Explanation Kepler’s third law states that the ratio of the squares of the periods of any two planets revolving around the sun is equal to the ratio of the cubes of their mean distances from the sun. The perihelion is the distance of a planetary orbit with major-axis 2 a from the sun. The aphelion is the farthest distance from the sun. Given: Saturn’s orbit has eccentricity e = 0.056 . The ratio T / a 3 2 is equal to a constant C for all planetary orbits around the sun, where T is the period (time for a complete orbit) and a is the semi major-axis. Formula Used: The perihelion and aphelion are calculated by: Perihelion = a ( 1 − e ) Aphelion = a ( 1 + e ) Calculation: a. A period for the earth is 365 days. It is given that C = T a 3 2 where T = 365 and the semi-major axis of the earth’s orbit a = 150 × 10 6 . So, C = T a 3 2 = 365 ( 150 × 10 6 ) 3 2 ≈ 2.433 × 10 − 6 days/kilometers Thus, C = 2.433 × 10 − 6 days/kilometers b. It is given that Saturn’s semi-major axis is approximately 1.43 × 10 9 km. So, C = T a 3 2 T = C a 3 2 T = 2.433 × 10 − 6 × 1...

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

See similar textbooks

Concept explainers

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the se…

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integratio…

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects th…

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.

Videos

Question

Chapter 12.5, Problem 64E

To determine

We need to compute

a. C in units of days and kilometers, given that the semi-major axis of the earth’s orbit is $150 \times 10^{6}$ km.

b. The period of Saturn’s orbit, given that its semi-major axis is approximately $1.43 \times 10^{9}$ km.

c. The perihelion and aphelion of Saturn.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 12.5, Problem 63E

Chapter 12.5, Problem 65E

Chapter 12 Solutions

CALCULUS (CLOTH)

Ch. 12.1 - Prob. 1PQ Ch. 12.1 - Prob. 2PQ Ch. 12.1 - Prob. 3PQ Ch. 12.1 - Prob. 4PQ Ch. 12.1 - Prob. 5PQ Ch. 12.1 - Prob. 6PQ Ch. 12.1 - Prob. 7PQ Ch. 12.1 - Prob. 1E Ch. 12.1 - Prob. 2E Ch. 12.1 - Prob. 3E

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Recommended textbooks for you

Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:9781133382119

Author:Swokowski

Publisher:Cengage

SEE MORE TEXTBOOKS

Area Between The Curve Problem No 1 - Applications Of Definite Integration - Diploma Maths II; Author: Ekeeda;https://www.youtube.com/watch?v=q3ZU0GnGaxA;License: Standard YouTube License, CC-BY

We need to compute a. C in units of days and kilometers, given that the semi-major axis of the earth’s orbit is 150 × 10 6 km. b. The period of Saturn’s orbit, given that its semi-major axis is approximately 1.43 × 10 9 km. c. The perihelion and aphelion of Saturn.

Solution Summary: The author explains that Kepler's third law states that the ratio of squares of the periods of any two planets revolving around the sun is equal to their cubes.

Concept explainers

Videos

We need to compute

a. C in units of days and kilometers, given that the semi-major axis of the earth’s orbit is $150 \times 10^{6}$ km.

b. The period of Saturn’s orbit, given that its semi-major axis is approximately $1.43 \times 10^{9}$ km.

c. The perihelion and aphelion of Saturn.

Want to see the full answer?

Chapter 12 Solutions

We need to compute a. C in units of days and kilometers, given that the semi-major axis of the earth’s orbit is 150 × 10 6 km. b. The period of Saturn’s orbit, given that its semi-major axis is approximately 1.43 × 10 9 km. c. The perihelion and aphelion of Saturn.

Solution Summary: The author explains that Kepler's third law states that the ratio of squares of the periods of any two planets revolving around the sun is equal to their cubes.

Concept explainers

Videos

We need to compute a. C in units of days and kilometers, given that the semi-major axis of the earth’s orbit is 150×106 km. b. The period of Saturn’s orbit, given that its semi-major axis is approximately 1.43×109 km. c. The perihelion and aphelion of Saturn.

Want to see the full answer?

Chapter 12 Solutions

We need to compute

a. C in units of days and kilometers, given that the semi-major axis of the earth’s orbit is $150 \times 10^{6}$ km.

b. The period of Saturn’s orbit, given that its semi-major axis is approximately $1.43 \times 10^{9}$ km.

c. The perihelion and aphelion of Saturn.