A-B-Cs of Sun-Synchronous Orbit Mission Design€¦ · A-B-Cs of Sun-Synchronous Orbit Mission...
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A-B-Cs of Sun-Synchronous Orbit Mission Design
Ronald J. Boain
AAS/AIAA Space Flight Mechanics Conference Maui, Hawaii
8-12 February 2004
Jet Propulsion Laboratory California Institute of Technology
9 February 2004
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Earth’s orbital
MLT MLT = Mean Local Time of Ascending Node 9 February 2004
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Sun-Synchronous Condition: Inclination vs. Altitude (e = 0)
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9 February 2004 h
Altitude, km
Reckoning Time
Understanding how time is reckoned is a complex subject - Sidereal time - Apparent solar time - Mean solar time
Sidereal time is based on the earth’s rotation rate relative to the starshernal equinox and is not useful for reckoning time since it loses approximately 4 minutes per day measured in mean solar time Apparent solar time is inconvenient since the sun’s motion is not regular with respect to the background stars and can vary > I6 min per day - Obliquity of the ecliptic, i.e., sun’s change in declination - Elliptic earth orbit, i.e., The Equation of Time
Only mean solar time based on the mean sun crossing the mean solar meridian is consistent with 86400 seconds per day The MLT for SS-Os is also based on the mean solar meridian
9 February 2004
System Engineering the Mission Design I Stated Science Requirements1
Desires I Limitation on the range to a target; viewing angle constraints
Number and distribution of targets to be observed (for discrete targets)
Area coverage to be provided (for continuous targets) I
~~~
Frequency with which targetdareas are to be sampled I Sun-lighting conditions to be provided (for optical measurements)
Seasonal considerations of observations
Overall duratiodperiod of time necessary to measure some
Motivating Objective or instrument Characteristic
Instrument sensitivity, resolution, field of viewkwath-width, allowable elongation/ distortion over a footprint, etc.
Unique geographic targets to be measured
Percentage of earth's surface to
be accessible for observation
Allowable time interval before a repeat observation is possible
Consistent sun shadows for targets
Visual access to Antarctica (for example) during Antarctic summer
Life expectancy for instruments, system, mission life
Traceable Orbit C haracteristiclParameter
Orbit altitude
Orbit altitude, inclination; groundtrack grid density; groundtrack tied point to achieve over-flight of specific latllon
Orbit inclination, altitude
Orbit altitude
Orbit nodal position and/or nodal Mean Local Time; orbit inclination
Orbit nodal position and/or nodal Mean Local Time; orbit inclination
Orbit altitude
9 February 2004
Delta ELV Performance to SS-0 Altitude
NASA ELV Performance Estimation Curve(s) LEO Circular with inclination Sun- Sy nchronous
Please note ground rules and assumptions below.
3,800
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.--. 2,800
2,600 m
$ 2,400
= 2,200
2,000
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200 400 600 800 1,000 1,200 1,400 1,600 1,800 2,000
Altitude &m) 9 February 2004
Orbit Parameters for SS-Os
Orbital Period, sec
with an Integer Number of Revs in One-Day
Equator Dist Altitude, betw/ Adj km GTs, km
Five solutions, corresponding to 12, 13, 14, 15, & 16 revs per day, exist over a range of altitudes desired for low earth SS-Os The equatorial altitude for these solutions ranges between 250 and 1680 km These solutions have coarse GT grids, Le., >2500 km between adjacent groundtracks - q is the angle subtended from
the nadir direction to the adjacent groundtrack
Although interesting orbits, they provide only localized coverage
7200.00
Revs per Day, ##
1680.86 3339.59 (q=51.5")
12
6646.1 5 13 1262.09 3082.69 (q=56.1")
15
61 71.43
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893.79 2862.50 (q=61 .I ")
5760 .OO 566.89 2671.67 (y66.7")
5400 .oo 274.42 2504.69 (qz72.7")
9 February 2004
SS-Os with Finer GT Grids
Next consider SS-Os which repeat their GT in two-days: - If solutions exist for all integers between 12 and 16 for the one-
day repeat, then solutions exist for integers between 24 and 32 for the two-day repeat:
24, 25, 26, 27, 28, 29, 30,31, 32 - Apparently 9 possible solutions
A quick calculation shows that solutions for 24, 26, 28, 30, and 32 are degenerate with 12,. . . 16 for one-day repeats, Le., they have identically the same periods, with the integer solutions for the one- day repeat - Therefore, there are only four new solutions for the two-day
repeat, but these have 25,27,29, and 31 revs, thereby decreasing the spacing between nodes at the expense of increasing the re-visit time ("access'l)
9 February 2004
Notation for Solutions with R Revs in D Days
Extending the previous reasoning, repeat GT orbits can be found for 3,4,5,6,7 ,... and so forth days Example: Thee-day repeat orbits
Removing the degenerate solutions yields 8 unique solutions which repeat their GT in three-days: 37, 38,40,41,43,44,46,47
A convenient notation for one of these solutions is:
36, 37, 38, 39,40,41,42,43,44,45,46,47,48
3D43R = 3-day repeat in exactly 43 revs or 3D47R = 3-day repeat in exactly 47 revs and so forth
Another example: Seven-day repeat orbit solutions => 7D85R, 7D86R, 7D87R, ... 7D109R, 7D111 R
9 February 2004
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Analemma in Declination - Equation of Time Space
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Equation of Time
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9 February 2004 Mean Sun at Coordinates = (0,O)
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9 February 2004
Orbit Plane Geometry for Computing the Time Spent in Shadow
Given Spherical Triangle A-B-C, the Law of Cosines gives:
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9 February 2004 Earth Earth's figure
Summary
SS-Os are defined as low earth orbits which have a nodal precession rate equal to the earth’s Mean Motion - There is a unique coupling between orbit altitude and inclination
to achieve this precession rate as implied by Eq. 1 - This precession has the effect of making the position of the
nodes with respect to the mean sun remain fixed (to first order) SS-0 altitudes can be selected to provide a repeat groundtracks in an integer number of revs in an integer number of days Sun-lighting conditions on the orbit and for observations made from the orbit can be determined by selecting the MLT The paper provides several simple algorithms that enable the calculation of altitude (hence inclination) and MLT to satisfy common mission requirements
9 February 2004
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