I’ve heard that the Oort Cloud contains trillions of icy bodies. What would be the average distance between these bodies?

In movies you usually see an asteroid belt full of rocks close to one another. In reality, this would be an unstable situation because objects that are close to one another will collide often as they orbit the Sun. Any belt of objects will grind down the population until collisions are rare, and thus the objects generally will not be found near each other in a stable long-lived belt.

In our main asteroid belt between Mars and Jupiter, between about 2.1 and 3.3 astronomical units (AU; 1 AU is the average Sun-Earth distance, 93 million miles [150 million kilometers]) from the Sun, there are some 1 million to 1.5 million asteroids larger than 0.6 mile (1 km). Each of these asteroids is on average 1.8 million miles (3 million km) apart, or about eight times the Earth-Moon distance. These asteroids are small compared with our Moon and thus would generally not be observable from each other. Collisions between asteroids still do happen, with a few per year that create dust clouds we can detect with telescopes.

The Oort Cloud has many more objects than the main asteroid belt, some trillion objects larger than a kilometer, but it also occupies a much larger volume of space from 5,000 AU to beyond 20,000 to 50,000 AU from the Sun. Oort Cloud objects larger than 1 km have some 31 million miles (50 million km) between each other. This is about the distance between Earth and Mars at their closest approach.

The large distances between small objects in our solar system make empty space the norm and mean spacecraft can travel safely among the planets.