Question

Choose the best answer to each of the following. 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) Earth has summer in January and winter in July.

Short answer

(b) Earth travels faster in its orbit around the Sun in January than in July.

Step-by-step solution

Understanding Kepler's Second Law

Kepler's second law, often referred to as the law of equal areas, states that a line joining a planet and the Sun sweeps out equal areas during equal intervals of time. This implies that when a planet is closer to the Sun, it travels faster due to the gravitational pull being stronger.

Identifying Earth's Orbital Position

The problem states Earth is closer to the Sun in January. According to Kepler's second law, Earth should travel faster in its orbit when it is closer to the Sun.

Analyzing the Options

Option (a) claims that Earth travels faster in July, which contradicts the information provided since Earth is further from the Sun in July. Option (c) mentions seasonal changes, which are unrelated to Kepler's laws. Option (b) correctly states that Earth travels faster in January, aligning with Kepler's second law.

Choosing the Best Answer

Given the analysis of Kepler's second law and the fact that Earth is closer to the Sun in January, the correct answer is (b) Earth travels faster in its orbit around the Sun in January than in July.

Key concepts

Earth's Changing Distance from the Sun

Earth's orbit around the Sun is not a perfect circle, but rather an ellipse. This means that at certain times of the year, Earth is closer to the Sun, while at other times, it is further away. During the month of January, Earth reaches its closest point to the Sun, known as perihelion. This proximity to the Sun affects several aspects of Earth's motion, including its speed. The elliptical nature of Earth's orbit is essential in understanding how our planet's speed changes throughout the year as explained by Kepler's laws. By acknowledging this unique orbital path, we can better understand why certain times of the year bring different climatic and speed variations.
A key point to remember is that Earth's closeness to the Sun influences its speed in orbit, but not the seasons. Seasons are caused primarily by the tilt of Earth's axis rather than its distance from the Sun.

Principles of Planetary Motion

Planetary motion refers to the movements of planets around the Sun within our solar system. These motions are governed by Kepler's laws, which describe how planets such as Earth move in elliptical orbits. Kepler's Second Law, also known as the "Law of Equal Areas," tells us that a planet will move faster when it is closer to the Sun, and slower when it is further away. This is due to the gravitational forces between the Sun and the planet.
Understanding planetary motion involves grasping how these gravitational dynamics work combined with the planet’s inertia. While the primary laws demonstrate the elliptical path of the orbits, they also help identify how the speed of a planet changes depending on its position in orbit.
This understanding is crucial, for it links the observed changes in orbital speed to fundamental physical laws that describe how everything in the universe moves.

Impact of Orbital Speed Variations

Orbital speed is the velocity at which Earth or any planet orbits around the Sun. Variations in this speed arise from gravitational interactions and the planet's position in its orbital path. According to Kepler's Second Law, when a planet is closer to the Sun in its elliptical orbit, it travels faster due to the stronger gravitational pull.
This concept is evident in Earth's own orbit—where our planet's speed increases as it moves closer to perihelion in January and decreases as it reaches aphelion in July. These speed variations are intrinsic to the elliptical nature of orbits and are central to understanding the dynamics of our solar system.
Ultimately, recognizing how orbital speed changes allows us to predict and explain variations in the motion of planets and contributes to our broader understanding of celestial mechanics.