THM-MMS coordination 1 HSO Optimization ARTEMIS THEMIS ARTEMIS THEMIS Regarding revised MMS launch elements (RAP=274, AOP=170) relative to the 3/24/14 MMS-SWT to optimize THM-MMS conjunctions in Phase 1B Vassilis Angelopoulos, Cindy Russell and Sabine Frey

THM-MMS coordination 2 HSO Optimization ARTEMIS THEMIS ARTEMIS THEMIS At the MMS-SWT the THEMIS team presented the need for revised MMS launch elements (RAP=255deg, RAAN=72deg, AOP=183deg) to match the THEMIS elements in space. We used preliminary THEMIS and MMS elements to demonstrate the process. In particular, we used a high MMS perigee (PER=1600km) in order to avoid perigee maintenance and did not account for lunisolar perturbations to the THEMIS drift due to lack of time. Reducing perigee to realistic (1200km) and lower (1000km) values and including lunisolar perturbations to the excel spreadsheet optimizer resulted in a modification to the needed elements. This.ppt describes these modifications. Initial request to the launch vehicle by GSFC flight dynamics (AOP=176) was consistent with a realistic MMS perigee (1200km). Since then, it became evident (pages 3-6) that reducing MMS perigee below 1200km moves the conjunction region in RAAN-APER space. Also, that perigee reduction to 1000km does not require perigee maintenance and saves fuel, and is beneficial for increasing MMS drift rate closer to THEMIS. Including lunisolar perturbations to the optimizer resulted in faster precession for THEMIS (RAP drift rate) that necessitated an increased target RAP. We addressed the drift rate problem by optimizing THM-MMS conjunctions for Phase1B, while using any remaining fuel of the limit-spacecraft, P5, for good Phase1A conjunctions, consistent with the large Z-separation there (p7). As a result the optimal RAP increased to ~273deg. Initial concerns regarding low conjunctions for RAP~274deg were addressed by apogee raise by 0.5Re, which resulted in considerably higher yield (~280hrs) for fuel costs bracketed by perigee reduction savings (p. 9-11) Remaining concerns regarding the THM-MMS conjunction geometry in Phases 1A, 1B, comparing the old (SWT) and the revised elements, are addressed in the remainder (p. 12+). The findings are that the new elements provide superior conjunction quality and are recommended. Further optimization can occur by THEMIS (perigee raise) assuming MMS will target the recommended elements, which are relatively immune to the launch date. PREAMBLE: From MMS-SWT to now.

THM-MMS coordination 3 HSO Optimization ARTEMIS THEMIS ARTEMIS THEMIS SWT Optimized (Draft) Vary AOP, RAAN. LongShadows: Left; NS Conjunctions: Middle; LongShadows+Conjunctions: Right Phase2b shadows RAP= 255 Optimal region ( ) Shadows (min) in red and conjunctions (hrs) in blue Optimal window for Mar 7 th launch at 18LT (RAP=255 o ): RAAN= 72 o +/- 5 o, AOP= 183 o -/+ 5 o ( ) Neutral Sheet Conjunctions (hrs)Max Long Term Shadows (min) PRG=1600 (old runs; LD=Mar 7)

THM-MMS coordination 4 HSO Optimization ARTEMIS THEMIS ARTEMIS THEMIS Optimized Solution (Draft) Extended further in RAAN Vary AOP, RAAN (2D). LongShadows: Left; NS Conjunctions: Middle Neutral Sheet Conjunctions (hrs)Max Long Term Shadows (min) RAP= 255 ( ) RAP= 255 Old optimal region ( ) PRG~1600 (LD=Mar 15).

THM-MMS coordination 5 HSO Optimization ARTEMIS THEMIS ARTEMIS THEMIS Optimal Option 3, Reduced Perigee Vary AOP, RAAN (2D). LongShadows: Left; NS Conjunctions: Middle PRG~1200 (LD=Mar 15). Neutral Sheet Conjunctions (hrs)Max Long Term Shadows (min) RAP= 255 ( ) RAP= 255 Optimal region AOP= 176 ( )

THM-MMS coordination 6 HSO Optimization ARTEMIS THEMIS ARTEMIS THEMIS Optimal Option 3. Reduced Perigee (Adheres to >800km) Vary AOP, RAAN (2D). LongShadows: Left; NS Conjunctions: Middle PRG~1000 (LD=Mar 15). Neutral Sheet Conjunctions (hrs)Max Long Term Shadows (min) RAP= 255 ( ) RAP= 255 New optimal region AOP= 176 ( )

