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Communications Mars Space Science

New Kind of Orbit Could Ease Mars Communications 127

japan_dan writes "An interesting way to enable Earth-Mars communication when the Sun occludes the direct radio line-of-sight: ESA proposes placing a pair of continuous-thrusting relay satellites, using a solar electric propulsion system — one in front and ahead of Mars, the other behind and below — with both following non-Keplerian, so-called 'B-orbits'. This means the direction of thrust is perpendicular to the satellites' direction of flight, allowing them to 'hover' with both Earth and Mars in view. Quoting from the Q&A: 'We found that a pair of relay satellites would only have to switch on their thrusters for about 90 days out of every 2.13-year period, and this solution would only increase the one-way signal travel time by one minute, so it could be effective.'" Here is the paper describing non-Keplerian orbits (PDF).
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New Kind of Orbit Could Ease Mars Communications

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  • by Lord Lode ( 1290856 ) on Friday October 16, 2009 @11:05AM (#29768887)
    That's good news for the diplomatic Human / Martian relations.
    • Re: (Score:2, Funny)

      by Chris Burke ( 6130 )

      You'd think, but the fools are assuming the extra minute of round-trip communication time isn't a problem because it doesn't seriously affect their reaction times. But they fail to understand that in the Martian language, time is a critical component of meaning! And extra minute of latency could make the difference between saying "We accept your offer of peaceful relations. We will begin transmitting cultural information immediately," and "We accept your offer of peaceful relations... Psych! We will beg

      • by gnick ( 1211984 )

        I don't think that we should attempt communication communication with the martians at all until they contact us. From what I've read [wikipedia.org], they can grok our meaning without much trouble (partially due to psychic abilities). However, their lack of adherence to our conservative moral platforms and religious dogma may doom our relations to tragic failure...

      • by dissy ( 172727 )

        But they fail to understand that in the Martian language, time is a critical component of meaning!

        The only martins we are interested in speaking with are generally speaking English, Chinese, or Russian. So that will not be a concern.

      • by Anonymous Coward

        "So will you be pulling your troops out of our city?"
        "..."
        "Pull your troops out or we will be forced to liberate it ourselves."
        "..."
        "Are you looking for a fight?"
        "Yes."
        "You have it then! "
        "Don't worry, we will have the troop out in no time"
        "No certainly not, we will withdraw peaceably"
        "Wait, what!?!"

    • Why the fuck would that be? Now we don't have to wait a few months to cool down before sending off an asinine reply to whatever stupid shit the Martians throw at us next. Now we can insult them with only a 11 minutes of lag. That can in no way be good for diplomatic relations.

      You're a dumbass.

    • Laugh, but just the fact that we're collectively trying to work out the problems of interplanetary communication now that we'll certainly have in the future (if we don't destroy ourselves) made my day.

    • by mabhatter654 ( 561290 ) on Friday October 16, 2009 @01:16PM (#29770447)

      As long as we don't go bombing their planet to look for water.... that's BAD for relations.

      • by maharb ( 1534501 )

        But if they have water then they could have plants which means there could be oil. The oil is worth bombing for, so the water is too, right?

    • Why not put two satellites 120 degrees in front of and behind Mercury?
      -one of them is always visible to both Mars and Earth
      -they are Kepler orbits requiring no thrust
      -the gravitation pull of Mercury at 120 degress is on average 0.0000000556 that of the Sun. =SunMass/MercuryMass/sqrt(2-2cos120)

      Maybe the answer is below
      -to get to Mercury-like orbit requires 4.6 times more energy than to get to Mars-like orbit from the Earth. (MercuryMass/MercuryRadius-EarthMass/EarthRadius)/(MarsMass/MarsRadius-EarthM
  • by mark-t ( 151149 ) <markt.nerdflat@com> on Friday October 16, 2009 @11:12AM (#29768961) Journal
    ... to park such a device at L4 or L5, where you wouldn't require *ANY* fuel to keep it in position?
    • Re: (Score:1, Informative)

      by Nadaka ( 224565 )

      sure, except that you are ~doubling the distance the signal has to travel.

