Outer planet trajectory design versus the asteroid belt

Question

Several space probes have been launched to destinations beyond the asteroid belt: Pioneers 10 and 11, Voyagers 1 and 2, Ulysses, Galileo, Cassini, New Horizons, and Juno, at least.

While the odds of hitting an asteroid on any random Jupiter-or-beyond-bound trajectory are pretty small, it may be worth trying to minimize the risk. Furthermore, a trajectory might be altered significantly by the gravity of the largest minor planets in the belt.

Therefore, I am guessing that the trajectories for these missions were checked against the orbits of the largest asteroids, but that smaller asteroids, being generally less well-observed, and their orbits not as accurately known, might not be considered.

Verifying that any single asteroid doesn't endanger the spacecraft reduces the actual risk to the mission only infinitesimally, but I imagine it would be uncomfortable to try to explain to your boss how your spacecraft managed to collide with Vesta.

How many asteroids' orbits are checked against the trajectories of outer-planets probes? How has this number changed over the years from Pioneer 10 to Juno?

Answer 1

I cannot give you a valid answer for later Missions, but here something about Pioneer and Voyager:

As Scientists discover there is a very rare planet constellation in the 70/80ies allowing to pass all large outer planets with one mission, they had been very keen in doing this mission (Voyager). BUT: In fact they have not known if it is possible to cross the asteroid belt. We did not know enough about the belt, how dense it is, how many small rocks are there etc. So one of the main tasks and goals of the Pioneer mission was simply: try if it possible to get through the asteroid belt.

Long story short: For the earliy missions, there was no checks against single asteroids, insted they used Pioneers to proof if Voyager can succeed.

EDIT: sources:

Smithonian nat. air and space museum - Pioneer

The primary purpose of the missions was to travel through the asteroid belt,...

Wikipedia Pioneer 10

On July 15, 1972, Pioneer 10 was the first spacecraft to enter the asteroid belt,[38] located between the orbits of Mars and Jupiter. The project planners expected a safe passage through the belt, and the closest the trajectory would take the spacecraft to any of the known asteroids was 8,800,000 kilometers (5,500,000 mi). One of the nearest approaches was to the asteroid 307 Nike on December 2, 1972.

Assuming that the closest approach to a known asteroid was known prior to the launch, this would imply that Pioneer 10's trajectory was checked against at least hundreds, and possibly over 1000 asteroids known at the time of the mission.

and last but not least:

Wikipedia Pioneer 11

[E]arly mission objectives were defined as: [...] Investigate the nature of the asteroid belt from the scientific standpoint and assess the belt's possible hazard to missions to the outer planets.