Transcript ASEN 5050 SPACEFLIGHT DYNAMICS

ASEN 5050
SPACEFLIGHT DYNAMICS
Mission Orbits, Constellation Design
Prof. Jeffrey S. Parker
University of Colorado – Boulder
Lecture 35: Orbits
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Announcements
• STK Lab 3 due Friday 12/5
• STK Lab 4 due 12/12
– Planetary ephemerides should be changed to DE421 instead
of “Default”
• Final Exam on 12/12, due 12/18
– Take-home, open book open notes
• Final project and exam due 12/18
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Schedule from here out
• 12/3: Mission Orbits, Constellation Design
• 12/5: Spacecraft Navigation
• 12/8: Final Review, part 1
• 12/10: Final Review, part 2
• 12/12: Deep Impact
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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
•
Instructions for delivery of the final project:
•
Build your webpage with every required file inside of a directory.
–
–
–
•
Name your main web page “index.html”
–
•
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.
–
We will move this directory around, and the links have to work!
•
Test your webpage! Change the location of the page on your computer and make
sure it still works!
•
Zip everything up into a single file and upload that to the D2L dropbox.
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Space News
• Japan’s Hayabusa 2 launched last night!
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Space News
• Japan’s Hayabusa 2 launched last night!
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Space News
• Orion’s Exploration Flight Test 1: Thurs 12/4 at 7:04 am
Eastern Time (5:04 am Mountain!). Duration: 4.5 hours.
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ASEN 5050
SPACEFLIGHT DYNAMICS
Mission Orbits
Prof. Jeffrey S. Parker
University of Colorado – Boulder
Lecture 35: Orbits
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Satellite Populations
Molniya
28.5
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Satellite Populations
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Satellite Populations
Molniya, GNSS
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Satellite Populations
Gabbard classes
GEO
GNSS
GTO
ISS
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Satellite Populations
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Frozen Orbits
• Molniya orbits are designed to
have a critical inclination, such
that the argument of perigee
does not change over time.
• Example plots for NROSS’
frozen orbit characteristics:
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Repeat Groundtracks
• Exact Repeat Groundtracks
– A satellite’s ground track returns to exactly the same
latitude/longitude that it began.
• Should occur within ~50 days for this classification
– The satellite never flies over much of the Earth.
• Near-exact Repeat Groundtracks
– A satellite’s ground track returns to a point very near its
starting point.
– The drift provides a dense coverage of the Earth.
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Repeat Groundtracks
• Example exact repeat groundtracks
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Repeat Groundtracks
The nodal crossings occur in a pattern
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Some Period Definitions
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General Perturbation Techniques
The secular change of the orbital elements due to J2 is given from
the Lagrange Planetary Equations as:
2
W SEC
3nRÅ J 2
=cos(i )
2
2p
wSEC
3nRÅ J 2
2
(
=
4
5sin
(i ))
2
4p
2
3nRÅ J 2 1 - e 2
2
(
M 0 SEC = 3sin
(i )- 2 )
2
4p
and a = e = i = 0
2
J2 = 0.00108262693
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Nodal Period
æ
ö
æ
ö
÷
ç
÷
2p
2p
2p ç
1
1
ç
÷ = PK ç
÷
PW =
=
=
M +w n + M0 +w
n ç M0 +w ÷
çç 1+ M 0 + w ÷÷
ç 1+
÷
è
è
n ø
n ø
For small eccentricities, we can ignore terms containing e 2 :
2
3nJ 2 æ RÅ ö
2
2
M0 +w »
ç
÷ 2 - 3sin i + 4 - 5sin i
4 è a ø
æ
ç
1
Therefore PW @ PK ç
ç 3nJ æ R ö2
2
2
ç 1+
ç Å ÷ 3 - 4sin i
2 è a ø
è
1
Since
= 1- x + O(x 2 )
1+ x
é 3nJ æ R ö2
ù
2
Å
2
Then PW @ PK ê1ç
÷ 3- 4sin i ú
2 è a ø
êë
úû
{(
)}
) (
(
(
Lecture 35: Orbits
)
ö
÷
÷ + O(e 2 )
÷
÷
ø
)
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Exact Repeat Constraint
TERP =
2p N ERP
= PqG N ERP
wÅ - W
N ERP = Exact repeat period in integer number of nodal days (10 for TOPEX)
TERP = Exact repeat period in solar days (9.9156 for TOPEX)
K = number of revolutions per a repeat period (K =127 for TOPEX)
Only certain combination of K and N ERP
will yield valid orbits (will specify the orbit radius, r)
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Altitude/Inclination vs NERP/K
NERP/K
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Groundtrack Drift
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TOPEX Crosstrack Drift
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Altimetry Missions
• Consider Topex/Poseidon, Jason, Jason-2, and the like.
