Solutions Manual for Orbital Mechanics for Engineering Students by Howard D. Curtis | Complete Engineering Study Guide 2026

NICS
ard D.FOR
Curtis
OLUTIONS
ENGINEERING
Embry-Riddle
MANUAL STUDENTS
Aeronautical
to accompany
Howard
University
ORBITAL
D. Daytona
CurtisMECHANICS
Embry-Riddle
Beach, Florida.pdf!@(*)(#&*UY&*$($H(&U@*$*$*&U$*H*@$HN$($
FOR
Aeronautical
ENGINEERING
University
STUDENTS
Daytona Beach,
HowardFlorida.pdf!@(*)(#&*UY&*$($H(&U@*$*$*&U$*H*@$HN
D. Curtis Embry-Riddle
$$N($OJ$J$HJ$M(*$J($(*$*98
Aeronautical University Daytona




NICS
ard D.FOR
Curtis
OLUTIONS
ENGINEERING
Embry-Riddle
MANUAL STUDENTS
Aeronautical
to accompany
Howard
University
ORBITAL
D. Daytona
CurtisMECHANICS
Embry-Riddle
Beach, Florida.pdf!@(*)(#&*UY&*$($H(&U@*$*$*&U$*H*@$HN$($
FOR
Aeronautical
ENGINEERING
University
STUDENTS
Daytona Beach,
HowardFlorida.pdf!@(*)(#&*UY&*$($H(&U@*$*$*&U$*H*@$HN
D. Curtis Embry-Riddle
$$N($OJ$J$HJ$M(*$J($(*$*98
Aeronautical University Daytona

,NICS
ard D.FOR
Curtis
OLUTIONS
ENGINEERING
Embry-Riddle
MANUAL STUDENTS
Aeronautical
to accompany
Howard
University
ORBITAL
D. Daytona
CurtisMECHANICS
Embry-Riddle
Beach, Florida.pdf!@(*)(#&*UY&*$($H(&U@*$*$*&U$*H*@$HN$($
FOR
Aeronautical
ENGINEERING
University
STUDENTS
Daytona Beach,
HowardFlorida.pdf!@(*)(#&*UY&*$($H(&U@*$*$*&U$*H*@$HN
D. Curtis Embry-Riddle
$$N($OJ$J$HJ$M(*$J($(*$*98
Aeronautical University Daytona




SOLUTIONS MANUAL

to accompany


ORBITAL MECHANICS FOR ENGINEERING STUDENTS




Howard D. Curtis
Embry-Riddle Aeronautical University
Daytona Beach, Florida




NICS
ard D.FOR
Curtis
OLUTIONS
ENGINEERING
Embry-Riddle
MANUAL STUDENTS
Aeronautical
to accompany
Howard
University
ORBITAL
D. Daytona
CurtisMECHANICS
Embry-Riddle
Beach, Florida.pdf!@(*)(#&*UY&*$($H(&U@*$*$*&U$*H*@$HN$($
FOR
Aeronautical
ENGINEERING
University
STUDENTS
Daytona Beach,
HowardFlorida.pdf!@(*)(#&*UY&*$($H(&U@*$*$*&U$*H*@$HN
D. Curtis Embry-Riddle
$$N($OJ$J$HJ$M(*$J($(*$*98
Aeronautical University Daytona

,NICS
ard D.FOR
Curtis
OLUTIONS
ENGINEERING
Embry-Riddle
MANUAL STUDENTS
Aeronautical
to accompany
Howard
University
ORBITAL
D. Daytona
CurtisMECHANICS
Embry-Riddle
Beach, Florida.pdf!@(*)(#&*UY&*$($H(&U@*$*$*&U$*H*@$HN$($
FOR
Aeronautical
ENGINEERING
University
STUDENTS
Daytona Beach,
HowardFlorida.pdf!@(*)(#&*UY&*$($H(&U@*$*$*&U$*H*@$HN
D. Curtis Embry-Riddle
$$N($OJ$J$HJ$M(*$J($(*$*98
Aeronautical University Daytona




NICS
ard D.FOR
Curtis
OLUTIONS
ENGINEERING
Embry-Riddle
MANUAL STUDENTS
Aeronautical
to accompany
Howard
University
ORBITAL
D. Daytona
CurtisMECHANICS
Embry-Riddle
Beach, Florida.pdf!@(*)(#&*UY&*$($H(&U@*$*$*&U$*H*@$HN$($
FOR
Aeronautical
ENGINEERING
University
STUDENTS
Daytona Beach,
HowardFlorida.pdf!@(*)(#&*UY&*$($H(&U@*$*$*&U$*H*@$HN
D. Curtis Embry-Riddle
$$N($OJ$J$HJ$M(*$J($(*$*98
Aeronautical University Daytona