      • Not when Mars is occluded by the sun it wouldn't be double.
        • Which would be the whole reason, IIRC. You only need to get around the sun once in a great while; the rest of the time it's simple line-of-sight.

          Still, if this is closer than L5 even during occlusion, by several minutes, it could be worth it. I assume "only" 90 days of rocket time every 2+ years (I presume an ion drive) is a decent, long-term solution for such a satellite.

          • And by the time we have a permanent human presence on Mars that necessitates this kind of year-round communication, some interesting new propulsion options might well be on the table.
      • Not quite (Score:5, Informative)

        by pavon ( 30274 ) on Friday October 16, 2009 @12:14PM (#29769709)

        Would it?

        Mars has an aphelion (maximum distance from sun) of 250 Gm, and the Earth has an aphelion of 150 Gm. So when the sun is occluding their line of sight, they are on opposite sides of the sun and are separated by at most 400 Gm. If you had a satellite in the Earth's L4 or L5 point, then this would form a 150,350,400 Gm triangle with Mars. Thus the total signal distance would be 500 Gm. This would add 100 Gm, increasing the transit time by 5.5 minutes (from 22.2 to 27.7 minutes). Not as good as the solution presented but not twice as long.

        Placing these in the Earth's orbit, rather than Mars', would have the added advantage of solving the solar occlusion problem for anything we send out into the solar system, not just for things on Mars.

        • Re:Not quite (Score:4, Interesting)

          by Nadaka ( 224565 ) on Friday October 16, 2009 @12:56PM (#29770233)

          The original article was mentioning satellites following/leading mars. With the satellites in mars Lagrange points, the distance would be longer, though not entirely double.

          What the hell, I'll bother to do the math this time, using your figures of 150 Gm and 25 Gm that would result in a maximum distance from earth the a mars Lagrange point at about 350 Gm, plus the 250 Gm to mars gives a distance of ~600 Gm vs the strait line of 400 Gm. so its a ~50% increase in time.

          Of course I could get pedantic and claim I was talking about the difference in time. But that would be fudging to cover my my lazy ass failing to math.

          • Well, it would be 50% longer only when they actually needed to use the Lagrange satellites for communication with Mars. Most of the time the Sun is not in the way, so most of the time communications will be straight-line between Earth and Mars. Also, I might question the need for a SHORT additional delay in this communication; barring an SF gadget like an "ansible" it's not like we will ever being remotely controlling anything on Mars in real-time, since the minimum delay is always at least about 10 minut
        • Placing these in the Earth's orbit, rather than Mars', would have the added advantage of solving the solar occlusion problem for anything we send out into the solar system, not just for things on Mars.

          Plus putting in them in Earth's orbit keeps them closer for maintenance, refueling, etc.... Would suck to have to run out to Mars every time you need to fix a solar panel or something.

          • Re: (Score:3, Informative)

            by Rakishi ( 759894 )

            Satellites as a rule aren't maintained or refueled, they're simply shoved somewhere where their decrepit hulks can hit anything useful. Cheaper that way oddly enough.

            • I guess I was think if it is firing it's thrusters "90 days out of every 2.13-year period" that it would eventually need some refueling.

              You make a good point, but I was under the impression that most of the other satellites we've sent out of Earth orbit have minimal thrusters for initial push and then rides inertia for the the bulk of its trip.

        • This is a much more elegant solution.
    • Re: (Score:3, Informative)

      by hey ( 83763 )

      I didn't know about L4 and L5 so looked it up:
      http://en.wikipedia.org/wiki/Lagrangian_point [wikipedia.org]

      I think any satellite requires some fuel for thrusters to correct the orbit.

      • Re: (Score:3, Informative)

        by Chris Burke ( 6130 )

        L4 and L5 are actually the most stable lagrange points. The satellites would end up basically orbiting the lagrange point itself.

      • Planck and Herschel circulate around L2 of Earth-Moon. It needs little (but still) fuel to correct the orbit.

        L4/L5 are better ... that's where the Trojans are ;-) (L4/L5 attract matter).

