SOLUTION MANUAL FOR Orbital Mechanics for Engineering Students 4th Edition by Howard D. Curtis ISBN: 978-0323853453 COMPLETE GUIDE ALL CHAPTERS COVERED 100% VERIFIED A+ GRADE ASSURED!!!!!NEW LATEST UPDATE!!!!!

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, SOLUTIONS MANUAL st




to accompany
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ORBITAL MECHANICS FOR ENGINEERING STUDENTS
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Howard D. Curtis
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Embry-
Riddle Aeronautical University Daytona Bea
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ch, Florida
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, Solutions Manual s t Orbital Mechanics for Engineering Students st st st st Chapter 1 st




Problem 1.1 st


(a)
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
A A  Axiˆ  Ayˆj  Azkˆ  Axiˆ  Ayˆj  Azkˆ
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
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
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 Axiˆ Axiˆ  Ayˆj  Azkˆ  Ayˆj Axiˆ  Ayˆj  Azkˆ  Azkˆ  Axiˆ  Ayˆj  Azkˆ
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
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 st
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 st
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
 Ax2 iˆ iˆ AxAy iˆ ˆj  AxAz iˆ kˆ   AyAx ˆjiˆ  Ay2 ˆjˆj  AyAz ˆjkˆ         
ts ts ts ts ts ts ts ts


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   
  2  ˆ ˆ
 
s t s t


 ˆ
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ˆ ˆ ˆ
 AzAx k i  AzAy k  j  Az k k st
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ts
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ts st ts st

 
 Ax2 1 AxAy 0 AxAz 0  AyAx 0 Ay2 1 AyAz 0  AzAx 0 AzAy 0 Az2 1
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   
ts st ts st ts st ts st ts st ts st

s t s t


 s t s t



 Ax2  Ay2  Az2
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s t
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
But, according to the Pythagorean Theorem, A x 2  Ay 2  zA 2  A2 , where A  A , the magnitude of
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the vector A. Thus A  A  A .
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(b)
iˆ ˆj kˆ
A B  C A  Bx
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Cx Cy Cz

 Axiˆ  Ayˆj  Azkˆ iˆ ByCz  BzCy  ˆjBxCz  BzCx  kˆ BxCy  ByCx 
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
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 
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
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 Ax ByCz  BzCy  Ay BxCz  BzCx  Az BxCy  ByCx st
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st  ts
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
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
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or

A  B  C  AxByCz  AyBzCx  AzBxCy  AxBzCy  AyBxCz  AzByCx
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(1) s




Note that A  B C  C A  B, and according to (1)
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C  A  B  CxAyBz  Cy AzBx  Cz AxBy  CxAzBy  Cy AxBz  Cz AyBx
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(2) s




The right hand sides of (1) and (2) are identical. Hence A   B  C  A  B C.
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(c)
iˆ ˆj kˆ iˆ ˆj kˆ
A B C Axiˆ  Ayˆj Azkˆ  Bx
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 ts
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ts
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
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s t By Bz s t
Ax By s t
Ay Bz s t
Az
Cx Cy  Cz  BzCy st
st Cx  BxCy st
st BxCy  ByCx s t
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Cz


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 
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 Ay BxCy  ByCx  Az BzCx  BxCz iˆ  Az ByCz  BzCy  Ax BxCy  ByCx ˆj

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 A B C  B C  A B C  B C kˆ

x z x x z y y z z y

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
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 
 AyBxCy  AzBxCz  AyByCx  AzBzCx iˆ  AxByCx  AzByCz  AxBxCy  AzBzCy ˆj  st
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 x z x y z y x x z y y z
 A B C  A B C  A B C  A B C kˆ st st st



 Bx AyCy  AzCz  Cx AyBy  AzBz iˆ  By AxCx  AzCz  Cy AxBx  AzBz ˆj
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 
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 
z x x y y z x x y y
 B A C  A C  C A B  A B kˆ st st st ts


 
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1

, Solutions Manual
s t Orbital Mechanics for Engineering Students
st st st st Chapter 1
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Add and subtract the underlined terms to get
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2