MarsSat: Assured Communication with Mars

ANNALS OF THE NEW YORK ACADEMY OF SCIENCES Volume 1065

NEW TRENDS IN ASTRODYNAMICS AND

APPLICATIONS

Edited by Edward Belbruno

The New York Academy of Sciences New York, New York

2005

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International Conference on New Trends in Astrodynamics and Applications (2nd: 2005 : Princeton University) New trends in astrodynamics and applications: an international conference / edited by Edward Belbruno.

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Includes bibliographical references and index. ISBN 1-57331-630-X (cloth: alk. paper)−ISBN 1-57331-631-8 (pbk. : alk. paper) 1. Astrodynamics. I. Belbruno, Edward, 1951-. II. Title. III. Series. QI1.N5 vol. 1065 [TLl055] 500 s-dc22 [629.4'11]

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ISBN 1-57331-630-X (cloth) ISBN 1-57331-631-8 (paper)

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Ann. N.Y. Acad. Sci.

1065: 1–15 (2005). ©2005 New York Academy of Sciences.doi: 10.1196/annals.1370.007

MarsSat

Assured Communication with Mars

THOMAS GANGALE

OPS-Alaska, Petaluma, California, USA

A

BSTRACT

: The author developed the MarsSat concept during the 1990s. Forthis task, he designed a class of orbits to solve the problem of communicatingwith crews on Mars when the planet is in solar conjunction as seen from Earth,a planetary configuration that occurs near the midpoint of a conjunction classmission to Mars. This type of orbit minimizes the distance between Mars andthe communications satellite; thus, minimizing the size, weight, and powerrequirements, while providing a simultaneous line-of-sight to both Earth andMars. The MarsSat orbits are solar orbits that have the same period as Mars,but are inclined a few degrees out of the plane of the Mars orbit and also differin eccentricity from the orbit of Mars. These differences cause a spacecraft inthis orbit to rise North of Mars, then fall behind Mars, then drop South ofMars, and then pull ahead of Mars, by some desired distance in each case—typically about 20 million kilometers—in order to maintain an angular sepa-ration of a couple of degrees as seen from a point in the orbit of Earth on theopposite side of the Sun. A satellite in this type of orbit would relay communi-cations between Earth and Mars during the period of up to several weeks,when direct communication is blocked by the Sun. These orbits are far superi-or for this purpose when compared to stationing a satellite at one of the Sun–Mars equilateral Lagrangian points, L

4

or L

5

, for two reasons. First, L

4

and L

5

are 228million kilometers from Mars, about 10 times the distance of a space-craft in one of the MarsSat orbits, and by virtue of the inverse-square law, allother things being equal, the signal strength received at L

4

or L

5

would be onepercent of the signal strength received by a spacecraft in one of the MarsSatorbits. Thus, a relay satellite stationed at L

4

or L

5

would have to be that muchmore powerful to receive data at the same rate, with concomitant increases inspacecraft size and weight. Second, a number of Martian Trojan asteroidshave been discovered at the Sun–Mars L

4

and L

5

points, and there are proba-bly countless smaller objects that have collected in these regions that pose a sig-nificant threat to any spacecraft located there.

K

EYWORDS

: MarsSat; communication Mars; human mission; manned mission; Lagrangian points

STATEMENT OF NEED

In early September 2004, the deep space network (DSN) lost contact with theMars exploration rovers

Spirit

and

Opportunity

on the surface of Mars, and with the

Mars Global Surveyor

and

Mars Express

spacecraft in orbit around Mars. Several

Address for correspondence: Thomas Gangale, OPS-Alaska, 2262 Magnolia Avenue, Peta-luma, CA 94952, USA. Voice and Fax: 707-773-1037.