,NICS
ard D.FOR
Curtis
OLUTIONS
ENGINEERING
Embry-Riddle
MANUAL STUDENTS
Aeronautical
to accompany
Howard
University
ORBITAL
D. Daytona
CurtisMECHANICS
Embry-Riddle
Beach, Florida.pdf!@(*)(#&*UY&*$($H(&U@*$*$*&U$*H*@$HN$($
FOR
Aeronautical
ENGINEERING
University
STUDENTS
Daytona Beach,
HowardFlorida.pdf!@(*)(#&*UY&*$($H(&U@*$*$*&U$*H*@$HN
D. Curtis Embry-Riddle
$$N($OJ$J$HJ$M(*$J($(*$*98
Aeronautical University Daytona


Solutions Manual Orbital Mechanics for Engineering Students Chapter 1


Problem 1.1
(a)
( )(
A ⋅ A = Ax iˆ + Ay ˆj + Az kˆ ⋅ Ax iˆ + Ay ˆj + Az kˆ )
( ) ( )
= Ax iˆ ⋅ Ax iˆ + Ay ˆj + Az kˆ + Ay ˆj ⋅ Ax iˆ + Ay ˆj + Az kˆ + Az kˆ ⋅ Ax iˆ + Ay ˆj + Az kˆ ( )
( ) ( ) ( )
=  Ax 2 ( iˆ ⋅ iˆ ) + Ax Ay iˆ ⋅ ˆj + Ax Az ( iˆ ⋅ kˆ )  +  Ay Ax ˆj ⋅ iˆ + Ay 2 ˆj ⋅ ˆj + Ay Az ˆj ⋅ kˆ 
   
( )

( )
+  Az Ax ( kˆ ⋅ iˆ ) + Az Ay kˆ ⋅ ˆj + Az 2 ( kˆ ⋅ kˆ ) 

=  Ax (1) + Ax Ay ( 0 ) + Ax Az ( 0 ) +  Ay Ax ( 0 ) + Ay 2 (1) + Ay Az ( 0 ) +  Az Ax ( 0 ) + Az Ay ( 0 ) + Az 2 (1)
2
     
= Ax 2 + Ay 2 + Az 2


But, according to the Pythagorean Theorem, Ax2 + Ay 2 + Az 2 = A2 , where A = A , the magnitude of
the vector A . Thus A ⋅ A = A2 .

(b)
iˆ ˆj kˆ
A ⋅ ( B × C ) = A ⋅ Bx By Bz
Cx Cy Cz

(  ) (
= Ax iˆ + Ay ˆj + Az kˆ ⋅  iˆ By Cz − Bz C y − ˆj ( Bx Cz − Bz Cx ) + kˆ Bx C y − By Cx 
)  ( )
( )
= Ax By Cz − Bz C y − Ay ( Bx Cz − Bz Cx ) + Az Bx C y − By Cx ( )
or

A ⋅ ( B × C) = AxBy C z + Ay Bz C x + Az BxC y − AxBz C y − Ay BxC z − Az By C x (1)

Note that ( A × B) ⋅ C = C ⋅ ( A × B) , and according to (1)

C ⋅ ( A × B) = C x Ay Bz + C y Az Bx + C z AxBy − C x Az By − C y AxBz − C z Ay Bx (2)

The right hand sides of (1) and (2) are identical. Hence A ⋅ ( B × C) = ( A × B) ⋅ C .

(c)
iˆ ˆj kˆ iˆ ˆj kˆ
(
A × ( B × C ) = Ax iˆ + Ay ˆj + Az kˆ × Bx ) By Bz = Ax Ay Az
Cx Cy Cz By Cz − Bz C y Bz Cx − Bx C y Bx C y − By Cx

=  Ay Bx C y − By Cx − Az ( Bz Cx − Bx Cz )  î +  Az By Cz − Bz C y − Ax Bx C y − By Cx  ˆj
( ) ( ) ( )
   
)
+  Ax ( Bz Cx − Bx Cz ) − Ay By Cz − Bz C y  k̂
  (
= Ay Bx C y + Az Bx Cz − Ay By Cx − Az Bz Cx iˆ + Ax By Cx + Az By Cz − Ax Bx C y − Az Bz C y ˆj
( ) ( )
+ ( Ax Bz Cx + Ay Bz C y − Ax Bx Cz − Ay By Cz ) k̂

= Bx ( Ay C y + Az Cz ) − Cx ( Ay By + Az Bz )  î + By ( Ax Cx + Az Cz ) − C y ( Ax Bx + Az Bz )  ĵ
   
+ Bz ( Ax Cx + Ay C y ) − Cz ( Ax Bx + Ay By )  k̂
 

Add and subtract the underlined terms to get




1


NICS
ard D.FOR
Curtis
OLUTIONS
ENGINEERING
Embry-Riddle
MANUAL STUDENTS
Aeronautical
to accompany
Howard
University
ORBITAL
D. Daytona
CurtisMECHANICS
Embry-Riddle
Beach, Florida.pdf!@(*)(#&*UY&*$($H(&U@*$*$*&U$*H*@$HN$($
FOR
Aeronautical
ENGINEERING
University
STUDENTS
Daytona Beach,
HowardFlorida.pdf!@(*)(#&*UY&*$($H(&U@*$*$*&U$*H*@$HN
D. Curtis Embry-Riddle
$$N($OJ$J$HJ$M(*$J($(*$*98
Aeronautical University Daytona