THM-MMS coordination 7 HSO Optimization ARTEMIS THEMIS ARTEMIS THEMIS Optimizer with realistic PRG, INC drift rates (RAP accurate to within 1-2deg)

THM-MMS coordination 8 HSO Optimization ARTEMIS THEMIS ARTEMIS THEMIS Optimal Option 3 Vary AOP, RAAN (2D). LongShadows: Left; NS Conjunctions: Middle PRG~1000 (LD=Mar 15). Neutral Sheet Conjunctions (hrs)Max Long Term Shadows (min) RAP= 255 ( ) RAP= 255 New optimal region AOP= 176 ( ) RAAN=103 (-3, +7) RAP= 273 (-3, +7) AOP= 170 ( ) RAP= 273 (-3, +7) RAAN=102 (-7, +3) RAP= 273 (-3, +7) AOP= 168 ( ) RAP= 270 (-7, +3) AOP=176 : not good AOP=170 : unoptimized (conjunctions reduced: 220hrs requires optimization with UT) AOP=168: better than 170 but still low conjunction hours. Bottomline: these have to be revised further.

THM-MMS coordination 9 HSO Optimization ARTEMIS THEMIS ARTEMIS THEMIS Shadows [min] NS Conjunctions [hrs] Colors = choice of ma Scale is at bottom as Cold – to – warm is 00 – 21 Go from 235hrs to 255hrs Shadows [min] NS Conjunctions [hrs] Colors = choice of ma Scale is at bottom as Cold – to – warm is 00 – 21 Increased from 230hrs to 250hrs Shadows [min] NS Conjunctions [hrs] Colors = choice of ma Scale is at bottom as Cold – to – warm is 00 – 21 Increased from 220hrs to 240hrs Optimization with mean anomaly (ma) in Phase 2b midnight) Vary UT of apogee at midnight in Phase2b as proxy of mean anomaly (ma) of insertion into Phase 2b. With MMS apogee = 25R E optimization with mean anomaly at placement for AOP=170 deg results in no significant increase in # of hrs (220  240). Same exercise for AOP=168 deg and 166 deg also results in only modest gains (with typical conjunction hrs increasing, as expected, as AOP is reduced). This does not bode well for RAP – which would have to go down with lower AOPs since not only AOP decreases but RAAN too (shadows move left).

THM-MMS coordination 10 HSO Optimization ARTEMIS THEMIS ARTEMIS THEMIS However, optimization of mean anomaly (ma) in Phase 2b midnight) but for APG=25.5R E is succesful (280hrs) With MMS apogee = 25.5R E optimization with mean anomaly at placement for AOP=170 deg results in significant increase in # of hrs (220  265 hrs) depending on exact RAAN. Recipe: Once RAAN is known after apogee raise maneuvers, perform optimization of insertion: obtain optimal (target) value of by timing insertion maneuver  V  apg=+0.5Re ~ +10m/s Compare with savings from prg reduction (1200  1000km):  V  prg=-100km ~ -12m/s. Shadows [min] NS Conjunctions [hrs] Colors = choice of ma Scale is at bottom as Cold – to – warm is 00 – 21 Increased from 220hrs to >265hrs Target: RAAN=104deg, RAP=274deg, Yields: conj. ~ 280hrs, shad. = 210min

THM-MMS coordination 11 HSO Optimization ARTEMIS THEMIS ARTEMIS THEMIS Optimizer *v6.xlsx results (similar to v5.xlsx above, but with new RAP for completeness)

THM-MMS coordination 12 HSO Optimization ARTEMIS THEMIS ARTEMIS THEMIS What about Phases 1A, 1B? The original elements provided a formation strategy for Phases 1A, 1B, but the strategy was notional. Here it becomes real because it is linked with tail strategy because of the limit RAP and APER needed for optimizing shadows and conjunctions. The RAP=255deg solution Phase 1 apogees are shown for THM&MMS in the next page (p.13). Yellow are the THM&MMS apogees when MMS is at the subsolar point +/- 4 orbits. While THM&MMS apogees are aligned in local time (XY-projection) in Phase1A, they are not aligned in 1B. This is very important because these tracks are not orbit projections. The lines of apsides separation in Phase 1B makes conjunctions in 3D to have large separations and be short-lived. The RAP=274deg solution (next page, p.14) reduces the apogee separation in LT in Phase 1B (where small scale separations are needed) at the expense of Phase 1A. The following 2 pages show the orbits in 3D for Phase 1A and Phase 1B – THEMIS P5 is used as the limit-fuel spacecraft. Red lines with no arrows connect the apogees and lines with arrows the optimal conjunctions. It is evident that the RAP=274 solution results in smaller separations for longer times in the orbit, than the RAP=255 solution. The last page shows

