Transcript ASEN 5050 SPACEFLIGHT DYNAMICS

ASEN 5050
SPACEFLIGHT DYNAMICS
Interplanetary
Prof. Jeffrey S. Parker
University of Colorado – Boulder
Lecture 28: Interplanetary
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Announcements
• HW 8 is out now!
– Due in one week: Wednesday, Nov 12.
– J2 effect
– Using VOPs
• Mid-Term handed back today!
• Concept quiz after today’s lecture, due 8 am Friday
– Not quite ready, but I’ll send out an email.
• Reading: Chapter 12
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Schedule from here out
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11/5: Interplanetary 1
11/7: Interplanetary 2
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11/10: Entry, Descent, and Landing
11/12: Low-Energy Mission Design
11/14: STK Lab 3
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11/17: Low-Thrust Mission Design (Jon Herman)
11/19: Finite Burn Design
11/21: STK Lab 4
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Fall Break
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12/1: Constellation Design, GPS
12/3: Spacecraft Navigation
12/5: TBD
• 12/8: TBD
• 12/10: TBD
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• 12/12: Final Review
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Final Project
• Due 12/18. If you turn it in by 12/12, I’ll forgive 5 pts of
deductions.
• Worth 20% of your grade, equivalent to 6-7 homework assignments.
• Final Exam is worth 25%.
• Find an interesting problem and investigate it – anything related to
spaceflight mechanics (maybe even loosely, but check with me).
• Requirements: Introduction, Background, Description of
investigation, Methods, Results, Conclusions, References.
• You will be graded on quality of work, scope of the investigation,
and quality of the presentation. The project will be built as a
webpage, so take advantage of web design as much as you can
and/or are interested and/or will help the presentation.
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Final Project
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Instructions for delivery of the final project:
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Build your webpage with every required file inside of a directory.
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Name your main web page “index.html”
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Name the directory “LastName_FirstName” i.e., Parker_Jeff/
there are a lot of duplicate last names in this class!
You can link to external sites as needed.
i.e., the one that you want everyone to look at first
Make every link in the website a relative link, relative to the directory structure
within your named directory.
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We will move this directory around, and the links have to work!
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Test your webpage! Change the location of the page on your computer and make
sure it still works!
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Zip everything up into a single file and upload that to the D2L dropbox.
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HTML
• If you’ve never coded in HTML, don’t fret (but don’t
wait to try it out).
• Lots of tutorials online
– One student suggested this page for HTML tutorials:
http://www.codecademy.com/dashboard
• Think of a webpage as a blank canvas, fill it with
invisible tables, lists, links, animations, pictures, and text.
• Word, LaTex, and other programs can save documents as
HTML, but then it’s awful to edit / personalize.
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Space News
• China’s lunar swingby vehicle successfully landed.
• Philae lands next week.
• Neat video of the Aurora Australis, viewed from the
ISS:
http://www.usatoday.com/story/weather/2014/11/04/a
urora-new-zealand-space-station/18470015/
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ASEN 5050
SPACEFLIGHT DYNAMICS
Mid-Term
Prof. Jeffrey S. Parker
University of Colorado – Boulder
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Statistics
• High score: 98
• Mean: 88
• I tried my best to knock down your grades, but couldn’t
find many holes.
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ASEN 5050
SPACEFLIGHT DYNAMICS
Interplanetary
Prof. Jeffrey S. Parker
University of Colorado – Boulder
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Interplanetary Missions
Destination
Missions
Mercury
Mariner 10, MESSENGER
Venus
LOTS
Mars
LOTS
Asteroids, Comets
ISEE-3/ICE, NEAR, Deep Impact, Galileo, Dawn,
Rosetta, etc.
Jupiter
Pioneer 10, 11, Voyager 1, 2, Ulysses, Galileo,
Cassini, New Horizons, Juno
Saturn
Pioneer 11, Voyager 1, 2, Cassini
Uranus
Voyager 2
Neptune
Voyager 2
Pluto / KBO
New Horizons
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History of Interplanetary Exploration
Earth
This timeline may be found here:
http://nssdc.gsfc.nasa.gov/planetary/chronology.html
Moon
Moon
1st Mission to get close to the
Moon
1st Mission to impact the Moon
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History of Interplanetary Exploration
Moon
Mars
Moon
Venus
1st Mission to fly by Venus
Moon
Moon
Venus
Americans fly by Venus
Moon
Mars
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History of Interplanetary Exploration
Americans successfully impact
the Moon
First Mars Flyby
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History of Interplanetary Exploration
1st Soft Lunar Landing
1st American soft lunar landing
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History of Interplanetary Exploration
1st Venus Atmospheric probe
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History of Interplanetary Exploration
Humans are at the Moon!
