How likely is it that the Voyager spacecrafts haven't yet been damaged by micrometeoroids?

Question

Both Voyagers have been traveling at over $60,000$ km/h for well over four decades and still seem to function properly, taking into account the slowly dropping power and warmth available from their radioisotope generators.

In terms of volume, they've basically traversed a cylinder of length $23.3\times10^9$ km and diameter of order $\mathcal{O}(1)$ m. At those speeds even a few grains of sand could potentially cause massive damage, let alone after over 45 years of flight.

Is space really that empty?

Answer 1

This is a great question, I'm no planetary scientist but I'll give a partial answer to get things started.

Interplanetary dust is ubiquitous in the solar system and interplanetary spacecraft including the Voyagers detect impacts regularly via the electric field (low frequency "radio") pulses produced by the expanding hemispherical plasma cloud (negative electrons move faster than positiv ions) after each impact.

From that Wikipedia article:

The Pioneer spacecraft observations in the 1970s linked the zodiacal light with the interplanetary dust cloud in the Solar System.⁸ Also, the VBSDC instrument on the New Horizons probe was designed to detect impacts of the dust from the zodiacal cloud in the Solar System.⁹

• ⁸Hannter; et al. (1976). "Pioneer 10 observations of zodiacal light brightness near the ecliptic - Changes with heliocentric distance"
• ⁹Horányi, M.; Hoxie, V.; James, D.; Poppe, A.; Bryant, C.; Grogan, B.; Lamprecht, B.; Mack, J.; Bagenal, F.; S. Batiste; Bunch, N.; Chantanowich, T.; Christensen, F.; Colgan, M.; Dunn; Drake, G.; Fernandez, A.; Finley, T.; Holland, G.; Jenkins, A.; Krauss, C.; Krauss, E.; Krauss, O.; Lankton, M.; Mitchell, C.; Neeland, M.; Resse, T.; Rash, K.; Tate, G.; Vaudrin, C.; Westfall, J. (2008). "The Student Dust Counter on the New Horizons Mission" (PDF). Space Science Reviews. 140 (1–4): 387–402. . doi:10.1007/s11214-007-9250-y

and

Spacecraft that have carried dust detectors include Helios, Pioneer 10, Pioneer 11, Ulysses (heliocentric orbit out to the distance of Jupiter), Galileo (Jupiter Orbiter), Cassini (Saturn orbiter), and New Horizons (see Venetia Burney Student Dust Counter).

I found abstract P42A-04 for the American Geophysical Union, Fall Meeting 2011 Dust Impacts In the Outer Solar System Detected by Voyagers 1 and 2 Gurnett, D. A. ; Persoon, A. M. ; Granroth, L. J. ; Kurth, W. S. which confirms your expectation that they should be "taking hits" regularly.

The plasma wave instruments (PWS) on the Voyager 1 and 2 spacecraft, which are currently at about 119 and 97 AU, have been consistently detecting a low rate of dust impacts as the spacecraft proceed outward from the Sun into interstellar space. Because of the high radial velocity of the spacecraft, ~ 17 and 15 km/sec, when a dust particle strikes the spacecraft it is almost instantly vaporized and ionized, thereby producing a rapidly expanding cloud of plasma that causes a voltage pulse in the PWS electric antenna. The voltage pulse has a very rapid rise time of about 10 μs and is an easily identifiable waveform in the wideband electric field data. Due to a failure in the Voyager 2 waveform receiver no impact data are available from Voyager 2 beyond about 60 AU. However, the Voyager 1 waveform receiver is still working. Because of the very high data rates involved, 115.2 kb/s, antenna voltage waveforms can only be recorded for less than a minute per week, so the effective observing time is very small. Nonetheless, once the regions around the outer planets are excluded, a consistent background impact rate of a few impacts per hour is observed by both spacecraft. The impact rate appears to be increasing slightly with increasing radial distance, from about 3 ± 1 impacts per hour at 30 AU, to 6 ± 4 impacts per hour at 110 AU. If the impact cross-section of the spacecraft is assumed to be determined by the spacecraft high gain antenna, which has an area of 10.75 square meters, the corresponding particle flux varies from about 0.75 x 10^-14 m^-2 s^-1 at 30 AU, to about 1.5 x 10^-14 m^-2 s^-1 at 110 AU. Although we have no reliable method of estimating the size or origin of the particles, we note that this flux is consistent with the flux of submicron particles (10^-15 to 10^-9 g) arriving from interstellar space as detected by the Ulysses spacecraft at radial distances inside of 5 AU. Therefore, we believe that the particles are probably of interstellar origin.

Consider also that the Cassini spacecraft flew through Saturn's ring system "unscathed".^1,2

size distribution

The thing that makes long interplanetary missions so possible is the size distrbituion of interplanetary dust. The density of grains large enough to be able to do "massive damage" is sufficiently low that the probability of catastrophic impacts per mission is also low.

Also the following links for some potentially helpful perspective:

• this answer to How much cosmic dust is there in the asteroid belt?
• What is the origin of the dust near the sun? shows a log plot of grain mass distribution from 10^-15 to 10^-2 grams, but at only 0.1 AU.
• Where to read about early work in the detection of dust impacts on solar observing spacecraft?
• Debris in interstellar flight not directly comparable - it asks about flying at 0.9c between the stars, but adds some perspective.
• If a spacecraft travels at 10% c will it be destroyed by interstellar dust and particles? ditto.
• What are the chances a space probe will make it to another star without hitting a bit of space dust?

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• ¹ Spaceflight Now's April 27, 2017 Cassini contacts Earth after flying inside Saturn’s rings

Engineers were confident the spacecraft would make the trek through the ring gap unscathed. The trajectory took Cassini around 200 miles (300 kilometers) from the visible edge of Saturn’s innermost D ring, and pictures showed no sign of any icy ring particles in the craft’s path.

Models suggested that if any particles were present where Cassini flew, they would be similar in size to microscopic smoke particles, according to NASA.

But managers took no chances with Wednesday’s flyby, pivoting the spacecraft to point its 13-foot (4-meter) radio antenna in its direction of travel to take the brunt of any debris impacts, which could have damaged or destroyed the probe.

• ² https://ell.stackexchange.com/a/257115/120483 (Sopranos reference)