# Updated Slides-6 Sep 2023

```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
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
```