Current Trends in Spaceflight Research:

From Galileo to Cassini and Beyond

Mrinal KumarAssistant Professor, MAE

306 MAE-Amrinalkumar@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

• Astronautics: astron + nauticus: navigation through the stars

• Astronomy: astron + nomos: related field, observation of stars etc.

Old school; only natural bodies like stars, planets, asteroids

More contemporary; study motion under gravity in general, including natural objects and especially, spacecraft

www.fascinatingly.com

www.gpsmagazine.com

www.nasa.gov

IAU

The Cradle of Mathematics

• Geometrical Analysis: Tycho Brahe, Johannes Kepler

• Calculus: Isaac Newton, Gottfried Leibniz

• Calculus of Variations: Leonhard Euler, Joseph Lagrange, Pierre-Simon 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

GalileoCopernicusBraheKepler

Pre- 1700’s 1700’s

Newton calculus (simultaneously /w Leibniz)law of universal gravitationlaws of motionPrincipia Mathematica

Euler calculus of variations, PDE theoryrigid body dynamicsfluid mechanicsauthor of numerous papers

Gaussprobability theorysystem of equationsboundary value problemsDisquisitiones AritmeticaeTheoria Motus

“pauca sed matura”

Galileo Copernicus Brahe Kepler

A While Ago: A History of Celestial Mechanics

1800’s

Jacobicalculus of variationsrigid body dynamicsspecial functions and PDEs

Lagrangecalculus of variationsanalytical mechanicsMecanique Analytique

Hamiltoncalculus of variationscanonical equations of mechanicsquaternions, rotational dynamics

Laplace

special functions and PDEslinear equationspotential theory

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 vector analysismatrix theorythermodynamics

Einstein quantum mechanicsgeneral and special relativitymodern physics

Cayley matrix analysisdifferential equationslinear 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

Trajectory design and Navigation

Sensor technology

Contemporary Celestial Mechanics (USA)

UCLA: Sam Herrick (1911 – 1974)

Purdue: James Longuski Kathleen Howell

MIT: Richard Battin; Jonathan How

Boulder: George Born, Robert Culp; Dan Scheeres, Hanspeter Schaub

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

Explore: Gravity assists, Patched conics

Deep Space Exploration/Advanced Mission Design:

www.nasa.gov

Some Current Problems of Interest

Deep Space Exploration/Advanced Mission Design:

An Interplanetary Superhighway

Objectives:

• Minimize fuel weight• Maximize Solar system exploration

Explore: Lagrange points, Halo orbits, Lissajous Orbits

People: Dan Scheeres, Boulder Martin Lo, JPL Shane Ross, VTech

www.nasa.gov

Some Current Problems of Interest

Aerocapture/Aerobraking Technologies:

Some Current Problems of Interest

Aerocapture/Aerobraking Technologies:

Explore: Mars Global Surveyor,Mars Odyssey Entry corridorAtmospheric 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

Flower constellations

4-1-4

3-1-50

Explore: Clohessy-Wiltshire Eqns.Discrete number theoryGPS constellationsFlower constellations

People: Daniele Mortari (TAMU) John Junkins (TAMU) Hanspeter Schaub (Boulder) Jonathan How (MIT)

Formation Flying: Spacecraft Constellations

Some Current Problems of Interest

Novel Control Methods:

•High Earth Orbits•Control Neighboring S/C within 10-1000 m•Nearly “propellant-less control”

Coulomb Spacecraft Formation Control

People: Hanspeter Schaub (Boulder)

Some Current Problems of Interest

Novel Control Methods:Navigation with Solar Sails

•Fragile spacecraft•Operates on radiation pressurePeople: Dan Scheeres (Boulder)

NASA/MFSC (Alabama)

Some Current Problems of Interest

Space Debris Management:

View of debris in LEO Expanded view of debris to include HEO

• Defunct spacecraft • Broken up spacecraft• New collisions

• Threat to active spacecraft• Threat to astronauts

www.nasa.gov www.nasa.gov

Some Current Problems of Interest

Space Debris Management:

Space shuttle window damage Collision between Iridium 33 and Cosmos 2251 on Feb 10, 2009, 490 miles over Siberia

Explore: Cloud propagationTethered Spacecraft

People: Mrinal Kumar(UF) David Spencer (Penn State) Dan Scheeres (Boulder) NASA Orbital Debris Program

www.nasa.gov

Some Current Problems of Interest

Uncertainty in Space:

Space collisions: Asteroid + Planet Debris + Spacecraft

Space object tracking: Nonlinear Filtering Theory

Asteroid 4581-Asclepius(1989-FC)

• Near Earth Asteroid (NEA) Program

• Potentially Hazardous Asteroids (PHA’s)

Project LINEARProject SpacewatchProject Neat

www.nature-talk.com

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 SystemsProbability FlowFokker-Planck equationNonlinear 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!!