[email protected]

nta07.fm Page 1 Friday, December 9, 2005 11:59 AM

2 ANNALS NEW YORK ACADEMY OF SCIENCES

weeks passed before communications were reestablished with the vehicles. Thishiatus was not caused by any hardware or software failure; rather, it was an inevita-ble consequence of planetary orbital mechanics. During this period, Mars passedbehind the Sun as seen from Earth, a planetary configuration known as solar con-junction. Fortunately, links were reestablished at the end of May and these spacecraftare continuing their missions. During the nearly three Mars years during which the

Viking 1

lander operated, there were three such lengthy communication blackoutsdue to solar conjunctions. This Mars–Sun–Earth alignment occurs at 780-day inter-vals on average, varying from 766 to 803days, due principally to the eccentricityof the Mars orbit. T

ABLE

1 gives communications outage periods for other Marsmissions.

T

ABLE

1. Solar conjunction communications outage periods

Spacecraft Outage Period

Viking 1 Orbiter

5 November–14 December, 1976

Viking 2 Orbiter

8 November–14 December, 1976


29 April–1 June, 1998

22 June–12 July, 2000

1–18 August, 2002

7–25 September, 2004

Spirit and Opportunity

5–23 September, 2004

Mars Express

22 August–27 September, 2004

Mars Reconnaissance Orbiter

7 October–8 November, 2006 (planned)

FIGURE 1. Conjunction class mission profile.


3GANGALE: ASSURED COMMUNICATION WITH MARS

Various mission profiles have been proposed for human expeditions to Mars.Among these is the conjunction class mission, which utilizes minimum-energyHohmann trajectories both to and from Mars. However, the use of Hohmann trans-fers on both the outbound and inbound legs of the mission requires roughly a 500-sol layover on Mars to await the proper planetary configuration for the return flight.As can be seen in F

IGURE

1, solar conjunction occurs near the midpoint of this 500-sol stay on Mars. Although the use of the conjunction class scenario on initial humanMars missions is an issue yet to be decided, undoubtedly this type of mission profilewill be flown at some point in a human Mars exploration program, not only becauseit is the most propellant-efficient profile, but also because it maximizes stay time onMars, while minimizing travel time to and from Mars with respect to other missionprofiles using the same class of propulsion systems.

Until the tracking and data relay satellite system was completed in the 1980s,human missions historically endured short-duration interruptions in communica-tions. These blackouts would last for a few minutes while passing between groundstations or during reentry. There were communications losses of as much as an hourduring the Apollo program when vehicles passed behind the Moon. However, it ishard to imagine that a communications outage on the order of one month will be tol-erated on a human Mars mission. The specific duration of the interruption during asolar conjunction depends on several factors, such as the amount of link margindesigned into the communications system, as well as the minimum data rate that isacceptable from a mission standpoint. Nevertheless, regardless of how much robust-ness is designed into the communications links, the minimum blackout period willalways be on the order of weeks, not the few minutes or hours that have been expe-rienced during previous human space missions.

Communications interruption by the Sun will become even more of a problem ashuman Mars operations build up to permanent bases. The conjunction blackout willof course hold true for a Mars base as well as for a conjunction-class mission, butfurthermore, such a base will also have to contend with oppositions, which are, fromthe Martian point of view, inferior conjunctions of Earth; that is, when Earth passesin front of the Sun as seen from Mars. During oppositions, Earth will be able toreceive signals from Mars, but transmissions from Earth to Mars will be drowned outby radio noise from the Sun.

Morabito and Hastrup

1

have investigated six conjunctions from June 2015 to Jan-uary 2026. In five of these, Mars will pass within one degree of the Sun, and inNovember 2023 Mars will pass directly behind the Sun. Among their conclusions are:

• “A significant improvement in telemetry data return can be realized by usingthe higher frequency 32GHz (Ka-band), which is less susceptible to solareffects.

• “Other options [are] the use of FSK, frequency semaphores, and spatial andfrequency diversity….

• “For five of these six conjunctions, where the signal source is not occulted bythe disk of the Sun, continuous communications with Mars

should

be achiev-able. Only during the superior conjunction of 2023 is the signal source atMars expected to lie behind the disk of the Sun for about one day and withintwo solar radii (0.5

°

) for about

three days

[emphasis added].”



Two comments must be made, however:

• How good is “should?”

• As the

Apollo 13

mission demonstrated, three days can be exciting.

