1. ASEN 5050 SPACEFLIGHT DYNAMICS Mission Orbits, Constellation Design
Prof. Jeffrey S. Parker
University of Colorado – Boulder
Lecture 35: Orbits

2. 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
Lecture 35: Orbits

3. 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
Lecture 35: Orbits

4. 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.
Lecture 35: Orbits

5. Final Project Instructions for delivery of the final project:
Build your webpage with every required file inside of a directory.
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.
Name your main web page “index.html”
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.
Lecture 35: Orbits

6. Space News
Japan’s Hayabusa 2 launched last night!
Lecture 35: Orbits

7. Space News
Japan’s Hayabusa 2 launched last night!
Lecture 35: Orbits

8. 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.
Lecture 35: Orbits

9. ASEN 5050 SPACEFLIGHT DYNAMICS Mission Orbits
Prof. Jeffrey S. Parker
University of Colorado – Boulder
Lecture 35: Orbits

10. Satellite Populations
Molniya
28.5
51.5
Lecture 35: Orbits

11. Satellite Populations
Lecture 35: Orbits

12. Satellite Populations
Molniya, GNSS
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13. Satellite Populations
Gabbard classes
GEO
GNSS
GTO
ISS
Lecture 35: Orbits

14. Satellite Populations
Lecture 35: Orbits

15. 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:
Lecture 35: Orbits

16. 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.
Lecture 35: Orbits

17. Repeat Groundtracks Example exact repeat groundtracks
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18. Repeat Groundtracks The nodal crossings occur in a pattern
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19. Some Period Definitions
Lecture 35: Orbits

20. General Perturbation Techniques
The secular change of the orbital elements due to J2 is given from the Lagrange Planetary Equations as:
Lecture 35: Orbits

21. Nodal Period
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22. Exact Repeat Constraint
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23. Altitude/Inclination vs NERP/K
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24. Groundtrack Drift
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25. TOPEX Crosstrack Drift
Lecture 35: Orbits

26. 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.
Lecture 35: Orbits

27. 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.
Lecture 35: Orbits

28. 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:
Lecture 35: Orbits

29. Altimetry Missions The loss of energy over time due to drag:
Varies with time
Lecture 35: Orbits

30. Altimetry Missions The change in energy over time: Integrate:
Integrate over one orbit period:
Lecture 35: Orbits

31. 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.
Lecture 35: Orbits

32. 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:
Lecture 35: Orbits

33. Altimetry Missions Circular orbits: Minimum: between 1200 – 1300 km
Lecture 35: Orbits

34. 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!
Lecture 35: Orbits

35. Altimetry Missions
Polar Crossing Angle: psi
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36. Altimetry Missions
Desirable > 40 deg
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37. Altimetry Missions Less Desirable Desirable > 40 deg
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38. Altimetry Missions Orbit Period Considerations Tidal Aliasing
Want to avoid this:
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39. Altimetry Missions
Tidal Aliasing, the frequencies, periods, and amplitudes of the most significant tidal constituents:
Lecture 35: Orbits

40. Primary Lunar Tide
Lecture 35: Orbits

41. 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.
Lecture 35: Orbits

42. 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 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.
Lecture 35: Orbits

43. 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.
Lecture 35: Orbits

44. Altimetry Missions
Tidal Aliasing, the frequencies, periods, and amplitudes of the most significant tidal constituents:
Lecture 35: Orbits

45. Altimetry Missions
Tidal Aliasing, the frequencies, periods, and amplitudes of the most significant tidal constituents:
Lecture 35: Orbits

46. 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:
Lecture 35: Orbits

47. Altimetry Missions
For Topex/Poseidon’s day repeat period orbit, the primary alias periods are:
Lecture 35: Orbits

48. Each of these is different by at least several days
Altimetry Missions
For Topex/Poseidon’s day repeat period orbit, the primary alias periods are:
Each of these is different by at least several days
Lecture 35: Orbits

49. 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
Lecture 35: Orbits

50. Altimetry Missions
Spatial vs. Temporal Resolution
Lecture 35: Orbits

51. Altimetry Missions Tide Gauges and Ground Track Placement
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52. Altimetry Missions
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53. Topex/Poseidon’s Options
1335 km, deg inclination
1252 km, deg inclination
1255 km, deg inclination
1173 km, 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.
Lecture 35: Orbits

54. ASEN 5050 SPACEFLIGHT DYNAMICS Constellation Design
Prof. Jeffrey S. Parker
University of Colorado – Boulder
Lecture 35: Orbits

55. 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
Lecture 35: Orbits

56. Constellation Designs
A-train (Afternoon Sun-Synch, coordinated)
BGAN
Compass Navigation system
Disaster Monitoring Constellation
Globalstar
GLONASS
Orbcomm
RapidEye
Sirius Satellite Radio
TDRSS
XM Satellite Radio
And others!
Lecture 35: Orbits

57. 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
Lecture 35: Orbits

58. 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.
Lecture 35: Orbits

59. 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”
Lecture 35: Orbits

60. GPS 6 circular orbits, 12-sidereal hour period, 55 deg inclination
4+ satellites per orbit, evenly spaced over 360 deg
Lecture 35: Orbits

61. Disaster Monitoring Constellation
International, coordinated, Sun-Synch orbit
10:15 am local time Northward equator crossing
Lecture 35: Orbits

62. Globalstar LEO ~50 satellites Inclination: 52 deg 1400 km altitude
Communication, short latency
5 ms 1-way light time.
Lecture 35: Orbits

63. 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
Lecture 35: Orbits

64. Orbcomm 29 satellites LEO: 775 km altitude Telecommunication system
Lecture 35: Orbits

65. 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
Lecture 35: Orbits

66. 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.
Lecture 35: Orbits

67. 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.
Lecture 35: Orbits

68. Announcements STK Lab 3 due Friday 12/5 STK Lab 4 due 12/12
Any issues with v9 versus v10?
STK Lab 4 due 12/12
Final Exam on 12/12, due 12/18
Take-home, open book open notes
Final project and exam due 12/18
Lecture 35: Orbits