Foundations of Space Dynamics

Preface xiii
 
1 Introduction 1
 
1.1 Space Flight 1
 
1.1.1 Atmosphere as Perturbing Environment 1
 
1.1.2 Gravity as the Governing Force 4
 
1.1.3 Topics in Space Dynamics 5
 
1.2 Reference Frames and Time Scales 5
 
1.2.1 Sidereal Frame 5
 
1.2.2 Celestial Frame 8
 
1.2.3 Synodic Frame 8
 
1.2.4 Julian Date 8
 
1.3 Classification of Space Missions 10
 
Exercises 10
 
References 11
 
2 Dynamics 13
 
2.1 Notation and Basics 13
 
2.2 Plane Kinematics 14
 
2.3 Newton's Laws 16
 
2.4 Particle Dynamics 17
 
2.5 The n-Body Problem 20
 
2.6 Dynamics of a Body 24
 
2.7 Gravity Field of a Body 27
 
2.7.1 Legendre Polynomials 29
 
2.7.2 Spherical Coordinates 31
 
2.7.3 Axisymmetric Body 34
 
2.7.4 Spherical Body with Radially Symmetric Mass Distribution 37
 
Exercises 37
 
References 40
 
3 Keplerian Motion 41
 
3.1 The Two-Body Problem 41
 
3.2 Orbital Angular Momentum 43
 
3.3 Orbital Energy Integral 45
 
3.4 Orbital Eccentricity 46
 
3.5 Orbit Equation 49
 
3.5.1 Elliptic Orbit 53
 
3.5.2 Parabolic Orbit 56
 
3.5.3 Hyperbolic Orbit 56
 
3.5.4 Rectilinear Motion 58
 
3.6 Orbital Velocity and Flight Path Angle 60
 
3.7 Perifocal Frame and Lagrange's Coefficients 63
 
Exercises 65
 
4 Time in Orbit 69
 
4.1 Position and Velocity in an Elliptic Orbit 70
 
4.2 Solution to Kepler's Equation 75
 
4.2.1 Newton's Method 76
 
4.2.2 Solution by Bessel Functions 78
 
4.3 Position and Velocity in a Hyperbolic Orbit 80
 
4.4 Position and Velocity in a Parabolic Orbit 84
 
4.5 Universal Variable for Keplerian Motion 86
 
Exercises 88
 
References 89
 
5 Orbital Plane 91
 
5.1 Rotation Matrix 91
 
5.2 Euler Axis and

Ashish Tewari is a Professor in the Department of Aerospace Engineering at IIT Kanpur. He specializes in flight mechanics and control.