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Chapter 3: Problem 31

The speed of a planet in its orbit varies in its journey around the Sun. a. At what point in its orbit is the planet moving the fastest? b. At what point is it moving the slowest?

Short Answer

Expert verified
The planet moves fastest at perihelion and slowest at aphelion.

Step by step solution

01

- Understanding Kepler's Second Law

Kepler's Second Law, also known as the Law of Equal Areas, states that a line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time. This means that a planet moves faster when it is closer to the Sun and slower when it is farther from the Sun.
02

- Identifying the Closest Point

The point in the orbit where the planet is closest to the Sun is called the perihelion. According to Kepler's Second Law, the planet moves fastest at perihelion.
03

- Identifying the Farthest Point

The point in the orbit where the planet is farthest from the Sun is called the aphelion. As per Kepler's Second Law, the planet moves slowest at aphelion.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

headline of the respective core concept
To better understand the varying speed of a planet in its orbit, let's dive into the key concepts mentioned in the exercise.
Perihelion
The perihelion is the point in a planet's orbit where it is closest to the Sun. The word 'perihelion' comes from the Greek words 'peri,' meaning near, and 'helios,' meaning sun.
During this stage, the gravitational pull from the Sun is at its strongest, causing the planet to move at its fastest speed.
According to Kepler's Second Law, a line segment from the planet to the Sun sweeps out equal areas in equal times. This means that when the planet is close to the Sun, it must move quickly to cover the area.

Important points to remember about perihelion:
  • The planet is closest to the Sun.
  • Gravitational pull is strongest.
  • The planet moves the fastest.
Aphelion
In contrast to the perihelion, the aphelion is the point where the planet is farthest from the Sun. The term 'aphelion' is derived from 'apo,' meaning away from, and 'helios,' meaning sun.
At this farther distance, the gravitational force exerted by the Sun is weaker. As a result, the planet's speed is at its minimum. According to Kepler's Second Law, during this stage, the planet does not need to move quickly as the area covered can be achieved with slower speed.

Key details about aphelion:
  • The planet is farthest from the Sun.
  • Gravitational pull is weakest.
  • The planet moves the slowest.
Planetary Motion
Planetary motion refers to the movement of planets around the Sun in elliptical orbits. This motion is governed by Kepler's Laws of Planetary Motion which are:
  • Kepler's First Law (Law of Ellipses): Planets orbit the Sun in elliptical paths with the Sun at one focal point.
  • Kepler's Second Law (Law of Equal Areas): A planet moves faster when it is closer to the Sun and slower when it is farther from the Sun.
  • Kepler's Third Law (Law of Harmonics): The square of a planet's orbital period is proportional to the cube of the semi-major axis of its orbit.
By understanding these laws, we can better predict the variations in a planet's speed during its orbit around the Sun. Perihelion and aphelion are just two critical points that highlight how distance from the Sun affects orbital speed.

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Most popular questions from this chapter

The distance that Neptune has to travel in its orbit around the Sun is approximately 30 times greater than the distance that Earth must travel. Yet it takes nearly 165 years for Neptune to complete one trip around the Sun. Explain why.

What is the difference between speed and acceleration?

A planet with an eccentricity of 0.5 has a. nearly equal semimajor and semiminor axes. b. a longer semiminor axis than semimajor axis. c. a longer semimajor axis than semiminor axis. d. the Sun at the center of its orbit.

Place the following in order from largest to smallest semimajor axis. a. a planet with a period of 84 Earth days b. a planet with a period of 1 Earth year c. a planet with a period of 2 Earth years d. a planet with a period of 0.5 Earth year

Planets with high eccentricity may be unlikely candidates for life because a. the speed varies too much. b. the period varies too much. c. the temperature varies too much. d. the orbit varies too much.
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