @Erik said? $\endgroup$
    – TildalWave
    Commented Jul 27, 2013 at 18:42

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I'm looking through Heinrich Klinkrad's 2006 book (Space Debris: Models and Risk Analysis) where he describes this very hazard (p.26).

The total amount of NaK released (tentative!): 208 kg, at 13 kilos per event.

Orbit: inclination 65 degrees, altitudes 900-950 km.

The text states that possible size of droplets remaining in the initial orbit and not taken off by drag or evaporation is from 10 to 55 mm, with the total mass less than 60kg.

The density is stated to be similar to water (I presume that calculations were based on drag terms in ballistic equations, although the density of liquid NaK is around 0.855 g/cm^3).

klinkrad-1

Now on to damage from hypervelocity impact:

  • at hypervelocities, all solids behave like liquids ("the resulting impact damage for an aluminum projectile is almost unaffected by its solid or liquid state)

  • droplets with round shape will have lower penetration capability than elongated projectiles

  • NaK alloy in the droplets has density like water ($~1.0 g/{cm^3}$), approx. 7.8 times less than steel. Let's assume we're talking about projectiles weighing 30 grams each. The NaK droplet will have diameter of 3.855 cm, the steel bullet - 1.9439 cm.

Ballistic limit of a NaK droplet will be 1.409 times smaller than that of a round steel bullet (for the same angle and velocity, the maximum thickness of a wall penetratable by a steel bullet will be 1.409 times more than that penetratable by a NaK droplet): we use ESA parameters $\lambda=1.056$ and $\beta=0.519$. $\lambda$ is for the diameter, and $\beta$ is for projectile density. You can grab Klinkrad's book and re-do the computations for another density of the droplets.

$$t_{t, lim}=K_1 d^\lambda_p \rho^\beta_p \rho^\kappa_t v^\gamma_p {(\cos \alpha_p)}^\xi$$

$K_1$ - calibration factor

$t_{t, lim}$ - ballistic limit (min. required single-wall thickness), cm

$d_p$ - diameter of the projectile, cm

$\lambda, \beta, \kappa, \gamma, \xi$ - calibration exponents

$\rho_t, \rho_p$ - densities of the target and projectile, $g/{cm^3}$

$v$ - projectile velocity at impact, $km/s$

$\alpha_p$ - impact angle (w.r.t. surface normal), degrees

An important caveat: do not trust simple back-of-the-envelope computations; do numerical simulations, and above all, experiment!

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