(a) Explanation Consider the polar equation of the ellipse e with semi major axis a is r = a ( 1 − e 2 ) 1 + e cos θ . The maximum and minimum values of r can be evaluated when d r d θ = 0 as follows. r = a ( 1 − e 2 ) ( 1 + e cos θ ) − 1 d r d θ = a ( 1 − e 2 ) ( − 1 ) ( 1 + e cos θ ) − 2 ( − e sin θ ) 0 = a ( 1 − e 2 ) ( e sin θ ) ( 1 + e cos θ ) 2 sin θ = 0 θ = 0 , π Now, substitute θ = 0 , π in r = a ( 1 − e 2 ) 1 + e cos θ (b) To determine To evaluate: The closeness of each planet in our solar system comes to the sun and the farthest distance each planet gets from the sun using the table in problem 76.

14th Edition

ISBN: 9780134654874

Author: WEIR

Publisher: VST

See similar textbooks

Concept explainers

Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is…

Videos

Question

Chapter 11.7, Problem 75E

(a)

To determine

To prove: That r=a(1−e) when the planet is closest to the sun and r=a(1+e) when the planet is farthest from the sun.

(b)

To determine

To evaluate: The closeness of each planet in our solar system comes to the sun and the farthest distance each planet gets from the sun using the table in problem 76.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 11.7, Problem 74E

Chapter 11.7, Problem 76E

Students have asked these similar questions

Ministry of Higher Education & Scientific Research Babylon University College of Engineering - Al musayab Automobile Department Subject :Engineering Analysis Time: 2 hour Date:27-11-2022 کورس اول تحليلات تعمیر ) 1st month exam / 1st semester (2022-2023)/11/27 Note: Answer all questions,all questions have same degree. Q1/: Find the following for three only. 1- 4s C-1 (+2-3)2 (219) 3.0 (6+1)) (+3+5) (82+28-3),2- ,3- 2-1 4- Q2/:Determine the Laplace transform of the function t sint. Q3/: Find the Laplace transform of 1, 0≤t<2, -2t+1, 2≤t<3, f(t) = 3t, t-1, 3≤t 5, t≥ 5 Q4: Find the Fourier series corresponding to the function 0 -5

Ministry of Higher Education & Scientific Research Babylon University College of Engineering - Al musayab Subject :Engineering Analysis Time: 80 min Date:11-12-2022 Automobile Department 2nd month exam / 1" semester (2022-2023) Note: Answer all questions,all questions have same degree. کورس اول شعر 3 Q1/: Use a Power series to solve the differential equation: y" - xy = 0 Q2/:Evaluate using Cauchy's residue theorem, sinnz²+cosz² dz, where C is z = 3 (z-1)(z-2) Q3/:Evaluate dz (z²+4)2 Where C is the circle /z-i/-2,using Cauchy's residue theorem. Examiner: Dr. Wisam N. Hassan

Chapter 11 Solutions

EBK THOMAS' CALCULUS

Ch. 11.1 - Finding Cartesian from Parametric...Ch. 11.1 - Finding Cartesian from Parametric...Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E Ch. 11.1 - Prob. 6E Ch. 11.1 - Prob. 7E Ch. 11.1 - Prob. 8E Ch. 11.1 - Prob. 9E Ch. 11.1 - Finding Cartesian from Parametric...

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.

To prove: That r = a ( 1 − e ) when the planet is closest to the sun and r = a ( 1 + e ) when the planet is farthest from the sun.