        But as TorKlingberg points out below, the sun will move between Mars-L4/L5 or L4/L5-Earth.
        I assume you planned to use L4/L5 of Sun/Mars. TFA suggests moving out of the ecliptic plane, circulating around Mars. Maybe some oscillation/periodicity can be exploited?

        • by CrimsonAvenger ( 580665 ) on Friday October 16, 2009 @12:30PM (#29769895)

          But as TorKlingberg points out below, the sun will move between Mars-L4/L5 or L4/L5-Earth.

          Doesn't matter. If the sun is between Mars-L4/5 and Earth, then Mars is visible from Earth. Likewise, if the Sun is between Earth-L4/5 and Mars, then Mars is visible from Earth.

          The only case where you need these relays is if the Sun is between Mars and Earth (or close enough to a direct line to make a hash of radio communications between Mars and Earth), and in any such case, none of the L4/5 points (either Mars or Earth) will be blocked from either of the two planets.

          • Re: (Score:3, Interesting)

            The only case where you need these relays is if the Sun is between Mars and Earth (or close enough to a direct line to make a hash of radio communications between Mars and Earth)

            The idea isn't exactly new, you know. George O. Smith wrote a series of stories about a relay station in the L4 point of Venus, The Venus Equilateral series, [wikipedia.org] back in the '40s. It was a communications hub for the entire Solar System, and a hotbed of technological innovation. Great stories, still worth reading.

          • You assume two redundant communication points: One on mars, and one in L4/5.

            But the point is to use only one between Earth and Mars.

            • by asaz989 ( 901134 )

              You assume two redundant communication points: One on mars, and one in L4/5.

              But the point is to use only one between Earth and Mars.

              Actually, I don't see that mentioned anywhere as the point - the point is to reduce communication time from Mars to Earth in the worst case of occlusion by the Sun. Having only one communication point is pretty impractical (any such relay satellite, no matter what its orbit, would, if orbiting the Sun or any body orbiting the sun, have to be occluded at least once a year unless it leaves the plane of the ecliptic, which would be a pain)

            • You assume two redundant communication points: One on mars, and one in L4/5.

              But the point is to use only one between Earth and Mars.

              There has to be something on Mars that can transmit and receive, so the addition of one in either L4 or L5 is about the minimum you can deal with without communications blackouts.

              The point of TFA is to use a complicated powered orbit to do what can be done with a satellite in a free orbit at an L4/L5 point.

              The advantage of the complicated powered orbit is that it would redu

    • Re: (Score:3, Informative)

      Wouldn't the Lagrange points also be occulted by the sun, though not at the same time as the planet? Also the distance would be a lot longer, as Nadaka said above.

      • I started to right the same message, but did some research first. The l4 and L5 points are 60 degrees off of the minor body's position. Therefore when Earth-Mars is out of sight, a communication satellite at this point could be used.

      • by DutchUncle ( 826473 ) on Friday October 16, 2009 @12:20PM (#29769771)
        Yes, and that's the whole point - when the planet is blocked, the Lagrange points would be visible to use for a relay.

        Look up 1940's science fiction about the Venus Equilateral Relay Station by George O. Smith http://en.wikipedia.org/wiki/Venus_Equilateral [wikipedia.org]
        • Re: (Score:3, Insightful)

          by jamstar7 ( 694492 )
          Maybe I'm not getting it, but ion thrusters still need reaction mass, don't they? If these sats are under thrust for 90 days every 2 & a half years, eventually they'll run dry. From what I understand about the orbital parameters, they won't be cheap (in delta-vee) to reach for refueling, either. Now, we have a helluva time just scheduling a Hubble repair mission. How much more pain in the ass is a MarsComm sat refueling mission going to be? Or are they to be throwaways & replaced when they fall o
          • by Sparr0 ( 451780 )

            Ion thrusters use only energy and atmospheric (even space isn't a perfect vacuum) particles for reaction mass. There are some nifty underwater engine prototypes that use ionic thrust to accelerate water out a (very low speed) jet.

