In the heliocentric model, what causes the apparent retrograde motion of outer planets?

In the heliocentric model, the apparent retrograde motion of outer planets occurs when Earth overtakes them in their orbits.

Mars, Jupiter, Saturn, Uranus, and Neptune all orbit the Sun more slowly than Earth because they are farther from it. As Earth moves along its smaller, faster orbit, it periodically catches up with and passes one of these outer planets. During that interval, the planet's position against the distant background stars appears to drift backward, even though the planet continues moving forward around the Sun.

The effect is similar to passing a slower car on a highway: the slower car can seem to move backward relative to the roadside scenery, despite traveling in the same overall direction. Retrograde motion is therefore an apparent change in direction caused by changing viewpoints and orbital speeds, not a literal reversal of the planet's orbit.

Older geocentric astronomy explained retrograde loops with devices such as epicycles, deferents, and equants. Those terms are associated with mathematical models of apparent motion, but they are not the heliocentric cause described in this question.