– They perform remote sensing operations of the ocean surface,
including measuring the sea surface height, sea surface
smoothness, temperature, etc.
• Driving requirements:
– The orbit must be very well known and well determined.
• A meter error in height may make the ocean height estimation off by a
meter – very significant!
– The orbit should pass over a large portion of the ocean’s surface.
– The orbit should pass over the same points within a reasonably
short time period.
– The fly-over period should not alias any effects that significantly
contribute to the motion of water in the ocean, such as tides.
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Altimetry Missions
• Parke et al. (1987) developed the following requirements
for the orbit of Topex/Poseidon:
– The satellite’s altitude must be known to within 14 cm
• The orbit should be compatible with that sort of OD requirement. I.e.,
it would not work to orbit too close to the atmosphere or in an unstable
resonance with the gravity field.
– Minimize the spatial and temporal aliases on surface geotrophic
currents, geoid variations, etc.
– Subsatellite groundtrack should repeat within 1 km.
– Tidal aliases will not be aliased into semiannual, annual, or zero
frequencies or to frequencies close to these.
– The global grid of subsatellite points must extend as far south as
the southern limit of the Drake Passage (62 deg S)
– The ascending and descending tracks must cross at sufficiently
large angles to resolve the 2D geostrophic current.
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Altimetry Missions
• Station Keeping
• Atmospheric drag is one of the largest effects that drives
the ground track away from its reference, and therefore
must be compensated for using maneuvers.
• For a circular orbit and neglecting the Earth’s rotation:
• The loss of energy over time due to drag:
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Altimetry Missions
• The loss of energy over time due to drag:
Varies with time
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Altimetry Missions
• The change in energy over time:
• Integrate:
• Integrate over one orbit period:
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Altimetry Missions
• The change in energy over time:
• Integrate:
• If drag were estimated with 50% accuracy, then the
orbit error for the satellite will be < 1 cm for a
satellite above 1100 km.
– Recommendation: remain above 1100 km and preferably
above 1300 km.
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Altimetry Missions
• Effects of Solar Radiation Pressure.
• Since solar panels are virtually always pointing
toward the Sun, there is always a force acting on the
satellite, and it changes the circular orbit’s semimajor
axis:
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Altimetry Missions
• Circular orbits:
Minimum: between 1200 – 1300 km
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Altimetry Missions
Altitude
•Desirable to be as high as possible for OD
•Desirable to be 1200 – 1300 km for station keeping
– Good for link budgets too
•Desirable to be below 1500 km for radiation – Van
Allen Belts!
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Altimetry Missions
• Polar Crossing Angle: psi
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Desirable > 40 deg
Altimetry Missions
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Less Desirable
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Desirable > 40 deg
Altimetry Missions
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Altimetry Missions
Orbit Period Considerations
• Tidal Aliasing
– Want to avoid this:
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Altimetry Missions
• Tidal Aliasing, the frequencies, periods, and
amplitudes of the most significant tidal constituents:
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Primary Lunar Tide
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Vertical displacement
•If the Earth’s surface was in equilibrium with the
potential from the moon, the vertical displacement of
the surface would be in the shape of an ellipsoid
elongated toward the moon.
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The Principal Tide: M2
•The largest component of the tides is associated with the
potential due to the moon and with the frequency of the motion
of the Earth-moon system around its center of mass.
•The time from high moon to high moon:
1 lunar day (1 + 1 day/ 27.5 days) = 24 hours 50.47 minutes
•High tide separation is half of this:
–12 hours 25 minutes
•However, this component, like all of the semi-diurnal (and
diurnal) tides is not in equilibrium with the potential.
–A phase difference between high moon and high tide has been known for
centuries. The high tide generally lags behind the high moon.
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Tidal friction
•If there were no dissipation in the Earth systems, tides would lie
directly “under” MP :
•However, friction creates a delay in the tidal response.
•The Earth’s surface reacts to the tidal potential due to MP with a
lag. The tides peak ≈30 minutes later.
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Altimetry Missions
• Tidal Aliasing, the frequencies, periods, and
amplitudes of the most significant tidal constituents:
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Altimetry Missions
• Tidal Aliasing, the frequencies, periods, and
amplitudes of the most significant tidal constituents:
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Altimetry Missions
• In each cycle, the altimeter samples the phase of each
tide.
• A sun-synchronous altimeter sampling the S2
constituent would find a “frozen” tide with an infinite
aliasing period.
– ERS-1, ERS-2, Envisat, and NPOESS all did this.