Humans are at the Moon!
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History of Interplanetary Exploration
Apollo
‘Nuff Said
Apollo
Apollo
Robotic lunar sample return
Robotic lunar rover
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History of Interplanetary Exploration
Apollo
Mars orbiters
Apollo
1st Mission to Jupiter!
Apollo
Apollo
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Final Apollo mission
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History of Interplanetary Exploration
1st Mission to Saturn!
1st Mission to Mercury
1st Mars lander
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History of Interplanetary Exploration
Grand Tour
1st libration orbiter and Comet
flyby
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History of Interplanetary Exploration
1st Japanese mission
1st ESA mission
1st Jupiter Orbiter
1st Low-Energy Lunar Transfer
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History of Interplanetary Exploration
1st Asteroid Orbiter
1st Mars Rover
1st Saturn Orbiter
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History of Interplanetary Exploration
1st Comet Sample Return
1st Asteroid Sample Return
1st Low-Thrust Lunar Transfer
1st Mercury Orbiter
1st Comet Impact
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History of Interplanetary Exploration
1st Mission to Pluto/KBOs
1st Low-Thrust to Main Belt
Asteroids
1st Chinese mission
1st Indian mission
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Future Exploration
• Ongoing exploration at Mars
• Human exploration aiming for Mars
– Waypoints may include the Moon, L2, Asteroids, and/or
Phobos/Deimos.
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Europa
Enceladus
Titan Lakes
Uranus/Neptune systems
Other stars!?
• Plenty of proposals being submitted for every major (and
many minor) destinations in the solar system.
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Interplanetary Trajectories
• Pioneer 10’s Interplanetary Trajectory
– Earth – Jupiter
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Interplanetary Trajectories
• Pioneer 11’s Interplanetary Trajectory
– Earth – Jupiter – Saturn
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Interplanetary Trajectories
• Mariner 10’s Interplanetary Trajectory
– Earth – Venus – Mercury
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Interplanetary Trajectories
• Voyager 1’s and Voyager 2’s Interplanetary
Trajectories: Earth – Jupiter – Saturn & Beyond
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Interplanetary Trajectories
• Galileo’s Trajectory to Jupiter
– VEEGA (Venus – Earth – Earth Gravity Assist)
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Interplanetary Trajectories
• Cassini’s Trajectory to Saturn
– VVEJGA (Venus – Venus – Earth - Jupiter Gravity Assist)
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Interplanetary Trajectories
• Ulysses’ Trajectory past Jupiter
Image courtesy of: Planetary and Space Science, Volume 54, Issues 9–10, August 2006, Pages 932–956
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Interplanetary Trajectories
• Juno’s Trajectory to Jupiter
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Interplanetary Trajectories
• MESSENGER’s Trajectory to Mercury
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Interplanetary Trajectories
• DAWN’s Trajectory to Main Belt Asteroids
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Moon Tours
• Jupiter: Galileo
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Moon Tours
• Saturn: Cassini
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Cassini’s Extended Mission
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Cassini’s Extended Mission
Why are there no
small body flybys
here?
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Building an Interplanetary Transfer
• Simple:
– Step 1. Build the transfer from Earth to the planet.
– Step 2. Build the departure from the Earth onto the
interplanetary transfer.
– Step 3. Build the arrival at the destination.
• Added complexity:
– Gravity assists
– Solar sailing and/or electric propulsion
– Low-energy transfers
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Patched Conics
• Use two-body orbits
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Patched Conics
• Gravitational forces during an Earth-Mars transfer
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Sphere of Influence
• Measured differently by different astrodynamicists.
– “Hill Sphere”
– Laplace derived an expression that matches real trajectories
in the solar system very well.
• Laplace’s SOI:
– Consider the acceleration of a spacecraft in the presence of
the Earth and the Sun:
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Sphere of Influence
• Motion of the spacecraft relative to the Earth with the
Sun as a 3rd body:
• Motion of the spacecraft relative to the Sun with the
Earth as a 3rd body:
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Sphere of Influence
• Laplace suggested that the Sphere of Influence (SOI)
be the surface where the ratio of the 3rd body’s
perturbation to the primary body’s acceleration is
equal.
