The Space Congress® Proceedings 1968 (5th) The Challenge of the 1970's
Apr 1st, 8:00 AM
Deorbit Maneuver and Targeting Strategy for Unmanned Mars Landers
W. J. Pragluski Martin Marietta Corporation
D. Marquet
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Scholarly Commons Citation Pragluski, W. J. and Marquet, D., "Deorbit Maneuver and Targeting Strategy for Unmanned Mars Landers" (1968). The Space Congress® Proceedings. 3. https://commons.erau.edu/space-congress-proceedings/proceedings-1968-5th/session-6/3
This Event is brought to you for free and open access by the Conferences at Scholarly Commons. It has been accepted for inclusion in The Space Congress® Proceedings by an authorized administrator of Scholarly Commons. For more information, please contact [email protected] DEORBIT MANEUVER AND TARGETING STRATEGY FOR UNMANNED MARS LANDERS
by
W. J, Pragluski, D. Marquet Martin Marietta Corporation, Denver, Colorado
SUMMARY
Several deorbit maneuver strategies for unman certainties. This aspect of the error analysis ned Mars soft landers are evaluated in terms of pro leads to the definition of an entry corridor and pulsive efficiency, targeting capability, communica selection of potential landing areas for 'early tion link geometry, and sensitivity to system uncer missions. tainties. These strategies include (1) minimum de- orbit impulse, (2) minimum entry condition uncertain The final aspect of the analysis includes the ties, (3) minimum variation in the lander antenna effect of targeting flexibility on the post land aspect angle during entry, (4) minimum communication ing communication link characteristics between the range from the lander to the orbiting spacecraft dur lander and orbiting spacecraft. The influence of ing entry. The selected maneuver strategy is a com both aspects of the error analysis on the post bination of the above which restricts orbiter lead landing communication link is discussed. angles to the range between 0 deg and -10 deg. The analysis covers a range of elliptical orbits with ' INTRODtJCTION periapsis altitudes of 500 to 2500 KM and apoapsis altitudes of 10,000 to 20,000 KM. The nominal The analysis of deorbit maneuver strategy orbit which is selected in order to best satisfy only be meaningful if it is made within the bound all mission considerations is 1300 KM by 12,500 KM aries imposed by scientific objectives of the mis (hp x hA) . sion, system capabilities, and constraints imposed on the mission profile by subsystem design, consid Mission considerations include orbit orienta erations. To establish a deorbit maneuver strategy tion of the orbiting spacecraft for planet surface all of the flight operations in- the vicinity of mapping, landing site location between 15 to 30 Ma r s - mu st be considered i n c lud i ng or b i t, s e 1 ec t 1on 9 degrees from the terminator for entry TV imaging, deorbit impulse size.,, guidance subsystem accura and orbit characteristics which insure a 50-year cies, co iranu n i c a t ion subsystem 1 i nk geome t r i e s , and, orbit lifetime and non-occultation of either the last, but hardly least, the ability to place the Sun or Star Canopus for 30 days after encounter. lander at scientifically interesting landing areas. These constraints, coupled with the uncertainties The analysis presented 'below touches on many of introduced by trans-Mars navigation uncertainty and the more important aspects which must be considered. orbit insertion maneuver uncertainties, are used in It includes propulsion subsystem considerations for the definition of minimum targeting flexibility re orbit insertion, orbit trim, and deorbit, the error quired to land at a preselected location (latitude analysis associated with these maneuvers, targeting, and longitude) and the regions of Mars which can be capability, and communication subsystem link geom selected for landing. The selection of a landing etry 'characteristics. These analyses lead to the site after surveillance from orbit