THM-MMS coordination 13 HSO Optimization ARTEMIS THEMIS ARTEMIS THEMIS PHASE 1A PHASE 1B Target configuration Actual configuration Apg evolution, for RAP=255 MMS THM

THM-MMS coordination 14 HSO Optimization ARTEMIS THEMIS ARTEMIS THEMIS PHASE 1A Target configuration Actual configuration (controlling along- track separation) Apg evolution, for RAP=274 PHASE 1B

THM-MMS coordination 15 HSO Optimization ARTEMIS THEMIS ARTEMIS THEMIS Representative orbits, RAP=255, Phase 1A, LT=12 X gse Z gse MMS THM Line connects apogees Hourly ticks Possible THM configuration Y gse

THM-MMS coordination 16 HSO Optimization ARTEMIS THEMIS ARTEMIS THEMIS Representative orbits, RAP=255, Phase 1B, LT=12 X gse Y gse Z gse MMS THM Line without arrow connects apogees Red arrow shows instant of closest THM-MMS approach. Minimum THM-MMS separation is ~1.5R E Hourly ticks Possible THM configuration Conditions of small THM-MMS separation last only a short time (1hr) because orbits cross at large angle (away from apogee) and THM-MMS move fast away.

THM-MMS coordination 17 HSO Optimization ARTEMIS THEMIS ARTEMIS THEMIS Representative orbits, RAP=274, Phase 1A, LT=12 X gse Y gse Z gse MMS THM Line connects apogees Hourly ticks Possible THM configuration Y gse Conditions of optimal THM-MMS separation last several hours as THM distances are large (~2Re).

THM-MMS coordination 18 HSO Optimization ARTEMIS THEMIS ARTEMIS THEMIS Representative orbits, RAP=274, Phase 1B, LT=12 X gse Y gse Z gse MMS THM Hourly ticks Possible THM configuration Conditions of optimal THM-MMS separation last several hours because missions move along same direction. Minimum THM-MMS separation is ~1R E

THM-MMS coordination 19 HSO Optimization ARTEMIS THEMIS ARTEMIS THEMIS Tolerances, formation and P5 fuel RAP=274 (-3,+7), Phase 1B, LT=12 +7 o MMS RAP=274 o -3 o P4 P3 P5 (……) prg=1100km, raise Oct 27, 2015 P5 (solid line) prg=1100km raise Jul 1, 2015 AOP=180 o (good for Phase1B but bad for NS conjunctions) Increasing RAP further does not help. Decreasing RAP while preserving NS conjunctions decreases AOP  brings Z MMS away from Z THM (does not help) Increasing perigee increases AOP but results in slower RAP evolution. Lower RAP moves line of apsides away from P5 (even though OK for P3,4). RAP=274 o is optimal. Prg=1200km, RAP=274, AOP=176 o (good for P3, P4, but poor for P5)

THM-MMS coordination 20 HSO Optimization ARTEMIS THEMIS ARTEMIS THEMIS Representative orbits, RAP=274, Phase 1B, LT=10.5 X gse Y gse Z gse MMS THM Possible THM configuration (offset for clariry) Conditions of optimal THM-MMS separation last several hours because missions move along same direction. Minimum THM(P5)-MMS separation is ~1200km. P3, P4 can be at smaller separations to MMS.

THM-MMS coordination 21 HSO Optimization ARTEMIS THEMIS ARTEMIS THEMIS Proposed RAP, APER provide very good formation in Phase 1A and 1B. Can potentially be optimized further by THEMIS (early perigee raise, re-entry maneuver waiver). No other RAP provides as good a Phase 1b tetrahedral configuration or a combination of Phase 1 and Phase2b science. The proposed RAP, APER are optimal.

THM-MMS coordination 22 HSO Optimization ARTEMIS THEMIS ARTEMIS THEMIS An increase in MMS RAP from 255 to 274deg, together with reduction in PRG=1000km provide optimal THM-MMS alignment in Phase1b, appropriate for the small Z separations at the time. The nominal MMS apogee R a =25R E with RAP = 274deg reduces nominal Phase2b conjunctions to ~220hrs. Conjunction hours can be restored with an increased MMS apogee to R a =25.5R E and by tuning the mean anomaly of MMS near Phase2b start. The R a raise fuel is less than the fuel gains from the R p reduction. Recommended target elements are optimal compared to other equally good elements for NS conjunctions. They are also tolerant to small variations in launch elements and fairly independent of launch window. RAP=274 (-3,+7), AOP=170, RAAN=104 (-3,+7). Summary