            • Ion thrusters use only energy and atmospheric (even space isn't a perfect vacuum) particles for reaction mass. There are some nifty underwater engine prototypes that use ionic thrust to accelerate water out a (very low speed) jet.

              I was under the impression these sats were going to be a LONG way away from an atmosphere.

              Besides, power supplies can and do fail.

              • by Sparr0 ( 451780 )

                There is an atmosphere in space. Mostly hydrogen, some other light elements. It's just very sparse.

                If the power supply fails, it's screwed no matter what the thrust mechanism is (except a light sail... but that's science fiction for now)

      • Re: (Score:3, Funny)

        by AGMW ( 594303 )
        Wouldn't the Lagrange points also be occulted by the sun

        Witch ever way you slice there'd be no spell when both Earth and the satellites were blocked by the Sun so it's a wizard idea.

    • by BJ_Covert_Action ( 1499847 ) on Friday October 16, 2009 @11:37AM (#29769239) Homepage Journal
      The interviewee mentions that both LaGrange point orbits, as well as a few other options, are also being considered. Reading the interview, which is part of the article, can sometimes reveal useful information like this.

      Also, to be pedantic, you would still need some fuel on a LaGrange spacecraft for station-keeping purposes. Though this amount would be minimal, you can't justifiably claim that you wouldn't need *ANY* fuel.

      Cheers Mate.
    • Re: (Score:2, Funny)

      by RivenAleem ( 1590553 )
      Peer to peer downloads of heavy metal music would push the satellite out of the Lagrange point. Another reason why its BAD to fileshare

      ~Your friendly RIAA rep
    • Re: (Score:2, Interesting)

      I think the issue is better coverage on Mars.

      As I read it, the spacecraft would be positioned so that they each cover half Mars with no overlap or gaps.

      If the spacecraft were at the Legrange points, then the near/day side of Mars would have a large area that could see both spacecraft and far/night side of Mars would have a large area couldn't see either of them.

    • by Solandri ( 704621 ) on Friday October 16, 2009 @01:53PM (#29770889)

      ... to park such a device at L4 or L5, where you wouldn't require *ANY* fuel to keep it in position?

      The receiver/transmitter on these satellites and space probes are very small. Generally they transmit using only a few watts, and we rely on huge antennas like in the ubiquitous dishes in the Deep Space Network to gather enough of that minuscule signal to distinguish it from background noise. Going the other way, we use the same huge antennas to blast commands to these spacecraft at anywhere between 5-500 kW. By the time the signal reaches the spacecraft, it has dissipated substantially, but its original broadcast power was high enough that the spacecraft's relatively small antenna can still collect enough of it to distinguish the signal.

      Putting a repeater spacecraft at the L4 or L5 points would place them a substantial distance from Mars. Consequently the repeater would need a very large antenna and large amounts of power (though not as big/much as earth-based antennas) in order to relay signals to/from a spacecraft on Mars. The idea presented in the paper is more akin to what we do right now with the two Mars Rovers and several of our Mars orbiters. The Rovers themselves have weak antennas and can't communicate directly with Earth except at low data rates. Instead, they transmit their data to the orbiters (same antenna can achieve higher bandwidth since the distance is much less), which then relay it to Earth using their much larger and more powerful antenna.

      (Introduction to channel capacity [wikipedia.org] for those who may be wondering what the relationship is between data transmission speed and signal to noise ratio.)

    • Wouldn't it make more sense ... to park such a device at L4 or L5, where you wouldn't require *ANY* fuel to keep it in position?

      I'll second that.

      Jupiter might perturb the Mars L4 & L5 points too much. But the Earth's points should do just fine. They'd also have somewhat more solar power available and would be closer, fuel-wise, for installation, which should help as well.

      George O. Smith proposed essentially this solution in the _Venus Equilateral_ series, between 1942 and 1945. He sited his relay at

    • In theory something that is placed in an L4 or L5 point stays there forever. In reality perturbations from the various objects in the Solar System shake up thing a little, so some manoeuvers are needed to keep things stable.