where as much selection of a deorbit maneuver strategy and range targeting flexibility as possible is desired is of suggested orbits. also considered. Before proceeding with the analysis, a brief Two aspects of the error analysis are consid description of the total mission, profile is present ered. The first deals with the range of orbits ed below to provide, the proper perspective. This relative to a preselected nominal which might be includes the more important mission, constraints experienced. The sources leading to this range assumed in this analysis. Only the operations in uncertainty include cruise navigation, orbit in the vicinity of Mars are presented. In any detail* sertion maneuver, and orbit trim maneuver. The deorbit maneuver strategy must be capable of com MISSION PROFILE AMD COMSimilTS pensating for these orbit uncertainties if a pre selected landing site is to be acquired. Total Mission Profile
The second aspect of the error analysis deals The mission profile considered is shown In with the flight conditions at entry and landing Figure 1. The planetary vehicle, orbit ing space site acquisition accuracy. The uncertainty sources craft and lander , is inje.ct.ed onto a trans-Mars • considered here include orbit ephemeris determina trajectory from an Earth parking orbit* A Sun- tion accuracy, deorbit maneuver, and atmosphere un Ganopus attitude control system is employed during
6.3-1 the cruise mode. At least two midcourse maneuvers representative opportunity to discuss some of the might be required during the trip of about 200 days orbit insertion and orbit geometry considerations. duration. Based on Earth tracking and the desired The energy contours for a Type I mission are pre landing site, the orbit insertion command is calcu- sented in Figure 2. The relationship between _ lated and sent to the planetary vehicle. At a pro Earth departure energy, C~ 9 and Mars approach grammed time the orbit insertion maneuver is execu energy, V « 3 is illustrated. Two constraint bound ted, At least four orbits are assumed to determine aries are also shown. The lower limit on encounter the ephemeris of the resulting orbit from Earth- date is established by limiting the ¥„„ to less than based tracking. An orbit trim maneuver may be re 3,25 KM/SEC. The declination of the departure asymp- quired to compensate for the off-nominal orbit has been constrained tote, § HE® to be less than resulting from approach and orbit uncertainties, 35 deg from a range safety consideration. The cross Potential landing sites may be viewed from orbit hatched region is where the most favorable pay load and a site selected. Four to five days after orbit margins occur,- This is the combination of insertion, depending on the desired landing site which results in near maximum pay loads in orbit in?rill longitude, the lander is separated from the orbiting about Mars, Three circled points of interest are 'Spacecraft, The lander orients itself for deorbit shown. Points (1) and, (2) axe used for the discus firing during a ha If -hour coast phase required to sion of periapsis shift requirements presented below. separate the two vehicles by at least 300 meters, Point (3) is used for the example of occultation con The deorbit engine 'is fired and the lander then, straints. coasts to the desired atmospheric entry point. Be tween .deorbit firing and entry the lander is reor Constraints iented to provide a nominal entry angle of attack of aero degrees, A ballistic entry is followed by The mission constraints considered in this parachute deployment at an altitude of about 18,000 paper are given in Table I. below, along with a brief ft above the surface. Vernier ignition and para comment on their source and influence on the mission. chute jettison occur at an altitude of about 5000 ft, Vernier shutdown occurs 10 feet above the surface NEAR MRS. PROPULSIVE PHASES and the lander free-falls to the surface* The de tails of the terminal phase system are discussed in faother paper and are not considered here* The orbit insertion phase is discussed in terns of the impulse required and the associated errors. Only insertion at the periapsis of the approach fhe 1973 Mars mission is selected 'here as a hyperbola 'is discussed in this section., The influ-* mius i
