Foundations of Astronomy, Enhanced
Foundations of Astronomy, Enhanced
13th Edition
ISBN: 9781305980686
Author: Michael A. Seeds; Dana Backman
Publisher: Cengage Learning US
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Chapter 18, Problem 8P
To determine

The average density of the matter in the universe and the model of the universe.

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Draw a third quadrant vector C. (remember that boldface characters represent vector quantities). Show the standard angle 0 for this vector (= angle that C makes with the positive x- axis). Also show the angle that C makes with the negative y-axis: call the latter angle 8. Finally, show the smallest angles that C makes with the positive x-axis and the positive y-axis: call these angles p1 and p2, repectively. a) Prove the following formulas for the components of C involving the standard angle (hint: start with the formulas for the components based on the angle & and then use (look up if necessary) co-function identities linking cosine and sine of 8 to sine and cosine of 0 since 8 = 3π/2-8 (this will switch cosine and sine around and eliminate - signs as well)) - C=Ccose C₁=Csine b) Prove the following formulas for the components of C: C=Ccosp1 C=Ccosp2
Notation matters when working with vectors! In particular, it is important to distinguish between the vector itself (A) and its magnitude (A). Illustrate in four separate sketches that each of the following statements is possible: a) both R = A + B and R=A+B are correct b) R = A + B is correct, but R=A+B is incorrect c) R = A + B is incorrect, but R=A+B is correct d) both R = A + B and R=A+B are incorrect
You know from your math courses that an infinitesimal segment of a circular arc can be considered as a straight line segment. Imagine that you cover a full circle in, say, the clockwise direction, with infinitesimal displacement vectors dr. Then evaluate fdr and fdr (the circle symbol on the integral just reminds us that we have to go around the full circle).

Chapter 18 Solutions

Foundations of Astronomy, Enhanced

Ch. 18 - Prob. 11RQCh. 18 - If you accept the cosmological principle, how can...Ch. 18 - Why cant an open universe have a center? How can a...Ch. 18 - In which type of model universe is space-time...Ch. 18 - In which type of model universe is space-time...Ch. 18 - What is the fate of a closed universe? In what...Ch. 18 - In which model universe does the average density...Ch. 18 - Prob. 18RQCh. 18 - What evidence shows that the Universe is...Ch. 18 - Why couldnt atomic nuclei exist when the Universe...Ch. 18 - Why are measurements of the current density of the...Ch. 18 - What percentage of matter is ordinary matter? What...Ch. 18 - How does the inflationary universe hypothesis...Ch. 18 - Prob. 24RQCh. 18 - What is the evidence that the Universe was...Ch. 18 - Prob. 26RQCh. 18 - If the Universe is negatively curved, and dark...Ch. 18 - What is the difference between hot dark matter and...Ch. 18 - Prob. 29RQCh. 18 - What evidence can you cite that the Universe's...Ch. 18 - Prob. 31RQCh. 18 - Reasoning by analogy often helps make complicated...Ch. 18 - Prob. 33RQCh. 18 - Prob. 1DQCh. 18 - Prob. 2DQCh. 18 - Prob. 3DQCh. 18 - Prob. 1PCh. 18 - Prob. 2PCh. 18 - Prob. 3PCh. 18 - Measure the lengths of the two arrows in the left...Ch. 18 - Prob. 5PCh. 18 - Prob. 6PCh. 18 - Find the wavelength of maximum intensity of the...Ch. 18 - Prob. 8PCh. 18 - Prob. 9PCh. 18 - Prob. 10PCh. 18 - Prob. 11PCh. 18 - Prob. 12PCh. 18 - Prob. 1LTLCh. 18 - Prob. 2LTLCh. 18 - Prob. 3LTLCh. 18 - Prob. 4LTLCh. 18 - Prob. 5LTLCh. 18 - Prob. 6LTL
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