With humans on Mars, the rules of the game change radically. From the viewpointof crew safety, anything more than a few hours of lost voice communication andhealth and status telemetry will almost certainly be unacceptable. Without the sup-port of technical teams on Earth, the crew of

Apollo 13

would have perished. Somemeans of assuring uninterrupted communications between Earth and Mars will haveto be included in human Mars program planning. To satisfy this need, I propose arelay satellite concept that I call MarsSat.

PRELIMINARY SYSTEM TRADEOFFS

F

IGURE

2 depicts the connectivity for a Mars communications system designed tocircumvent the solar conjunction blackout, including Mars surface stations, lowMars orbit vehicles, a constellation of communications relays in Mars orbit, Mars-Sat, and the DSN.

The basic considerations in sizing a satellite communications system are embod-ied in the link budget, which includes the following parameters:

•

P

t

transmitter power,

•

G

t

transmitter antenna gain,

• SNR signal-to-noise ratio,

•

P

L

path loss,

•

P

s

received signal level,

•

G

r

receiver antenna gain,

•

N

f

receiver noise floor, and

•

P

n

noise in receiver bandwidth.

On a conceptual level, spacecraft weight (and, therefore, cost) is driven by the sizeof the antenna and the power requirements of the transmitter and receiver. These inturn are driven by the range over which the link is required to operate. Exact num-bers for the size, weight, and power of specific mission elements are a subject fordetailed system engineering, and thus, beyond the scope of this presentation. How-ever, the basic approach is to minimize size, weight, and power of spaceborne ele-ments of the communications system, since it is more economic to compensate withlarge, heavy, and power-consuming elements on Earth.

Ideally, it is the Earth-to-Mars link that should drive the overall system design,with the Earth-to-MarsSat and Mars-to-MarsSat links impacting system design aslittle as possible, since these alternative links represent additional costs. Assumingthat the range of the Earth-to-MarsSat link will be on the same order as that of theEarth-to-Mars link, the MarsSat communications equipment need only be compara-ble to the equipment on the near-Mars elements. The stressing case, however, will be



the Mars-to-MarsSat link, for size, weight, and power will be at a premium on allspaceborne mission elements. It is for this link that the system must be optimized,since in this case, there are no large ground stations to figure into the link budget. Toachieve minimum system impact, the maximum range over which the Mars-to-Mars-Sat link must operate should, therefore, be as short as possible. At the same time,however, a minimum angular separation between the MarsSat spacecraft and Mars,as seen from Earth during solar conjunction, must be maintained in order to reducethe impact of solar noise on the links. In general terms, this identifies the trade spaceto be investigated in the system engineering process.

For


, mission planners and telemetry engineers defined thesolar communications outage as occurring when the Sun–Earth–Mars angle waswithin seven degrees, and they planned for a loss of signal from 30 April to 26 Mayduring the 1998 conjunction. It was also noted that a quiescent Sun could havereduced this angle to five degrees. Several factors could reduce this minimum solarseparation angle for human missions. The link throughput requirements might belimited to voice communication and only such telemetry as is necessary for the safe-ty of the crew; science data taken during the conjunction period could be recorded

in situ

and transmitted to Earth after the conjunction. Additionally, the use of a lasercommunications system might offer advantages over a conventional radio system. Inmy preliminary analysis, required minimum solar separation angles between twoand three degrees were assumed. These may be unrealistically small angles from themission operations perspective, but they provided me with some stressing cases forevaluating orbit stability.

This leads to my next point. Another consideration in the location of the relayspacecraft is the stability of its position relative to Mars over the design life of thesatellite, since the more stable the orbit, the less fuel must be expended to maintain

FIGURE 2. System connectivity.



the position of the spacecraft—yet another factor affecting design weight. In thispaper, the eight-Mars-year (15-Earth-year) cycle over which the relative positions ofEarth and Mars more or less repeat is defined as the mission life of the MarsSat vehi-cle. Thus, the spacecraft would be required to provide communications through sev-en solar conjunctions.