IHElJJgEICK 1», Orbit lifetime of at least 50 years Non- sterilisation of the orbit Size of orbits ing spacecraft 2. Orbit insertion A V fl¥ less than Reasonable weights in orbit $ize of orbits and 1,75 shifts allowable 3% Inclination of orbit to Hartian Orbiting spacecraft mapping Allowable landing site lati equator greater than 30 deg mission tudes 4* * £Ton*occultation of either the Sun Orblt ing spacecraft at11tude Al lowable Incl ina tions a t or Ganopus for 30 days after en control reference and, power Mars counter source 5* Landing site located 'between, 15 to Entry TV imaging Allowable range of targeting 30 deg from the terminator parameter 6* Orbiter sub-periapsis between sero Orbiter TV imaging Allowable range of targeting to 45 deg from the terminator parameter and. periapsis shift 7* Orbit insertion, in view of Gold- Mi s s ion operat ions. Time of arrival; orbit orien stone tation
8* A VD < |,00 I/SIC leu sonable lander weights Allowable range of targeting parameter t, fu* < 3*25 KM/SBC 'Reasonable weights in orbit Allowable range of orbits and perlapsIs shlft ence of periapsis shift requirements on Z-iV T is maneuver impulse of 150 nips is assumed here with discussed later. Impulsive maneuvers are assumed. maneuver uncertainties of 5% of impulse (3
4,34 TABLE II
ORBIT INSERTION ERROR SUMMARY
(Deg) (Hrs) Error Source Magnitude (3 €T )
Navigation uncertainty at last maneuver 500 KM in hp .65
Navigation uncertainty at insertion calc. 300 KM in hp 1.69 .42
Misapplication of A V 3% parallel; 5% normal .89 .52 Combined RSS O.I. 2,02 Deg .66 Hrs
DEQKBITL ERROR SUMttKf Error Source (Deg)
(I) Navigation Uncertainty x« 18 KM i • .6 M/SBC y - 19 KM y - 3.3 M/SBC .19 38.2 (at entry .60 altitude) z • 12 KM z « 2,8 M/SBC
(2) Pointing .5 deg .30 ' 40.6 . 64 (3) Impulse ,333* .20 24.2 .38 (4) /**•,/• .12 'KefR Cf' CF'4/^, - 166 :»!3 /SlC
Total 1SS Errors at Entry ..425. 60*8 • .96
(5) Atmosphere Uncertainty VM-8 and VM-9 94.5 (on surface) 1.6
Landing Site Error 110. 1.87
are in the summary Table III. The errors at small, the importance of maintaining a near minimum entry due to these three sources can be expressed ^Vjp as part of the deorbit maneuver strategy is in terms of errors in entry flight path angle, clearly evident from the nature of the curves shown downrange angle (^ ), entry velocity, time of in Fig. 6, entry» and crossrange angle* The errors in Tf*^ The error In *jf'A due to source (3) is shown, in P are the most important for mission plan variation, with ning purposes* Fig* 1 for the same two orbits. The l\ VD is smaller and the magnitude of the 6*3-4 Entry Corridor. The entry corridor, as defined LANDING SITE ACCESSIBILITY here, is the relationship between the entry velocity and entry flight path angle which might be experienc Possible Landing Areas ed as a result of the above uncertainties. As a gen eralization, it is desirable to enter the light The possible landing sites are dependent upon Martian atmosphere with as shallow an entry flight the launch window chosen and the mission eotisfrraimfcs, path angle as possible. This results in more time Figures 11 (a) and ll(b) show the arrival geometry in the atmosphere for the entry vehicle to dissipate for a launch and arrival date corresponding to the entry velocity energy. The minimum criteria used points (1) and (2) of Fig. 2. For the early arrival here to define the entry corridor is to target for an (1) , the hyperbolic excess velocity vector Is just entry flight path angle at least 5 & of the entry beneath the Martian, equator, 4 deg, All orbits flight path angle uncertainty steeper than a conserv about Mars must include this vector. Any inclina ative skipout boundary. This