Current Trends in Spaceflight
Research:
From Galileo to Cassini and Beyond
Mrinal Kumar
Assistant Professor, MAE
306 MAE-A
mrinalkumar@ufl.edu
http://www.mae.ufl.edu/~mrinalkumar
Presentation Outline
o PAST
o PRESENT (including my research interests)
o FUTURE
Presentation Outline
o PAST
•
•
Centuries ago
Decades ago
o PRESENT (including my research interests)
o FUTURE
Many names, but not for the same thing…
• Celestial Mechanics: motion of celestial bodies
• Astrodynamics: astron + dynamics
• Orbital Mechanics: mechanics in orbit
• Space Dynamics: motion in space
Old school; only natural
bodies like stars, planets,
asteroids
More contemporary;
study motion under gravity in
general, including natural objects
and especially, spacecraft
• Astronautics: astron + nauticus: navigation through the stars
www.nasa.gov
• Astronomy: astron + nomos: related field,
observation of stars etc.
www.fascinatingly.com
IAU
www.gpsmagazine.com
The Cradle of Mathematics
• Geometrical Analysis: Tycho Brahe, Johannes Kepler
• Calculus: Isaac Newton, Gottfried Leibniz
• Calculus of Variations: Leonhard Euler, Joseph Lagrange, PierreSimon Laplace, William Rowan Hamilton
• Vector analysis: Josiah Gibbs
• Linear Algebra: Arthur Cayley
• Numerical methods: Carl Friedrich Gauss, numerous others
Long Long Ago: A History of Celestial Mechanics
1700’s
Pre- 1700’s
Newton
Euler
Galileo
Copernicus
Brahe
Kepler
Gauss
Galileo
Copernicus
Brahe
Kepler
calculus (simultaneously /w Leibniz)
law of universal gravitation
laws of motion
Principia Mathematica
calculus of variations, PDE theory
rigid body dynamics
fluid mechanics
author of numerous papers
probability theory
system of equations
boundary value problems
Disquisitiones Aritmeticae
Theoria Motus
“pauca sed matura”
A While Ago: A History of Celestial Mechanics
1800’s
Jacobi
Laplace
calculus of variations
rigid body dynamics
special functions and PDEs
special functions and PDEs
linear equations
potential theory
Hamilton
Lagrange
calculus of variations
analytical mechanics
Mecanique Analytique
calculus of variations
canonical equations of mechanics
quaternions, rotational dynamics
Problems of Interest: Two examples
The Lambert’s Problem
Kepler’s Time Equation
Not So Long Ago: Celestial Mechanics
Late 1800’s – Early 1900’s
Gibbs
Cayley
vector analysis
matrix theory
thermodynamics
matrix analysis
differential equations
linear algebra
Since 1900’s
No giants in particular, but
numerous smaller contributions
leading to development of the field
Numerical methods
Estimation theory: Kalman Filter
Optimization theory and control
Einstein
quantum mechanics
general and special relativity
modern physics
Trajectory design and Navigation
Sensor technology
Contemporary Celestial Mechanics (USA)
UCLA: Sam Herrick (1911 – 1974)
MIT: Richard Battin;
Jonathan How
Boulder: George Born, Robert Culp;
Dan Scheeres, Hanspeter Schaub
Purdue: James Longuski
Kathleen Howell
Texas A&M: John Junkins (Sam Herrick’s student at UCLA)
Daniele Mortari, Kyle Alfriend
Malcolm Shuster: Last academic appointment at UF
Some Current Problems of Interest
o Deep Space Exploration/Advanced Mission Design
o Aerocapture and Aerobraking Technologies
o Formation Flying: Spacecraft Constellations
o Novel Methods of Control
o Space Debris Management
o Uncertainty Handling in Space
Some Current Problems of Interest
Deep Space Exploration/
Advanced Mission Design:
www.nasa.gov
Explore: Gravity assists,
Patched conics
Some Current Problems of Interest
Deep Space Exploration/
Advanced Mission Design:
www.nasa.gov
Objectives:
• Minimize fuel weight
• Maximize Solar system exploration
Explore: Lagrange points,
Halo orbits,
Lissajous Orbits
An Interplanetary Superhighway
People: Dan Scheeres, Boulder
Martin Lo, JPL
Shane Ross, VTech
Some Current Problems of Interest
Aerocapture/Aerobraking
Technologies:
Some Current Problems of Interest
Aerocapture/Aerobraking
Technologies:
Explore: Mars Global Surveyor,
Mars Odyssey
Entry corridor
Atmospheric modeling
Ablatives
People: James Longuski
(Purdue)
Some Current Problems of Interest
Formation Flying:
Spacecraft Constellations
Simple formation: Docking
Complex formation:
Maintaining cluster shape
for max coverage
Some Current Problems of Interest
Formation Flying:
Spacecraft Constellations
3-1-50
4-1-4
Flower constellations
Explore: Clohessy-Wiltshire Eqns.
Discrete number theory
GPS constellations
Flower constellations
People: Daniele Mortari (TAMU)
John Junkins (TAMU)
Hanspeter Schaub (Boulder)
Jonathan How (MIT)
Some Current Problems of Interest
Novel Control Methods:
Coulomb Spacecraft
Formation Control
People: Hanspeter Schaub (Boulder)
•High Earth Orbits
•Control Neighboring S/C within 10-1000 m
•Nearly “propellant-less control”
Some Current Problems of Interest
Novel Control Methods:
Navigation with Solar Sails
People: Dan Scheeres (Boulder)
NASA/MFSC (Alabama)
•Fragile spacecraft
•Operates on radiation pressure
Some Current Problems of Interest
Space Debris Management:
• Defunct spacecraft
• Broken up spacecraft
• New collisions
www.nasa.gov
View of debris in LEO
• Threat to active spacecraft
• Threat to astronauts
www.nasa.gov
Expanded view of debris
to include HEO
Some Current Problems of Interest
Space Debris Management:
www.nasa.gov
Space shuttle window damage
Explore: Cloud propagation
Tethered Spacecraft
Collision between Iridium 33 and Cosmos 2251
on Feb 10, 2009, 490 miles over Siberia
People: Mrinal Kumar(UF)
David Spencer (Penn State)
Dan Scheeres (Boulder)
NASA Orbital Debris Program
Some Current Problems of Interest
Uncertainty in Space:
Space collisions:
Space object tracking:
Asteroid + Planet
Debris + Spacecraft
www.nature-talk.com
Nonlinear Filtering Theory
• Near Earth Asteroid
(NEA) Program
• Potentially Hazardous
Asteroids (PHA’s)
Asteroid 4581-Asclepius
(1989-FC)
Project LINEAR
Project Spacewatch
Project Neat
Some Current Problems of Interest
Uncertainty in Space: Space collisions:
Asteroid + Planet
Case in point:
99942 Apophis
Some Current Problems of Interest
Uncertainty in Space:
Explore: Stochastic Systems
Probability Flow
Fokker-Planck equation
Nonlinear Bayes’ Filtering
People: Mrinal Kumar (UF)
Don Yeomans, JPL
Suman Chakravorty (TAMU)
Dan Scheeres (Boulder)
Summary
• Spaceflight research has a LONG history
• It has continuously spurred development in mathematics
• Spaceflight research is extremely rich in mathematics
• Current space research is inherently multi-disciplinary
• Please
see me if you want to work on
one/more of the described problems!!