  • by Anonymous Coward on Friday October 16, 2009 @11:13AM (#29768977)

    Houston> We haven't talked for a day, what's up?
    Mars rover> Hey, I moved one meter!
    Houston> No shit!

  • Cita tion need ed (Score:2, Informative)

    by Anonymous Coward

    FYI: there is no article on Wikipedia to describe a non-Keplerian orbit.

    Even 2 simple diagrams describing the 2 orbits types would help.

    • Re: (Score:3, Insightful)

      by Nyeerrmm ( 940927 )
      Go write it then. You've got the journal article to work off of, which should be all the citations you need, since I think this is the definitive work on the subject right now.
    • Did you read the linked paper?

    • By non-Keplerian, they just mean a powered orbit. An orbit that needs the satellite to fire thrusters from time to time to keep on track. Maybe to shift from gravitational trough to gravitational trough, or maybe to keep the orbit from decaying.

  • I would've thought their may be an orbital resonance solution that wouldn't require any thrusters at all. But that may require an orbital resonance between Earth and Mars, a situation that clearly doesn't exist.

    Still, there may be something exotic that could be done.

  • Eh? (Score:3, Funny)

    by wcrowe ( 94389 ) on Friday October 16, 2009 @11:19AM (#29769061)

    I understand "behind and below". WTF is "in front and ahead"?

  • Bandwidth (Score:5, Insightful)

    by CheshireCatCO ( 185193 ) on Friday October 16, 2009 @11:43AM (#29769297) Homepage

    This is slightly tangential, but worth noting I think:

    This will be handy when we can't afford to lose contact with Mars for even a few days, but there's a bigger problem lurking in inter-planetary communications: bandwidth. We don't really have enough Deep Space Network dishes (particularly, the large 70-m ones) to talk to all of our missions as much as we should. We're sacrificing data collection on billion-dollar missions on a daily basis on the grounds that we don't have enough bandwidth to get it back. When we put people or even just more missions on Mars, that'll only get worse.

    • Re: (Score:3, Funny)

      by Rennt ( 582550 )
      Yeah, net neutrality goes right out the window. Spare a thought for our poor Martin pioneers. No bittorrent for you!
    • Re: (Score:2, Funny)

      by NEDHead ( 1651195 )
      Wireless is always less bandwidth than wired/fiber solutions. A direct, multistrand cable is called for.
    • Two words: Lunar dishes.

      Put the comm dishes on the Moon someplace. I'd recommend a set of 3, equally spaced around the equator of the Moon, thus, it'll always have 1 dish at least looking in the right direction.

      Second thought, a heavy comm laser setup, also Moon-based.

      • Why would putting them on the Moon help?

        And the problem isn't having dishes pointing in the right directions, it's having too *few* of them. For example, when Saturn and Mars are near conjunction in our sky, we have to choose whether to talk to Saturn or Mars with the 70-m dish.

    • by khallow ( 566160 )
      That goes to a complaint I heard recently. Namely, that the US government eagerly spends billions to develop and launch these missions, and grudgingly spends millions to maintain them. It makes sense, if you realize that the primary purpose of these missions is to funnel money to the NASA supply chain, not to do space science.
  • Immature (Score:5, Funny)

    by ZinnHelden ( 1549931 ) on Friday October 16, 2009 @11:45AM (#29769331)
    Sorry, I tried to read the summary but I didn't make it past 'continually-thrusting'.
  • ...we let go of the harakiri you're supposed to commit if you ever go out of cell phone range? I mean, surely we can outfit an expedition that doesn't need 24/7 babysitting from mission control, It's not like Columbus had queen Isabella call him up every night to ask "Are you there yet? Food supply ok? Your blood sugar values are low, you should eat more."

    • Re: (Score:3, Insightful)

      by DutchUncle ( 826473 )
      Totally. Why do the Shuttle crews need to get woken up over the radio? Don't they have a clock? maybe a watch? There are self-winding mechanical ones with alarms, no batteries to wear out. It seemed childish in the Apollo age when I was a kid with my own alarm clock for school; it's downright stupid now.
  • ANKOS... (Score:2, Funny)

    by smitty777 ( 1612557 )

    A New Kind Of Science...er...Orbit. I wonder if Wolfram will try to take credit for this, too. Maybe there's an automata to describe it.