insures that the entry tion orbit is possible, above A deg, ! Hiree of- the is at least 2 An important mission constraint is the non- Minimum Entry Condition Uncertainties occultation of either the Sun or Canopus for at The largest error source for entry flight path angle least 30 days after encounter. The resulting con dispersions is orientation as seen in Table III. The straint on orbiter inclinations is shown in Fig. 14 variation of the dispersion in entry flight path as a function of periapsis shift, A^1 * A middle angle, TPA* was snown ^ n Fig. 6 as a function of arrival date corresponding to point (2) of Fig. 2 A V . It was shown that the required A VQ to make is shown. For low periapsis altitude, 500 KM, only <"T /y\ equal to zero is only slightly higher than posigrade orbits from the south with inclinations be the minimum A V^. The associated orbiter lead tween about -20 deg and -70 deg are possible depend angles are very close to the values for the minimum ing upon A"^* For A W less than -45 deg, inclina A^Vpj. The use of this strategy allows lower nom tions must be below -60 deg. A higher periapsis inal T^A tnan those shown in Fig. 8, but has the altitude extends the possible range of inclinations same problem as strategy (1) at the higher 6 . and A^; A small range of PN inclinations exist an hp of 1500 KM, between about 20 deg and for Minimum Lander Antenna Aspect Angle (#3) . The Thus a small landing region in the northern 40 deg. relay communication link between the lander and hemisphere is possible for the higher hp. The vari orbiting spacecraft during the entry phase is shown contours is slight for the ation of the occultation in Fig. 15. The boresight of the lander antenna is of arrival dates considered. The variation range taken to be along the longitudinal axis. At entry than with hp. with is much less the lander is in a zero angle of attack orientation. A positive lander aspect angle, C< u , is measured Area Summary Landing counterclockwise from the boresight axis to the line of sight between the lander and orbiting spacecraft. The shaded areas in Fig. 11 (a) and 11 (b) show all h considered, the allowable landing regions for The maximum and minimum & ± during entry is 500 KM to 2500 KM. Inclinations less than 30 deg shown as a function of X in Fig. 16 for a ^ of are eliminated due to the orbiter mapping constraint. -30 deg. Both a large and a small orbit are shown. The landing site latitudes lie generally between A lead angle of about -12 deg centers the maximum -30 deg and -60 deg. For a given orbiter inclina and minimum variation about zero. The variation is tion the variation in landing site latitude with between + 2.5 deg and ± 40 deg depending on orbit targeting parameter is small. The higher the inclin size. The maximum positive cX^ occurs at entry and ation the larger the variation in landing site lati the maximum negative £X W occurs at touchdown. The tude with ^ . effect of ^ , in the range from 0 to 40 deg, is slight in determining the X which centers the DEORBIT MANEUVER STRATEGY variation. The corresponding A V D variation, with ^ in Strategies Considered for a X of -12 deg is very close to that given Fig. 5 for a X of -10 deg. The following five deorbit maneuver strategies 6.3-6 Minimum Communica tlon Range. (#4) . The communica The starting point of the lander position line is a tion range variation with X is shown in Fig. 16, function of targeting parameter, B , and spacecraft again for a @ of 30 deg. The variation with apoapsis lead angle at touchdown, X ro . The link time is altitude is slight. The lead angle which minimizes simply the time interval when the lander position the communication range during entry is between -2 line lies within the spacecraft contour. and +2 deg depending on hp. The cor Corresponding to these rectness of the technique has been lead angles the maximum verified with many ^ c is about 250 KM higher time history computer runs. than periapsis altitude and