ORBIT SIMULATION AND EVALUATION CRITERIA

MarsSat Simulation

To investigate candidate orbits, I developed a simulation that provides two split-screen graphic displays. F

IGURE

3 consists of the familiar solar system “overhead”view from above (North of) the ecliptic, and the in-the-ecliptic view along the vectorof the vernal equinox. F

IGURE

4 provides two views edge-on to the ecliptic plane.Both views are bore-sighted on Mars. The left side of the screen is a view from theperspective of the Sun and sighted along the acceleration vector of Mars (the Sun–Mars line); the right side of the screen is a view sighted along the velocity vector ofMars (perpendicular to the Sun–Mars line). The large divisions along the

x

and

y

axes of the two in-the-ecliptic views represent one degree of arc, measured from 400million kilometers, which is roughly the distance between Earth and Mars duringconjunction. It is these two Mars-centered views that generate information that isuseful in evaluating potential MarsSat orbits.

FIGURE 3. Coperiod out-of-plane oscillating satellite, solar system views.



Evaluation Criteria

Criteria for evaluating candidate MarsSat orbits include:

• Maximum range in kilometers from Mars (MARSMAX)—evaluated over aone-Mars-year cycle.

• Minimum angular separation in degrees from the Sun–Mars line (SUNMIN)for an observer at a distance of 400million kilometers.

• A figure of merit (FMERIT), defined as SUNMIN

×

10

7

/MARSMAX,expresses the optimization of minimum solar angular separation and maxi-mum range from Mars.

• Orbital drift—in kilometers.

• A second figure of merit (F2MERIT), defined as FMERIT

×

10

7

/DRIFT,expresses the optimization of minimum solar angular separation, maximumrange from Mars, and minimum orbital drift (not shown in the figures).

Not investigated were

Δ

V

requirements to insert satellites into candidate orbits,although it should be pointed out that this would be an important consideration inthe selection of a MarsSat orbit.

ORBIT CONCEPTS

Coorbital Leader/Trailer Satellites

The simplest orbit for a MarsSat vehicle would be one having the same parame-ters as that of Mars itself but slightly out of phase, that is, either leading or trailingMars by a few degrees in its orbit around the Sun. Ideally, a spacecraft in this orbit

FIGURE 4. Coperiod out-of-plane oscillating satellite, Mars-centered views.



FIGURE 5. Coorbital leader/trailer satellites.

FIGURE 6. Near Earth asteroid population size distribution: , Harris; , D’Abramo,et al. (LINEAR 00-01); , discovered as of July 2002; , Stuart 2001 (LINEAR);

, Rabinowitz, et al. 2000 (NEAT); , Rabinowitz, et al. 2000 (SW).



T

ABLE

2. Estimate of undiscovered Martian Trojans

Diameter Number

>

1,000 m 5.00

×

10

1

397–1,000 m 5.00

×

10

2

157–397 m 5.00

×

10

3

62–157 m 5.00

×

10

4

25–62 m 5.00

×

10

5

10–25 m 5.00

×

10

6

4–10 m 5.00

×

10

7

1.5–4 m 5.00

×

10

8

61–150 cm 5.00

×

10

9

24–61 cm 5.00

×

10

10

10–24 cm 5.00

×

10

11

4–10 cm 5.00

×

10

12

1.6–4 cm 5.00

×

10

13

0.6–1.6 cm 5.00

×

10

14

FIGURE 7. Stability regions at the Sun–Mars L4 and L5 points.



would remain stationary with respect to the Sun–Mars system. Unfortunately, sucha relationship can only be stable if the phase angle of the orbit is either

−

60

°

or

+

60

°

with respect to Mars, corresponding to the equilateral Lagrange points L4 and L5. Ascan be seen in FIGURE 5, satellites with phase angles of −2° and +2° exhibit verypoor stability, quickly departing from their assigned stations in the vicinity of Marstoward the L4 and L5 points.

