Lecture Slides Updated Till 6 Sep 2023 RAMA KRISHNA K MCL318: Introduction to Orbital Mechanics यान्त्रिकी अभियिण भििाग िारतीय प्रौद्योभगकी संस्थान भिल्ली Department of Mechanical Engineering Indian Institute of Technology Delhi MCL318: Introduction to Orbital Mechanics 1 Two Body Problem MCL318: Introduction to Orbital Mechanics 2 Introduction • Determine motion of two bodies solely due to their mutual gravitational attraction Two masses in inertial frame MCL318: Introduction to Orbital Mechanics Free body diagrams 3 Equations of Absolute Motion in Inertial Frame • Velocity of Center of Mass (G ) • Acceleration of Center of Mass (G ) MCL318: Introduction to Orbital Mechanics 4 Relative Motion in Inertial Frame • Position vector of • Let relative to be the unit vector pointing from MCL318: Introduction to Orbital Mechanics towards 5 Equations of Motion • Newton’s Equations of Motion Acceleration of C.M. is zero MCL318: Introduction to Orbital Mechanics 6 Equations of Relative Motion • Newton’s Equations of Motion Acceleration of C.M. is zero MCL318: Introduction to Orbital Mechanics 7 Equations of Relative Motion Gravitational Parameter • 3 Non-linear Second Order ODEs • Govern motion of MCL318: Introduction to Orbital Mechanics relative to 8 Some Equations MCL318: Introduction to Orbital Mechanics 9 Some Equations • Finally Eccentricity Vector • Line defined by is called APSE LINE MCL318: Introduction to Orbital Mechanics 10 Velocity Components • Periapsis and Apoapsis • Transverse Component • Radial Component MCL318: Introduction to Orbital Mechanics 11 Till Now MCL318: Introduction to Orbital Mechanics 12 Perifocal Frame • Natural Frame for Orbit centered at Focus • along Apse Line • at 90 deg to • normal to plane along where MCL318: Introduction to Orbital Mechanics 13 Position and Velocity in Perifocal Frame • Natural Frame for Orbit centered at Focus • Radial component of velocity is , • Transverse component of velocity MCL318: Introduction to Orbital Mechanics 14 Position and Velocity in Perifocal Frame • Substituting, we get MCL318: Introduction to Orbital Mechanics 15 Example Problem-1 • Problem • Solution MCL318: Introduction to Orbital Mechanics 16 Example Problem-2 • Problem • Solution (Why not fourth quadrant?) MCL318: Introduction to Orbital Mechanics 17 Thank You MCL318: Introduction to Orbital Mechanics 18