occurs near touchdown. The variation of A VD with ^ for this strategy Once the size of the spacecraft contours is can be seen from Fig. 5 where a \ of 0 deg is established (A**) » an analysis technique such as shown, that illustrated in Fig. 20 is used. The spacecraft /\ot band occurs every 360 deg. The existence of a Mi n i mum. Commu n i ca t ion F a d i ng Mar gin Lo s s e s (# 5 ) . A link on any given orbit number and orbital period multipath analysis was made on the relay link during requires that the orbit number line lie within the entry. The worst fading margin during entry is band. Thus, as an example from Fig. 20, a link will shown as a function of lead angle in Fig. 17. To exist after the first day on orbit No. 3 for orbits insure good system performance the lead angles should with periods between 4.6 and 8.1 hours. The actual be limited to the range + 10 deg time of the link can be determined from the & scale, interpreted as time, (i.e. 360 deg is 24.624 hours). Selected Maneuver Strategy The range of A<* for orbits with inclinations The selected maneuver strategy restricts lead between 30 to 50 deg and periapsis altitudes of 500 angles to the range 0 to -10 deg. The lead angle to 2500 KM and apoapsis altitudes of 10,000 to variation with & is shown as a function of orbit 20,000 KM is 135 to 185 deg. The minimum occurs for size in Fig. 18. At low ^ a X of 0 deg is used the 500 x 20,000 KM orbit, the maximum for the 2500 and continued until the minimum Z-iV^ is reached. x 10,000 KM orbit. The A( A# ) shift as a func The X is then varied between 0 and -10 deg along the tion of G (shown in Fig. 20) varies from approx minimum A VQ curve and then kept constant at -10 deg. imately 25 to 60 deg for ^ from 10 to 40 deg for A nominal a operating region for (3 has been selected 1500 x 15000 KM orbit. The variation is insensitive as 10 to 40 deg. For periapsis altitudes above about to apoapsis altitude and varies approximately 1500 +10 deg KM the X is always a constant, -10 deg. The per 1000 KM change in periapsis altitude. y variation with is shown in Fig. 5. These characteristics have been investigated to POST LANDING COMMUNICATION LINK establish the maximum orbital period for which a link is assured at least once Relay Link a day. These results are relatively insensitive to ^ and indicate a maxi mum orbital period varying from 9.2 to 12.5 The analysis of lander hours for to orbiter communication A<* between 135 and 185 deg, respectively. link geometry is always a troublesome The task. The use limits on orbit size and shape resulting from of highly elliptical orbits these complicates the task characteristics are presented below. even more. In an effort to gain better vision of the effects of targeting variations and uncertain Lander to Earth Direct Link ties on the link geometry, a somewhat different approach to the analysis was devised to replace the The direct link geometry is a function of land classical technique of running hundreds of orbit/ ing site latitude and date. The elevation angle landing site combination time of histories. The tech the Earth is shown in Fig. 21 as a nique, to be described function of in a future paper, is summar universal time for A ^ of ized below. -20 deg and -40 deg. The effect of date is shown. On February 2, 1974, the landing sites of -20° and -40° can view the As the spacecraft travels around its orbit, Earth for about eight hours of the day, assuming there is a period of time it can see the a 34 deg ground landing mask. A later arrival date site latitude. During that decreases the link time period, the right ascen to about six hours. sion, o( , of the visible landing site latitude can be defined. A representative contour is illustrated If a direct link is desired immediately after in Fig. 19 for a 1300 x 12,500 orbit, inclined 45 deg touchdown, the elevation angle of the Earth at touch to the Martian equator, and landing site latitude of down is of importance. Landing near the evening -37 deg.. The link constraints imposed on this con terminator results in low elevations, as seen in tour are a ground elevation mask of 34 deg and a Fig. 11 less than 34 deg., and the Earth is soon maximum communication range of 5000 KM. Since this below the horizon. Landing near the morning termina contour exists every orbit, it is only necessary to tor results in higher elevation angles and the see if the lander right ascension places it within land- Ing site is rotating toward the sub-Earth point. the contour on any given orbit. Since the lander right ascension increases linearly with time (i.e. ORBIT ...SELECTION CRITERIA planet rotation) , its time history can be superim posed on the spacecraft time history (Fig. 19) . The groundwork has now been laid for a reasonable 6.3-7 selection of nominal orbits which considers all mis .243 hours (3 (T ) if the total allocated 150 M/SEC- sion constraints. is used. This results in a longitude phasing error of 3.54 deg (3cr ) per orbit. Table II shows that The selection of minimum periapsis altitude is the total 3 o~ error in the periapsis location is based on the desire for an initial post touchdown 6.0 deg after orbit insertion which must also be communication link with the orbiting spacecraft of accounted for to hit a preselected sight. These two 3.5 to 5.0 minutes. The restrictions on orbit peri- error sources combined result in a total error of apsis altitude for different link times are shown in about 31 deg (3£T ) for deorbit on the 12th orbit. ,"ig. 22. For a given orbit a combination of high A targeting capability, /^^ , of 31 deg is then targeting parameter, @ , and orbiter lead angle, X , required. The results of the analysis of trading off result in the worst case for initial post touchdown orbit number show that deorbit on the fourth day, on link time. A value of 40 deg for @ and zero deg either the 12th or 13th orbit (depending upon the for X are used for the worst case based on the desired longitude), is reasonable. The required selected deorbit strategy given above. The required range of apoapsis altitudes as a function of periap hp for the worst case and 5 minutes lie between sis altitude and orbit number to allow landing at longitude during the 4th day is shown in Fig. 23. 1250 and 1400 KM for a 34 deg mask. The 3.5 minute any the range of limit requires a minimum hp of about 800 KM for a To use the 12th or 13th orbit requires 11,500 KM 15 deg ground mask. Assuming a 3 6.3-8 CONCLUSIONS AC Central angle traversed during entry (Deg) 1. Nominal hp = 1300 KM A Angle of arbiter periapsis shift from the 2. Nominal hA between 11,500 KM and 13,500 KM depen approach hyperbola periapsis; a positive ding on longitude of desired landing site shift places the orbiter periapsis further 3. Deorbit during 4th day on 12th or 13th orbit downrange (Deg) depending on longitude of landing site D True anomaly of the deorbit point (Deg) 4. Targeting capability, A0 > of 30 deg V Angle between periapsis of nominal orbit (10°< (9 < 40°) and periapsis of actual perturbed orbit (Deg) 5. Maximum A VD required is 300 M/SEC x Orbiter lead angle; central angle between 6. Orbiter lead angles restricted to -10 deg to lander and orbiter positions at the time of 0 deg range entry; positive if orbiter leads the lander (Deg) —————SYMBOLS X L Latitude of landing site (Deg) & Right ascension of visible landing site for post landing link (Deg) ^TD Orbiter lead angle at touchdown (Deg) L Antenna aspect angle of the lander; measured Gravitational parameter of Mars positively from the boresight to the line of (42830.KM3 /SEC 2 ) sight to the orbiting spacecraft (Deg) Communication distance between lander and orbi p Targeting parameter; angle measured positively ting spacecraft (KM) from the orbiter periapsis to the entry loca Standard deviation in entry flight path angle (Deg) tion opposite the orbital motion of the orbi- $ Standard deviation in orientation angle (Beg) Standard ting spacecraft (Deg) D