Question

Explain your reasoning with one or more complete sentences. Earth is closer to the Sun in January than in July. Therefore, in accord with Kepler's second law, (a) Earth travels faster in its orbit around the Sun in July than in January. (b) Earth travels faster in its orbit around the Sun in January than in July. (c) it is summer in January and winter in July.

Short answer

The correct answer is (b) Earth travels faster in January than in July.

Step-by-step solution

Understanding Kepler's Second Law

Kepler's second law states, "A line segment joining a planet to the Sun sweeps out equal areas during equal intervals of time." This implies that a planet moves faster in its orbit when it is closer to the Sun and slower when it is farther away.

Analyzing Earth's Orbit

Since Earth is closer to the Sun in January, according to Kepler's second law, it must travel faster in its orbit in January to sweep out the equal area as it does in July, when it is farther from the Sun.

Identifying the Correct Statement

Among the given options, (a) Earth travels faster in its orbit around the Sun in July than in January is incorrect as it contradicts Kepler's second law. Option (c) refers to seasons, which are influenced by Earth's axial tilt, not its orbital speed. Therefore, (b) Earth travels faster in its orbit around the Sun in January than in July matches Kepler's law.

Verifying with Seasonal Context

Although option (c) mentions seasons, it’s important to remember that Earth's seasons are caused by its axial tilt, not the distance from the Sun. Hence, Earth's proximity to the Sun does not cause seasons, confirming that option (b) is focused on the orbital speed, which is correct.

Key concepts

Earth's Orbit

Earth's orbit is an intriguing path that our planet takes as it travels around the sun. Imagine it as an elongated circle called an "ellipse," with the Sun positioned not in the center, but at one of the two foci. The result? Sometimes Earth is closer to the Sun, like in early January, and sometimes it's farther away, like in early July. This shape and positioning set the stage for the fascinating celestial mechanics dictated by Kepler's laws of planetary motion.
Kepler's Second Law, often named the "law of areas," reveals that as Earth orbits the Sun, it doesn’t move at a constant speed. Instead, it moves faster when it's nearer to the Sun and slower when farther away. This ensures that the line connecting Earth and the Sun sweeps out equal areas in equal time intervals. Thus, Earth's varying distance from the Sun results in a continual dance of speed changes throughout the year.
Understanding Earth's orbit helps us realize why statements involving Earth's position in relation to the Sun must consider these motions to accurately describe true celestial phenomena.

Orbital Speed

Orbital speed is pivotal to understanding a planet's journey around the Sun. It's the speed a planet travels on its elliptical path. For Earth, this speed isn't constant because of its elliptical orbit. Kepler’s second law shows that Earth speeds up when it nears the Sun and slows down when it moves away. So, in our orbit every year, Earth speeds up in January when it's close to the Sun, experiencing what we call "perihelion." Conversely, in July, when Earth is at its farthest from the Sun, known as "aphelion," it slows down.
Here’s a simple way to put it:

• Closer to the Sun = Faster Speed
• Farther from the Sun = Slower Speed

This shifting speed ensures the lovely balance of the equal areas principle in Kepler's law and highlights how speed and proximity to the Sun are intertwined. Next time you observe the seasons change or think about Earth's journey, remember that its speed is always adjusting based on its distance from our star.

Seasons

Seasons are an integral part of life on Earth, yet they're often misunderstood. Despite what some might think, the seasons have nothing to do with our planet’s distance from the Sun. Instead, they are governed by Earth's axial tilt. Earth tilts on its axis at about 23.5 degrees. This tilt, not the orbital speed or distance to the Sun, causes different parts of Earth to receive varying amounts of sunlight throughout the year. As a result, we experience seasonal changes:

• When the Northern Hemisphere leans toward the Sun, it enjoys summer, while the Southern Hemisphere experiences winter.
• Six months later, the reverse happens.

Another important factor is the angle of sunlight. During summer, sunlight strikes the Earth more directly, leading to warmer temperatures. In winter, the angle is shallower, spreading the sunlight over a larger area and thus cooling temperatures. So, while Earth does move closer to and further from the Sun, our seasonal shifts are all thanks to the axial tilt, adding confusion to the mix of celestial mechanics.

Axial Tilt

Axial tilt is the unsung hero behind Earth's seasonal variety. Imagine Earth as a spinning top tilted at an angle of 23.5 degrees relative to its path around the Sun. This tilt is the reason for the season, if you will! What this tilt does is change the intensity and distribution of sunlight over Earth's surface throughout the year. When the Northern Hemisphere tilts toward the Sun, it basks in the warmth of summer. The opposite hemisphere, meanwhile, sees cooler days and the chill of winter. Throughout Earth's annual journey, this axial tilt remains fixed in direction, leading to seasonal patterns we're familiar with. About halfway through orbit, during the equinoxes, both hemispheres receive roughly equal sunlight, bringing about spring and autumn.
The story of axial tilt is one of balance and predictability. Despite changes in speed and distance due to Earth's orbit, it is the persistent tilt that consistently directs the grand parade of seasons, linking our terrestrial experiences with the heavens above. So next time you feel the warmth of summer or the crisp air of fall, think of the gentle tilt that allows these wondrous transitions.