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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MLT MLT = Mean Local Time of Ascending Node 9 February 2004

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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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= 2,200

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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")

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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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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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