deviation in downrange angle (Deg) 'JP Entry flight path angle measured from the local Q A Astronomical symbol for the Sun horizontal at entry (Deg) ^ Astronomical symbol for the Earth S Declination of the departure asymptote at ^* HE *£ [J Astronomical symbol for Mars Earth; measured with respect to the Earth's Q Twice the energy per unit mass required to equator (Deg) transfer to Mars on a given launch and arrival /\ cx Size of orbiting spacecraft contour for post date (KM2 /SEC 2 ) land link (Deg) h Periapsis altitude, point of closest approach A(A Impulsive velocity required for orbit inser- 0.1. •• igr Inclination of the arbiter's orbital plane at tion (KM/SEC) Mars with respect to the Martian equator (Deg) 6.3-9 R^ Radius of Mars (3393 KM) 12. Required Periapsis Shift t/p Time, non-dimensionalized by orbital period 13. Orbit Limits Imposed by Periapsis Shift t c Coast time (Hrs) Vj|g Hyperbolic excess velocity at Mars - the Required velocity of the planetary vehicle with 14. Occultation Constraint on Orbital Inclina respect to Mars upon entering the Martian tion sphere of influence (KM/SEC) 15. Relay Communication Link During Entry x Axis system used for the covariance matrix of 16. Entry Communication Link Characteristics y position and velocity due to navigation un- 17. Frequency-Shift Keying Fading Margin z certainties at the time of deorbit; z-axis 18. Selected Deorbit Strategy is in the direction of the deorbit point; 19. Longitude Coverage by the Orbiting Space X-axis* is in the orbital plane rotated 90 deg craft clockwise from z when, looking down the angu 20. Link Dependence Upon Orbital Period lar momentum vector; y-axis is normal to the 21.. Direct Earth Link orbital plane and opposite the direction of 2.2. Post Landing Initial Relay Link the angular momentum vector 23* Apoapsis Altitude Selection Criteria. 24.. Final Orbit. Selection Limits FIBRES ' TABLES I. Mission Constraints 1. Mission Profile II. Orbit Insertion Error Summary ' ' 2. Ma r s 19 73-1. Energy Con tours III. Deorbit Error Summary 3. Orbit In.sertl.on. Impulse Capability REFERENCE 4. Deorbit Geometry JPL TR 32-820, "Geometric Aspects of Ground 5. Deorbit. Impulse Required Station/Satellite Communications'" by Roger D. Bourke, dated 15 October 1.965,., 6. Entry Plight Path Angle Dispersion due to . Pointing ACKNOWLEDGMENT 7 . En t r y F1 i gh t Pa t h Angl e Di sper s i on due to This work was performed, in part under Con tract 952001. for the Jet Propulsion Impulse Laboratory» California Institute of Technol ogy, as sponsored by the National Aeronautics 8* Entry Corridor and. Space Administration under Contract NAS7-10Q, 9. Deorbit Impulse: Effect of Entry Flight The. information contained herein, in no way Path, Angle constitutes a final decision, by NASA, or JPL or any other Government agency relative to 10* Range of Targeting Parameter its use in, a Voyager-type program* 11.(a)Early Arrival Geometry II,, (b)Late Arrival Geometry 4,3*10 (T) Ascent 2) Parking Orbit 3 Trans-Mars Injection First Mideourse Correction 5 Second M/C Correction Orbit Insertion (7) Orbit Coast (J) Orbit Trim MM Separation & Deorbit (lo) Descent Coast (Ty Entry (l2) Touchdown Fig* 1 Mission Profile 6.3-11 9 30 20 10 35 30 20^ 10 31 21 Most Favorable a) 11 Payload Margins 4J I i * 19 9 30 20 10 31 21 II 1 21 12 22 1 11 21 1 11 21 31 10 20 30 .9 19 29 9 May June July Aug Sept . Launch. Date: ;| 1973 Pig, 2 Mars 1973-1 Energy Co©towns 6,3-12 Note: AVo.; 1.75 Km/sec Insertion at natural periapsis" 18 o o o J5Q Year Lifetime 16 CL> T3 d V__ = 3.25 Km/sec U.LI 14 CO •H CO Cu cd O 12 3.10 10 < 500 1000 1500 2000 2500 3000 Perlaps Is Altitude, h (Km) Fig, 3 Orbit Insertion Impulse Capability 6.3-13 Apoapsis A Orbiter at Time of Entry Atmospheric Entry Point Orbiter Periapsis Fig. 4 Deorbit Geometry 6.3-14 600 I I I i i i 2,500 x 10,000 Km 2,500 x 20,000 Km 400 A = 0 deg A = -10 deg 1,500 x 10,000 Km 1,500 x 20,000 Km 500 x 10,000 Km 500 x 20,000 Km 20 40 60 0 20 Targeting