EBK UNDERSTANDING OUR UNIVERSE (THIRD E
3rd Edition
ISBN: 9780393631760
Author: Blumenthal
Publisher: VST
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Chapter 1, Problem 21QAP
To determine
The cosmic address of the planet Tau Ceti e.
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Draw a right-handed 3D Cartesian coordinate system (= x, y and z axes). Show a vector A with
tail in the origin and sticking out in the positive x, y and z directions. Show the angles between A
and the positive x, y and z axes, and call these angles α₁, α₂ and α3
Prove that Ax Acos α₁
Ay
= Acos α₂
A₂- Acos α3
solve for Vo
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
Chapter 1 Solutions
EBK UNDERSTANDING OUR UNIVERSE (THIRD E
Ch. 1.1 - Prob. 1.1CYUCh. 1.2 - Prob. 1.2CYUCh. 1.3 - Prob. 1.3CYUCh. 1 - Prob. 1QAPCh. 1 - Prob. 2QAPCh. 1 - Prob. 3QAPCh. 1 - Prob. 4QAPCh. 1 - Prob. 5QAPCh. 1 - Prob. 6QAPCh. 1 - Prob. 7QAP
Ch. 1 - Prob. 8QAPCh. 1 - Prob. 9QAPCh. 1 - Prob. 10QAPCh. 1 - Prob. 11QAPCh. 1 - Prob. 12QAPCh. 1 - Prob. 13QAPCh. 1 - Prob. 14QAPCh. 1 - Prob. 15QAPCh. 1 - Prob. 16QAPCh. 1 - Prob. 17QAPCh. 1 - Prob. 18QAPCh. 1 - Prob. 19QAPCh. 1 - Prob. 20QAPCh. 1 - Prob. 21QAPCh. 1 - Prob. 22QAPCh. 1 - Prob. 23QAPCh. 1 - Prob. 24QAPCh. 1 - Prob. 25QAPCh. 1 - Prob. 26QAPCh. 1 - Prob. 27QAPCh. 1 - Prob. 28QAPCh. 1 - Prob. 29QAPCh. 1 - Prob. 30QAPCh. 1 - Prob. 31QAPCh. 1 - Prob. 32QAPCh. 1 - Prob. 34QAPCh. 1 - Prob. 35QAPCh. 1 - Prob. 36QAPCh. 1 - Prob. 37QAPCh. 1 - Prob. 38QAPCh. 1 - Prob. 39QAPCh. 1 - Prob. 40QAPCh. 1 - Prob. 41QAPCh. 1 - Prob. 42QAPCh. 1 - Prob. 43QAPCh. 1 - Prob. 44QAPCh. 1 - Prob. 45QAP
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