• Otherwise, the change in phase of the tide during one
repeat period T is:
• The primary alias period:
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Altimetry Missions
• For Topex/Poseidon’s 9.916-day repeat period orbit,
the primary alias periods are:
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Altimetry Missions
• For Topex/Poseidon’s 9.916-day repeat period orbit,
the primary alias periods are:
Each of these is different
by at least several days
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Altimetry Missions
• If tidal aliasing does occur and/or the tidal
frequencies or their aliasing frequencies overlap,
there are ways to resolve the alias.
– Use along-track data
– Use cross-over points
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Altimetry Missions
• Spatial vs. Temporal Resolution
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Altimetry Missions
• Tide Gauges and Ground Track Placement
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Altimetry Missions
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Topex/Poseidon’s Options
1.
2.
3.
4.
1335 km, 64.80 deg inclination
1252 km, 62.01 deg inclination
1255 km, 65.84 deg inclination
1173 km, 62.69 deg
• Option 1 first choice, Option 3 as backup if a frozen orbit
is desired.
• Topex/Poseidon was placed in an exact repeat
groundtrack orbit with 127 revolutions per 10-day cycle.
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ASEN 5050
SPACEFLIGHT DYNAMICS
Constellation Design
Prof. Jeffrey S. Parker
University of Colorado – Boulder
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Constellation Designs
• GPS:
– 6 circular orbits, 12-sidereal hour period, 55 deg inclination
– 4+ satellites per orbit, evenly spaced over 360 deg
• Galileo, a “Walker Delta 56 deg:27/3/1”
– 3 orbital planes, 56 deg inclination
– 9+ satellites per orbit, evenly spaced over 360 deg
• Iridium, a “near-polar Walker Star”
– 6 orbital planes, 86.4 deg inclination
– 11 satellites per orbit, evenly spaced over 180 deg
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Constellation Designs
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•
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•
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•
•
•
A-train (Afternoon Sun-Synch, coordinated)
BGAN
Compass Navigation system
Disaster Monitoring Constellation
Globalstar
GLONASS
Orbcomm
RapidEye
And others!
Sirius Satellite Radio
TDRSS
XM Satellite Radio
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A-Train
• Coordinated constellation of French, American, Japanese, Canadian
satellites
• Sun-Synch
• 98.14 deg inclination
• 1:30 pm solar time equatorial crossing
•
•
•
•
•
•
•
GCOM-W1 (SHIZUKU), JAXA
Aqua (4 min behind), USA
CloudSat (2.5 min behind), USA and CSA
CALIPSO (15 sec behind), CNES, USA
Aura (15 min behind Aqua)
PARASOL (now retired)
OCO-2
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Compass / BeiDou-1
• Chinese navigation system
• Geostationary orbits
• The area that can be serviced is from longitude 70°E
to 140°E and from latitude 5°N to 55°N.
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BeiDou-2
• Chinese navigation system
• Supersedes BeiDou-1
• 35 satellites, completed by 2020
– 5 in geostationary orbit
– 27 in MEO
– 3 in inclined geosynch orbit
• Plans for up to 75 or more
satellites, covering “urban
canyons”
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GPS
• 6 circular orbits, 12-sidereal hour period, 55 deg
inclination
• 4+ satellites per orbit, evenly spaced over 360 deg
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Disaster Monitoring Constellation
• International, coordinated, Sun-Synch orbit
• 10:15 am local time Northward equator crossing
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Globalstar
•
•
•
•
•
LEO
~50 satellites
Inclination: 52 deg
1400 km altitude
Communication, short latency
– 5 ms 1-way light time.
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Iridium
• 66 active satellites
• LEO: 781 km altitude, inclination 86.4 deg
• 11 satellites in each of 6 orbital planes
• Iridium NEXT: 2nd generation communication system
• 66 more satellites, launched 10 at a time on Falcon 9
launches
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Orbcomm
• 29 satellites
• LEO: 775 km altitude
• Telecommunication system
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RapidEye
• German geospatial information provider.
• 5 satellites in the same orbital plane.
• Altitude 630 km
• Sun-synchronous, 11:00 am ascending time, 97.8 deg
inclination
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Sirius
• 3 satellites
• Highly elliptical, geosychronous orbits (“Tundra”
orbits)
• Each satellite spends 16 hours over the continental
US per orbit.
• XM Satellites: 2 geostationary satellites.
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TDRSS
• Tracking and Data Relay Satellite System
• A dozen GEO satellites – some equatorial and some
just off of the equator.
• Navigation and communication, largely of NASA’s
assets.
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Announcements
• STK Lab 3 due Friday 12/5
– Any issues with v9 versus v10?
• STK Lab 4 due 12/12
– Any issues with v9 versus v10?
• Final Exam on 12/12, due 12/18
– Take-home, open book open notes
• Final project and exam due 12/18
Lecture 35: Orbits
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