Parameter, p (deg) Fig. 5 Deorbit Impulse Required 6.3-15 _ h A * 10,000 Km "00) 0 200 400 600 Fig» 6 y, Dispersion Due to Orientation lift, W) Fig, 7 / A Dispersion .Due to Magnitude 6.3-17 20 cuW) 15 Same Terminal 50 Conditions 1o 10 PL| 4J top *,^ ^ fe Note; Skipout limit based on VM-8 atmosphere, 2 B = .4 slug/ft Posigrade, equatorial entry 3.6 3*8 4.0 4.2 4.4 4.6 Entry Velocity,, ¥ A (Km/sec) A Fig, 8 Entry Corridor 600 h * 1500 Km 500 P h A * 10,000 Km A e 400 p \ \ 0) CO \ r-1 300 /- a. S \ X o 200 a) P. 100 10 20 30 40 ,50 60 Targeting Parameter, p (deg) Fig. 9 Deorbit Impulse: Effect of Entry Flight Path Angle 6.3- 60 4) 01 4J 0) -20 CO HCQ PL, 4J 10,000 Km 0) 60 toM H 500 1000 1500 1 2000 2500 3000 Periapsis Altitude, h (Era) Fig, 10 Range of Targeting Parameter 4,3.20 :N U 4J O m W r^4 m > "W m I A en f-l>* N « W Earth 1973-1 Fig. 11(b) Late Arrival Geometry -— ^ r^ $- •* 20 ^-xT s s Ev eningI Terrninat or \ ...-ppr^ ..,.,,,..., \ -NT- / ^^ ».. -6 \ 0 -{- r \ -- f / ^ \ \ ^ X \ CO cu -y cu JL \ M 1 50 \; CD Q 1 Note: Land 22:5° from Terminator -40 6 = 25° \ Acp = 20° ——— Arrive Feb. 2, 1974 (T) v. = HE 3.15 km/sec — —Arrive _ -60 March 21, 1974 ©^•^ V_HJL 2.45 km/ sec CO Posigrade orbits " " "t n a, \ i -80* \ V i \ •H d \ 100 v / : X, ^v, •.*>* -^ F- 0**1 -i ~^rT^ ————-L-S 120 Mo- rning Tenrlinatcjr ,— — — — "" ^^ *•— •— ' ^rr -~. — —— . "^^^ 140 ^^ \\ -60 -40 -20 0 20 40 ' 60 Approach from South *«i—j—>- Approach from North Inclination to Martian Equator: i n (Beg) Fig, 12 Required Perlapsis Shift 6.3-23 I I I I Evening Terminator 15,000 10,000 5,000 '0) 14J *HI 4J -'•"-^--i——— T-— — - | •• ir Morning Termina t 01c AW =3 - •80° «a 15 .,,000 . ————————————— o Note: ' la:rid 22 .5° from Terminator - 2:5 11D n Zfp « 2G • y, , ———. AT rive Feb 2, 1974 '! 10,000 — _— Ar / rive Max 21, 1974 | « 1.75 km/ sec AV0",I, langent ial thrusting 5,000 0 1,000 2,000 3,000 Pferlapsis AltItude: hp (km) Fig, 13 Orbit Limits Imposed by (Degrees) Inclination Orbit H* m m 1 H- I_J ft rf o H» fto § a m cm s B § r I 0 G* n €» Entry Touchdown Periapsis Fig. 15 Relay Communication Link during Entry 150 60 OJ P 100 (U O CD pu CO CO ex ctf O -50 -30 -20 -10. 0 10 Lead Angle: A (Deg) \ \ \ \ 3,000 \ 500 x 10,000 km- \ \ \ \ 1,500 x 20,000 km \ \ = 30 C Max 2,000 Min' \ Max 50 a V \ Min • 1,000 o o -30 -20 -10 0 10 20 Lead Angle; A (Deg) Fig. 16 Entry Communication Link Characteristics 6,3-27 " ] Note; VM-8 P = 10" 3 a.v. Includes Time Delay cc ex 6 u -S 4 00 g W) ^*^ C ^ •H 'O 2 "% *m^f/ \\^ ' 0 JO -20 -10 0 10 20 3 Lead Angle: A (Deg) Fig. 17 Frequency-Shift Keying Fading Margin 6.3-28 ^ «•——— _ Nominal Opera ting^ ' Region ^ h = 20,000 km A ^—*-* *\ X-L5C)0 00 \ ^km) | 00 •^^ 25C )0 CD ^^ N \A -10 \ r< \ \ tv t—I0) 50 -10 10 20 30 40 10 20 (3 (deg) Fig. 18 Selected Beorblt Strategy 6.349 H^-A 0to) 1.1 —— |^ote; 1300 x 12,500 km K —— £a jj ;=-—*£ -~o —• 1.0 \ ' - 37 ° - RAAr 0.9 fn tvlli flu/f/t*tyw^ a. /^ 34° Elevation Mas k 0.8 ^~7\ t T . , > 6 Minutes ^JU Link 0.7 .Orbi ter G Jrounc\± Trac e VLa nder Grounid Trcace 0.6 !>- -h ^ 100 200 300 400 500 600 700 a (deg) Fig. 19 Longitudinal Coverage by Orbiting Spacecraft 100 200 300 400 500 700 a (deg) Fig. 20 Link Dependence upon Orbital Period 6,3-30 8 12 20 Time (hr) Fig. 21 Direct Earth Link 6.3-31 Couch down Link Time (minutes) i 3.f'"A r 1 - 0 ..x^" 3 .5 20 N If 4 7 18 ^ JL Note; o0 t—0 I Most Adver se p and A V^X ———— 34 <« 16 deg Ground Mas] c —— — 15 deg Ground Mas] c Ck 0) id 1 3 4-J U 14 T——1 10 tr 7 n1 1 500 1000 1500 2000 2500 3000 Periapsis Altitude, h (km) Fig. 22 Post Touchdown Initial Relay Link 6.3-32 Note,; Deorbit during 4th day o o o ,e<3 14 »\ 0) CO •H CO PU ctf o 500 1000 1500 2000 2500 Periapsis Altitude, h. (km) Fig. 23' Apoapsis Altitude Selection Criteria 6.3-33 3.5 Min 15° Mask 3d 'Range of -Possible ^--Orbits After Insertion Post Land TRelay o o o 0) T3 0) Cu § Evening Terminator Early Arrival 3000- Per laps Is Altitude,, h ( (km) Fig* 24 Orbit Selection Limits 43-34