When Earth catches up to a slower-moving outer planet and passes it in its orbit, the planet a. exhibits retrograde motion. b. slows down because it feels Earth's gravitational pull. c. decreases in brightness as it passes through Earth's shadow. d. moves into a more elliptical orbit.

Understanding the gravitational effect is essential when studying planetary motion. Gravity is a force that pulls objects toward each other. The stronger the masses and the closer the objects, the stronger the gravitational pull. However, in the vast expanse of space, distances between celestial objects are enormous. Even though Earth and an outer planet like Mars both exert gravitational forces, the distance between them minimizes Earth's impact on Mars.

Essentially, the Sun's gravity is the dominant force influencing the orbits of planets in our solar system. The gravitational force from the Sun is what keeps the planets in orbit around it. Therefore, when Earth passes an outer planet, Earth's gravity does not significantly affect the outer planet's motion. Instead, it is the Sun's gravity that continues to govern the orbits of the planets.

By understanding this concept, it's clear why option b from the exercise can be ruled out. Earth's gravity does not slow down an outer planet because the distance is too great for Earth’s gravity to have a considerable effect.

Planetary orbits are the paths that planets follow around the Sun. These paths are primarily elliptical, governed by the gravitational pull of the Sun. Each planet's orbit is shaped by its velocity and the Sun's gravitational force.

In ancient times, orbits were thought to be perfect circles. However, Johannes Kepler discovered that orbits are ellipses, explaining the varying speeds of planets. For example, a planet moves faster when closer to the Sun and slower when farther away due to the changing gravitational forces.

When Earth catches up and passes an outer planet, this does not cause the outer planet to move into a more elliptical orbit (as suggested in option d). The elliptical shape of an orbit depends on the planet's velocity and the Sun's gravity, not on the gravitational influence of Earth. Therefore, Earth's passing does not have the power to alter the shape of another planet's orbit.

The brightness of planets as seen from Earth can vary due to several factors. One primary factor is the distance between Earth and the planet. When a planet is closer to Earth, it appears brighter. Another factor is the reflection of sunlight off the planet's surface or clouds.

In the context of the given exercise, it is important to understand Earth's shadow and its influence. Earth's shadow only affects objects within it, such as the Moon during a lunar eclipse. Outer planets, positioned far beyond Earth's shadow, do not experience significant changes in brightness due to Earth passing them. This eliminates option c from being a possible explanation.

Retrograde motion, as described in option a, is the correct explanation for the apparent backward movement of outer planets. This apparent motion does not affect the planet’s intrinsic brightness, but observing retrograde motion is purely due to Earth's relative motion in its orbit.