The equilateral Lagrange points themselves are problematic for a couple of rea-sons. Six Martian Trojan asteroids are now known to lurk at these points, and theseare certainly only the tip of the iceberg. According to Tabachnik and Evans,2 “Crudeestimates suggest there may be as many as 50 undiscovered Martian Trojans with siz-es greater than 1km.” Additionally, Harris and Bowell3 provide a size distribution forthe near-Earth asteroid population. The result of regressing FIGURE 6, is that reducingobject size by 2.25 increases the population of that size range by 10. If the near-Marspopulation is similarly distributed, the implications are alarming (see TABLE 2). Onthe other hand, Tabachnik and Evans2 suggest that at inclinations less than 15degrees, the equilateral Lagrange points may be less cluttered (see FIGURE 7).

Even if the above evaluation of the debris threat is overstated, the equilateralLagrange points are nevertheless too far from Mars to be suitable stations for Mars-Sat, since links over this 230 million kilometer range would require spaceborne com-munications elements whose size, weight, and power would be on the order of a DSNground station (see FIGURE 8).

Coperiod In-Plane Oscillating Satellites

Another simple idea, one that would avoid the instability problem of the coorbitalleader/trailer concept, is an orbit in which a satellite alternately leads and then trailsMars, thus tending to balance out the gravitational influence of Mars. Such a schemecan be achieved by having the satellite in an orbit whose period is the same as thatof Mars, but whose eccentricity is either greater or less than that of Mars. FIGURE 9depicts the behavior of a spacecraft whose orbital elements are the same as Mars,except for an eccentricity of 0.05. It can be noted that from the Martian point of view,a spacecraft in this orbit appears to orbit around Mars, although in reality it is grav-itationally bound to the Sun. The MarsSat simulation indicates excellent stability forthis orbit over an eight-Mars-year period. Since the satellite circles Mars once everyMartian year, the perturbation effects of Mars gravity tend to cancel out.

An obvious disadvantage of this type of orbit is that since it is in the same planeas the Mars orbit, as seen from the Sun, the satellite transits Mars twice each Martianyear, and thus an unobstructed line-of sight with Earth during solar conjunction isnot assured by a single satellite. A second satellite, one whose longitude of perihe-lion is 90° out of phase, would be necessary.

Coperiod Out-of-Plane Oscillating Satellite

FIGURES 3 and 4 illustrate an orbit whose period is one Martian year, but whoseeccentricity and inclination both differ from that of Mars. As with the in-plane oscil-lating satellite, this out-of-plane orbit mimics the motion of a satellite in orbit around



Mars, although the satellite is not bound by the gravity of Mars, but is actually insolar orbit. In contrast to the in-plane oscillator, however, a minimum solar angularseparation from Mars is maintained as, referring to FIGURE 10, MarsSat (A) risesNorth of, (B) trails, (C) drops South of, and (D) leads Mars in their journey togetheraround the Sun. In such an orbit, only one satellite is necessary to assure line-of-sight with Earth during any solar conjunction. As with the in-plane oscillator orbit,

FIGURE 8. Lagrange point relays, “Goldstone in space.”



excellent orbit stability is demonstrated over a fifteen-year period (see FIGURE 11).This type of orbit, therefore, seems well-suited for the MarsSat concept. Now, if weneed to increase the solar separation angle beyond what I assumed in this study, orbitstability improves, since we increase our distance from the gravitational influence ofMars.

FIGURE 11 also shows that a minimum angular separation, as seen from Earth,between MarsSat and Mars, of 2.5° is achieved. The line-of-sight distance fromMarsSat and Mars is on the order of 22 million kilometers. Note that this is only one-tenth the distance that a relay satellite stationed at a Lagrange point would be fromMars. All other things being equal, signal strength is inversely proportional to thesquare of the distance, thus to gain the same signal strength across ten times the dis-

FIGURE 9. Coperiod in-plane oscillating satellite, Mars-centered views.

FIGURE 10. Assured line-of-sight during any conjunction.



tance, a Lagrange point satellite would need to be 100 times more powerful, affect-ing the weight of the spacecraft accordingly (see FIGURE 12). Thus, if we have todouble the separation angle to five degrees, the MarsSat link is still only one-fifth therange of a Lagrange point link, which represents a link budget savings of 25 to 1.

