Study spacecraft trajectories and orbital dynamics
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Orbital Mechanics is available on both platforms
iPhone/iPad: download the single MasterNow app from the App Store — Orbital Mechanics is included with all subjects. Android: download the dedicated Orbital Mechanics subject app from Google Play.
133
Sub Topics
326
MCQs
156
MCOs
244
True/False
120
Fill Blanks
42
Rearrange
129
Matching
70
Comprehensions
120
Flashcard Decks
Curriculum
What You'll Learn
01 Fundamentals of Orbital Mechanics 3 topics
1 Historical Development of Orbital Theory
- Ancient Astronomical Observations
- Kepler's Contributions
- Newton's Universal Gravitation
2 Basic Terminology and Definitions
- Orbital Elements
- Reference Frames
- Coordinate Systems
3 Mathematical Preliminaries
- Vector Analysis
- Differential Equations in Orbital Problems
- Numerical Methods in Orbital Mechanics
02 Two-Body Problem 4 topics
1 Derivation of the Two-Body Equation of Motion
- Conservation Laws
- Center of Mass Reference Frame
2 Orbital Energy and Angular Momentum
- Specific Mechanical Energy
- Angular Momentum Vector
3 Orbital Parameters
- Semi-major Axis
- Eccentricity
- Inclination
- Right Ascension of Ascending Node
- Argument of Periapsis
- True Anomaly
4 Elliptical, Parabolic, and Hyperbolic Orbits
- Mathematical Descriptions
- Physical Interpretations
- Boundary Conditions
03 Orbital Maneuvering 4 topics
1 Basic Orbital Maneuvers
- Hohmann Transfers
- Bi-elliptic Transfers
- Inclination Changes
2 Impulsive Maneuvers
- Delta-V Calculations
- Optimal Maneuvering Strategies
3 Low-Thrust Continuous Maneuvers
- Spiral Trajectories
- Constant Acceleration Trajectories
4 Rendezvous Techniques
- Phasing Orbits
- Terminal Approach Strategies
04 Orbital Perturbations 5 topics
1 Non-spherical Gravitational Fields
- Earth's Oblateness (J₂ Effect)
- Higher-order Gravitational Harmonics
2 Atmospheric Drag
- Atmospheric Models
- Drag Equations
- Orbit Decay Predictions
3 Third-body Perturbations
- Solar and Lunar Gravitational Effects
- Lagrange Points
4 Solar Radiation Pressure
- Direct Radiation Effects
- Albedo and Earth Radiation
5 Relativistic Effects
- Perihelion Precession
- Gravitational Time Dilation
05 Orbit Determination 4 topics
1 Classical Orbit Determination Methods
- Gauss' Method
- Laplace's Method
2 Modern Techniques
- Batch Least Squares Estimation
- Kalman Filtering
- Extended Kalman Filter
3 Observational Data Types
- Range and Range-Rate Measurements
- Angular Measurements
- GPS Observations
4 State Covariance Analysis
- Error Ellipsoids
- Propagation of Uncertainties
06 Interplanetary Trajectories 4 topics
1 Patched-Conic Approximation
- Sphere of Influence Concept
- Trajectory Design Using Patched Conics
2 Gravity Assist Maneuvers
- Physics of Gravity Assists
- Multiple Flyby Trajectories
3 Porkchop Plots and Launch Windows
- Transfer Energy Requirements
- Launch Window Analysis
4 Interplanetary Navigation
- Deep Space Network
- Optical Navigation
- Autonomous Navigation
07 Lagrangian Dynamics in Orbital Mechanics 4 topics
1 Lagrangian Formulation
- Generalized Coordinates
- Euler-Lagrange Equations
2 Hamiltonian Dynamics
- Canonical Transformations
- Hamilton-Jacobi Theory
3 Application to Orbital Problems
- Perturbed Two-Body Problem
- Restricted Three-Body Problem
4 Variational Methods in Trajectory Optimization
- Calculus of Variations
- Pontryagin's Maximum Principle
08 Three-Body and N-Body Problems 5 topics
1 Circular Restricted Three-Body Problem
- Equations of Motion
- Jacobi Integral
2 Lagrangian Points
- Stability Analysis
- Halo Orbits
- Lissajous Orbits
3 Periodic Orbits
- Families of Periodic Orbits
- Stability and Bifurcation
4 Chaos in Orbital Dynamics
- Lyapunov Exponents
- Poincaré Sections
5 N-Body Simulations
- Integration Techniques
- Hierarchical Methods
09 Attitude Dynamics and Control 4 topics
1 Rigid Body Dynamics
- Euler's Equations
- Moment of Inertia
2 Attitude Representations
- Euler Angles
- Quaternions
- Direction Cosine Matrices
3 Environmental Torques
- Gravity Gradient
- Magnetic Torque
- Solar Radiation Pressure
4 Attitude Control Systems
- Momentum Wheels
- Control Moment Gyros
- Thrusters
- Magnetic Torquers
10 Space Mission Design 4 topics
1 Mission Requirements Analysis
- Science Requirements
- Engineering Constraints
2 Orbit Selection Criteria
- Sun-Synchronous Orbits
- Geostationary Orbits
- Molniya Orbits
- Frozen Orbits
3 Launch Vehicle Selection
- Performance Capabilities
- Payload Fairing Constraints
4 End-of-Life Considerations
- Deorbit Planning
- Graveyard Orbits
- Space Debris Mitigation
11 Numerical Techniques in Orbital Mechanics 4 topics
1 Integration Methods
- Runge-Kutta Methods
- Predictor-Corrector Methods
- Symplectic Integrators
2 Error Analysis and Stability
- Truncation Errors
- Round-off Errors
- Step Size Selection
3 Special Perturbation Techniques
- Cowell's Method
- Encke's Method
- Variation of Parameters
4 Regularization Techniques
- Kustaanheimo-Stiefel Regularization
- Levi-Civita Transformation
12 Advanced Topics in Orbital Mechanics 5 topics
1 Relativistic Orbital Mechanics
- Post-Newtonian Approximations
- Schwarzschild Metric
2 Low-Energy Transfers
- Weak Stability Boundary Theory
- Interplanetary Superhighways
3 Formation Flying
- Relative Motion Dynamics
- J₂-Invariant Orbits
4 Non-Keplerian Orbits
- Solar Sails
- Electrodynamic Tethers
- Artificial Lagrange Points
5 Quantum Orbital Mechanics
- Quantum Effects on Orbital Motion
- Future Theoretical Developments
13 Appendices 4 topics
1 Constants and Reference Data
- Planetary Physical Parameters
- Astronomical Constants
2 Coordinate Transformations
- Earth-Centered Inertial to Earth-Centered Earth-Fixed
- Ecliptic to Equatorial
3 Reference Algorithms
- Time System Conversions
- Orbit Propagation
4 Case Studies
- Historical Space Missions
- Trajectory Design Examples
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