Passage VI

When viewed from Earth, the other planets in the solar system usually appear to move prograde (eastward relative to the stars). Occasionally, however, each planet appears to briefly move retrograde (westward relative to the stars). For example, Figure 1 shows Mars's position relative to the stars on 9 dates between July 24, 2005, and February 26, 2006.

Two hypotheses were proposed to explain why the planets occasionally appear to move retrograde.

Hypothesis 1

Earth is the solar system's central body, and the other bodies move around Earth in looped orbits. Each body (except Earth) has 2 circles associated with it: a deferent and an epicycle. Both circles rotate counterclockwise, and their combined motions result in a body following a looped orbit. In Figure 2, the left panel shows Mars's deferent and epicycle, and the right panel shows Mars's orbit.

As a body passes through a loop. the body's motion changes from prograde and back. The larger a body's deferent. the more loops in the body's orbit. and the more often that body passes through a loop.

Hypothesis 2

The Sun is the solar system's central body, and the planets move counterclockwise around the Sun in elliptical orbits. The larger a planet's orbit, the more time the planet takes to complete a revolution around the Sun. As a result, the line of sight from Earth to a given planet drifts over time. Figure 3 shows the orbits Earth and Mars, and the positions of Earth and Mars, on each of the 4 dates labeled in Figure 1. For each date, the line of sight from Earth to Mars is projected onto a view of the sky.

There are 2 rules for apparent retrograde motion:

• A planet with an orbit larger than Earth's appears to move retrograde whenever Earth passes between the Sun and that planet. The larger that planet's orbit, the more often a pass occurs.

• A planet with an orbit smaller than Earth's appears to move retrograde whenever that planet passes between the Sun and Earth. The smaller that planet's orbit, the more often a pass occurs.