FIGURE 11. Orbital stability through eight Martian years.

FIGURE 12. MarsSat versus Lagrange point relays.



ANALYSIS

The following parameters are used to characterize MarsSat orbits:e, eccentricity,i, inclination,ΔΩ, longitude of ascending node, referenced to that of Mars,

, longitude of perihelion, referenced to that of Mars, andΔL, longitude at epoch, referenced to that of Mars.

The sixth orbital parameter—a—is understood to be equal to the semimajor axis ofthe Mars orbit, since in all cases we want the period of the MarsSat orbit to be oneMartian year.

Several general observations can be made concerning MarsSat orbits:

• Increasing the delta eccentricity with respect to Mars increases the horizontal(in-plane) travel of the spacecraft as seen along the Sun–Mars line.

• Increasing the delta inclination with respect to Mars increases the vertical(normal to plane) travel of the spacecraft. To increase the minimum solar sep-aration angle (SUNMIN) requires simultaneous increases in delta eccentricityand inclination.

• For eMarsSat < eMars and ΔΩ < 0, the spacecraft rotates around Mars in a coun-terclockwise direction as viewed from the Sun.

• For eMarsSat < eMars and ΔΩ > 0, the spacecraft rotates around Mars in a clock-wise direction as viewed from the Sun.

Δω

FIGURE 13. F2 merit versus ascending node.



As long as the semimajor axis of the MarsSat orbit is identical to that of Mars, itsperiod is one Martian year. The other five orbital elements can be combined in a vastnumber of permutations to produce useful MarsSat orbits. For a specified SUNMINand ΔΩ, however, there is a unique combination of e, i, , and ΔL that producesan optimum F2MERIT, that is, optimizes minimum solar angular separation, maxi-mum range from Mars, and minimum orbital drift. This trade space can be charac-terized as a series of curves representing optimized F2MERIT for specifiedSUNMIN values plotted across the full range of ΔΩ (see FIGURE 13).

CONCLUSION

Selection of a specific MarsSat orbit must be left to future system engineeringtrade studies based on the optimum Mars-to-MarsSat range and the optimum Mars-to-MarsSat solar separation angle, as well as ΔV requirements to insert a satellite intoa given orbit. Human Mars mission studies should consider the minimum data ratethat would be acceptable during the conjunction period. For instance, transmissionto Earth of much of the science data recorded during the conjunction might bedeferred until after the conjunction, whereas the minimum acceptable data ratemight be primarily driven by voice links and engineering data relevant to missionsafety. The minimum solar separation angle, and therefore, the cost of the MarsSatsystem, would be reduced accordingly.

Most space systems have one or more levels of redundancy designed into them,and even though these additional components increase the cost of a system, they areincluded in the design with the hope that they will never need to be used at all! Incontrast, if assured communications with Mars throughout all phases of a humanmission is a firm system requirement, the necessity of MarsSat in providing that vitallink with Earth will be a certainty. Given that a human Mars program will cost tensof billions of dollars, a communications satellite adding less than one percent to theprogram cost represents a very small and very prudent investment in crew safety.

REFERENCES

1. MORIBITO, D. & R. HASTRUP. 2001. Communications with Mars during periods ofsolar conjunction: initial study results. IPN Progress Report 42-147. <http://ipnpr.jpl.nasa.gov/tmo/progress_report/42-147/147C.pdf>

2. Tabachnik, S. & N.W. Evans. 1999. Cartography for Martian Trojans. Astrophys. J.<http://arxiv.org/PS_cache/astro-ph/pdf/9904/9904085.pdf>.

3. HARRIS, A.W. & E. BOWELL. 2002. NEO Observations with LSST: populations andsurvey completeness. American Astronomical Society 201st AAS Meeting, #45.18.Bull. Am. Astro. Soc. 34: 1174. <http://pan-starrs.ifa.hawaii.edu/project/people/har-ris/AAS.ppt>.

Δω


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MarsSat: Assured Communication with Mars