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Sphere of Influence
• Laplace suggested that the Sphere of Influence (SOI)
be the surface where the ratio of the 3rd body’s
perturbation to the primary body’s acceleration is
equal.
Primary Earth Accel
Primary Sun Accel
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3rd Body Sun Accel
3rd Body Earth Accel
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Sphere of Influence
• Laplace suggested that the Sphere of Influence (SOI)
be the surface where the ratio of the 3rd body’s
perturbation to the primary body’s acceleration is
equal.
Primary Earth Accel
3rd Body Sun Accel
=
Primary Sun Accel
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3rd Body Earth Accel
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Sphere of Influence
• Find the surface that sets these ratios equal.
After simplifications:
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Sphere of Influence
• Find the surface that sets these ratios equal.
Earth’s SOI: ~925,000 km
Moon’s SOI: ~66,000 km
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Patched Conics
• Use two-body orbits
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Interplanetary Transfer
• Use Lambert’s Problem
• Earth – Mars in 2018
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Interplanetary Transfer
• Lambert’s Problem gives you:
– the heliocentric velocity you require at the Earth departure
– the heliocentric velocity you will have at Mars arrival
• Build hyperbolic orbits at Earth and Mars to connect
to those.
– “V-infinity” is the hyperbolic excess velocity at a planet.
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Earth Departure
• We have v-infinity at departure
• Compute specific energy of departure wrt Earth:
• Compute the velocity you need at some parking orbit:
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Earth Departure
Departing from a circular orbit, say, 185 km:
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Launch Target
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Launch Target
Earth Departure Op ons
Outgoing V ∞
Vector
Locus of all possible
interplanetary injection points
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Launch Targets
• C3, RLA, DLA
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Launch Targets
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Mars Arrival
• Same as Earth departure, except you can arrive in
several ways:
– Enter orbit, usually a very elliptical orbit
– Enter the atmosphere directly
– Aerobraking. Aerocapture?
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Aerobraking
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Comparing Patched Conics to HighFidelity
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Gravity Assists
• A mission designer can harness the gravity of other
planets to reduce the energy needed to get
somewhere.
• Galileo launched with just enough energy to get to
Venus, but flew to Jupiter.
• Cassini launched with just enough energy to get to
Venus (also), but flew to Saturn.
• New Horizons launched with a ridiculous amount of
energy – and used a Jupiter gravity assist to get to
Pluto even faster.
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Gravity Assists
• Gravity assist, like pretty much everything else, must obey the
laws of physics.
• Conservation of energy, conservation of angular momentum,
etc.
So how did Pioneer 10 get such
a huge kick of energy, passing
by Jupiter?
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Designing Gravity Assists
• Rule: Unless a spacecraft performs a maneuver or flies
through the atmosphere, it departs the planet with the
same amount of energy that it arrived with.
• Guideline: Make sure the spacecraft doesn’t impact the
planet (or rings/moons) during the flyby, unless by
design.
Turning
Angle
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How do they work?
• Use Pioneer 10 as an example:
OUT OF FLYBY
INTO FLYBY
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Gravity Assists
• We assume that the planet doesn’t move during the flyby
(pretty fair assumption for initial designs).
– The planet’s velocity doesn’t change.
• The gravity assist rotates the V-infinity vector to any
orientation.
– Check that you don’t hit the planet
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Gravity Assists
• We assume that the planet doesn’t move during the flyby
(pretty fair assumption for initial designs).
– The planet’s velocity doesn’t change.
• The gravity assist rotates the V-infinity vector to any
orientation.
– Check that you don’t hit the planet
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Designing a Gravity Assist
• Build a transfer from Earth to Mars (for example)
– Defines
at Mars
• Build a transfer from Mars to Jupiter (for example)
– Defines
at Mars
• Check to make sure you don’t break any laws of
physics:
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Gravity Assists
Please note!
This illustration is a
compact, beautiful
representation of gravity
assists.
But know that the
incoming and outgoing
velocities do NOT need
to be symmetric about the
planet’s velocity! This is
just for illustration.
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Gravity Assists
• We can use them to increase or decrease a
spacecraft’s energy.
• We can use them to add/remove out-of-plane
components
– Ulysses!
• We can use them for science
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