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Chapter 3: Problem 6

Suppose a planet is discovered orbiting a star in a highly elliptical orbit. While the planet is close to the star it moves________, but while it is far away it moves________. a. faster; slower b. slower; faster c. retrograde; prograde d. prograde; retrograde

Short Answer

Expert verified
a. faster; slower

Step by step solution

01

Understand orbital speed

A planet's orbital speed varies depending on its distance from the star it is orbiting. According to Kepler's laws of planetary motion, a planet travels faster when it is closer to the star and slower when it is farther from the star.
02

Apply 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 star sweeps out equal areas during equal intervals of time. This implies that the planet moves faster when it is near the star and slower when it is far from the star.
03

Match the options

Choose the option that correctly describes the planet's speed relative to its distance from the star. The correct choice is 'faster' when close, and 'slower' when far.

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Key Concepts

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

Orbital Speed
Orbital speed is the velocity at which a planet travels around a star. It depends on how far the planet is from the star. According to Kepler's laws, the closer a planet is to its star, the faster it moves. This happens because the gravitational pull is stronger when the distance is shorter. Conversely, the farther the planet is, the slower it travels. This variation is critical for understanding planetary motion and can be calculated through precise measurements and observations.
Elliptical Orbits
Planets do not revolve around their stars in perfect circles but rather in elliptical orbits. An elliptical orbit looks like a stretched out circle or an oval. Each ellipse has two focal points, and the star is located at one of these foci. This shape means that a planet’s distance from the star changes over the course of its orbit. As a result, the planet's speed also changes, being faster when it is closer to the star and slower when it is farther away. Understanding the shape of elliptical orbits helps explain a planet's varying speeds.
Law of Equal Areas
Kepler's second law, also known as the law of equal areas, plays a crucial role in explaining planetary motion. It states that a line segment connecting a planet to its star sweeps out equal areas during equal time intervals. This means that the planet moves more quickly when it is nearer to the star and more slowly when it is distant. For instance, if the planet is near the star, it must travel a longer path in a shorter time to cover an area that is equal to when it is farther away, traveling a shorter path over a longer time. This law ensures that the orbital motion is consistent and predictable.
Kepler's Second Law
Kepler's second law is integral to understanding why planetary speeds vary in an elliptical orbit. It complements the concept of orbital speed by showing that the speed adjustments are a natural outcome of the way planets move. A planet travels faster during the part of its orbit that brings it closer to the star, ensuring that the area swept out by the line segment from the star to the planet remains equal in equal times. This principle provides insight into the dynamic relationship between a planet and its star, contributing to the broader field of celestial mechanics.
Planetary Motion
Planetary motion encompasses the paths that planets take around their stars and the laws that govern these paths. Kepler's laws of planetary motion describe these paths with remarkable precision, showing that planets move in elliptical orbits and vary in speed according to their distance from the star. These motions are influenced by gravitational forces, which are stronger when the planet is closer to the star and weaker when further away. By understanding these motions, astronomers can predict planetary positions, plan space missions, and study the dynamic processes of our solar system and beyond.

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Most popular questions from this chapter

When riding in a car, we can sense changes in speed or direction through the forces that the car applies on us. Do we wear seat belts in cars and airplanes to protect us from speed or from acceleration? Explain your answer.

During the latter half of the 19 th century, a few astronomers thought there might be a planet circling the Sun inside Mercury's orbit. They even gave it a name: Vulcan. We now know that Vulcan does not exist. If a planet with an orbit one-fourth the size of Mercury's actually existed, what would be its orbital period relative to that of Mercury?

Galileo observed that Jupiter has moons. From this information, you may conclude that a. Jupiter is the center of the Solar System. b. Jupiter orbits the Sun. c. Jupiter orbits Earth. d. some things do not orbit Earth.

The time it takes for a planet to come back to the same position relative to the Sun is called its______ period. a. synodic b. sidereal c. heliocentric d. geocentric

When involved in an automobile collision, a person not wearing a seat belt will move through the car and often strike the windshield directly. Which of Newton's laws explains why the person continues forward, even though the car stopped?
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