Everything orbiting the sun, or passing through our system above escape velocity, is traveling through the Sun's gravity well which is like a big pit in spacetime with the Sun at the bottom of the pit. Objects are always doing one of two things, either "falling into" the gravity well which causes them to speed up, or "climbing out" of the gravity well which slows them down. Orbiting objects spend half their orbits speeding up toward their perihelion (closest point to Sun in their orbit) and the other half slowing down toward aphelion (farthest point from sun). Escape velocity objects like the Nauvoo or IRL Pioneer 10 & 11 and Voyager 1 & 2 are still being slowed down but are already going so fast that they will climb over the edge of the gravity well before losing enough velocity to fall back toward the Sun. Eventually they will reach a sort of "interstellar divide" where the edge of Sol gravity well intersects the edge of an extra-solar gravity well and the object then begins gaining speed and accelerating into the other gravity well. The most distant known objects in the solar system, Oort Cloud objects, are also relatively the slowest*. Conversely, Mercury the closest planet to the Sun, is also the fastest planet in the system.

'* The slower an object is, the more easily its orbit can be altered by gravitational interactions with other objects, thus the Oort Cloud is relatively highly subject to perturbations. This is a cause for concern because when our solar system passes close to another, or a rogue object like a brown dwarf approaches, or even an undiscovered massive planet deep in our own system, the interaction can disturb the Oort Cloud and cause a "shower" of long period comets to be directed into the inner solar system. The same goes to a lesser extent for the Kuiper Belt. This is how they have detected indications of Planet Nine by seeing a group of Kuiper Belt objects that were perturbed in a similar fashion. The same concept applies to the Nauvoo. The further out it is the less energy it will take to turn it around although more energy is spent catching up to it in the first place.

edit: an important concept here is that the total "orbital energy" of an object remains unchanged but there is a constant transition occurring between potential energy (height) and kinetic energy (speed). Objects slow down as they gain height, and gain speed as they lose height, but the total energy in the system stays the same. In this case "height" means altitude above Sol but the same concept applies to any ballistic object.