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

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

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

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

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

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

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

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

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

Satellite Populations Molniya 28.5 51.5 Lecture 35: Orbits

Satellite Populations Lecture 35: Orbits

Satellite Populations Molniya, GNSS Lecture 35: Orbits

Satellite Populations Gabbard classes GEO GNSS GTO ISS Lecture 35: Orbits

Satellite Populations Lecture 35: Orbits

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

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

Repeat Groundtracks Example exact repeat groundtracks Lecture 35: Orbits

Repeat Groundtracks The nodal crossings occur in a pattern Lecture 35: Orbits

Some Period Definitions Lecture 35: Orbits

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

Nodal Period Lecture 35: Orbits

Exact Repeat Constraint Lecture 35: Orbits

Altitude/Inclination vs NERP/K Lecture 35: Orbits

Groundtrack Drift Lecture 35: Orbits

TOPEX Crosstrack Drift Lecture 35: Orbits

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

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

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

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

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

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

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

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

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

Altimetry Missions Polar Crossing Angle: psi Lecture 35: Orbits

Altimetry Missions Desirable > 40 deg Lecture 35: Orbits

Altimetry Missions Less Desirable Desirable > 40 deg Lecture 35: Orbits

Altimetry Missions Orbit Period Considerations Tidal Aliasing Want to avoid this: Lecture 35: Orbits

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

Primary Lunar Tide Lecture 35: Orbits

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

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. Lecture 35: Orbits

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

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

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

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

Altimetry Missions For Topex/Poseidon’s 9.916-day repeat period orbit, the primary alias periods are: Lecture 35: Orbits

Each of these is different by at least several days 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 Lecture 35: Orbits

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

Altimetry Missions Spatial vs. Temporal Resolution Lecture 35: Orbits

Altimetry Missions Tide Gauges and Ground Track Placement Lecture 35: Orbits

Altimetry Missions Lecture 35: Orbits

Topex/Poseidon’s Options 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. Lecture 35: Orbits

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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