Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 4: Problem 15

What are Kepler's three laws? Why are they important?

Short Answer

Expert verified
Kepler's three laws are: 1) All planets move in elliptical orbits with the sun at one focus. 2) A line segment joining a planet and the sun sweeps out equal areas during equal intervals of time. 3) The square of the period of any planet is proportional to the cube of the semi-major axis of its orbit. These laws are fundamental in understanding the motion of celestial bodies and are critical to fields of study such as astrophysics, navigation, and satellite deployment.

Step by step solution

01

Explain Kepler's First Law

Kepler's First Law, also known as the Law of Orbits, states that all planets move in elliptical orbits, with the sun at one focus. This means the path of the planets around the sun is not a perfect circle, but an ellipse, a stretched out circle. The sun is not at the center but at a focus point inside the ellipse.
02

Explain Kepler's Second Law

Kepler's Second Law, or the Law of Equal Areas, says that a line segment joining a planet and the sun sweeps out equal areas during equal intervals of time. This means that, when a planet is closer to the sun in its orbit, it actually moves faster along its path, and when it is further away, it moves slower, yet the area it covers remains constant.
03

Explain Kepler's Third Law

Kepler's Third Law, also known as the Law of Periods, states that the square of the period of any planet is proportional to the cube of the semi-major axis of its orbit. This means if you know how long it takes for a planet to make one full orbit around the sun, you can find the distance from the planet to the sun.
04

Explain The Importance of Kepler's Laws

Kepler's laws are foundational principles in astrophysics. They describe the motion of celestial bodies, not just planets, but also comets and other objects in the solar system. They serve as the basis for understanding the dynamics of the solar system and the universe, and influences fields ranging from navigation to satellite deployment.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Suppose that you traveled to a planet with 4 times the mass and 4 times the diameter of the Earth. Would you weigh more or less on that planet than on Earth? By what factor?

At what point in a planet's elliptical orbit does it move fastest? At what point does it move slowest? At what point does it sweep out an area at the fastest rate?

A comet orbits the Sun with a sidereal period of \(64.0\) years. (a) Find the semimajor axis of the orbit. (b) At aphelion, the comet is \(31.5\) AU from the Sun. How far is it from the Sun at perihelion?

How did the models of Aristarchus and Copernicus explain the retrograde motion of the planets?

Imagine a planet like the Earth orbiting a star with 4 times the mass of the Sun. If the semimajor axis of the planet's orbit is \(1 \mathrm{AU}\), what would be the planet's sidereal period? (Hint: Use Newton's form of Kepler's third law. Compared with the case of the Earth orbiting the Sun, by what factor has the quantity \(m_{1}+m_{2}\) changed? Has \(a\) changed? By what factor must \(P^{2}\) change?)
See all solutions

Recommended explanations on Physics Textbooks

Conservation of Energy and Momentum

Read Explanation

Physics of Motion

Read Explanation

Wave Optics

Read Explanation

Torque and Rotational Motion

Read Explanation

Fundamentals of Physics

Read Explanation

Fluids

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free