  • by Brett Buck ( 811747 ) on Friday October 16, 2009 @12:00PM (#29769545)

    To clarify - this sort of "orbital" motion (not really "orbital" since it actively powered) is hardly a new idea. What is relatively new is the fact that you have engines that permit you do do it without prohibitive fuel consumption. It's different from a hovering rocket-propelled lander (like the DC-X) only in scale. The key feature, not clear in the article, is that you are intentionally thrusting along the local vertical, in the direction of gravity, to modify its effects. That was possible and everybody knew about it since, well, Newton figured out gravity. What we haven't been able to do is to maintain it for more than the briefest periods due to excess fuel consumption.

            The new part here is the Hall Current thruster, which is ~factor of 10 more efficient than traditional engines. The specific impulse of these is around 1800 seconds (lb-sec of impulse per lbm of fuel- hey I didn't invent the units, I just use them...) compared to maybe 180 for a hydrazine monopropellant thruster. These are not exactly "new" either, the Russkies have been using them for decades. Only recently has the western world begun to develop them, so it's new only in that sense. So the solution they are looking at is now looking reasonably practical, although no doubt still significantly limited by the fuel consumption.

            Brett

    • The specific impulse of these is around 1800 seconds (lb-sec of impulse per lbm of fuel- hey I didn't invent the units, I just use them...)

      That unit doesn't make sense - force and mass don't cancel each other out, even if you happen to be crazy and give the units the same name: lb-force is not the same thing as lb-mass.

      To put it another way:
      N × s / Kg
      See - no identical units to cancel.

      • Re: (Score:3, Informative)

        by Brett Buck ( 811747 )

        Hey, ISP is in seconds, it's an industry standard. The SI version isn't any better - kgf-sec/kg. It makes more sense when you realize it's proportional to the exhaust velocity, which is in, say, feet/second.

              Brett

        • >Hey, ISP is in seconds, it's an industry standard.

          Might be standard, but it's still crazy. Using weight instead of mass means you have to know how much gravity it was calculated for (a figure that isn't specified anywhere in the units), and means that the value given for ISP will change depending on the gravitational force you assume is in effect.

          The SI version isn't any better - kgf-sec/kg.

          That isn't the SI version - there is no such SI unit as "kgf". The SI unit for force is Newtons, giving you "Newton seconds per kilogram", which makes a lot more sense since there are no hidden coefficients.

        • by radtea ( 464814 ) on Friday October 16, 2009 @02:18PM (#29771219)

          Hey, ISP is in seconds, it's an industry standard.

          But it shouldn't be. N*s/kg is the correct unit for specific impulse. "Seconds" is only used by American engineers who don't understand the difference between weight and mass.

          When I was a kid I was deeply interested in space, but it wasn't until years later that I understood the meaning of Isp because of the idiotic convention of designating it in seconds, rather than force*time/mass, which makes its meaning completely obvious.

          If you want to turn people off an understanding of the most basic aspects of space travel, by all means go ahead and keep using seconds for Isp. But it's really time for the United States to get with the rest of the world and abandon Imperial units, although I guess as an imperial power they seem like a natural fit.

          [Ok, now wondering if this'll get more "troll" or "flamebait" mods. It should probably lean toward "flamebait", as the story is true: Isp in seconds really did confuse me for years. The egregious America-bashing is, well, egregious, so probably warrants a flamebait mod. But really, what's with the Imperial units, kids?]

    • These are not exactly "new" either, the Russkies have been using them for decades. Only recently has the western world begun to develop them, so it's new only in that sense.

      Not quite. SERT [wikipedia.org]

  • Slightly off-topic, but I have a question for the word-geeks out there. Now, I know that technically "Occults", used the way it is in this context, is technically correct (in fact, as far as I can tell, this is the *original* meaning of the word, and the other meanings have developed off of the original meaning, later). However, given that most people probably associate the word "Occult" with mysticism, mightn't it have been better to describing the Sun blocking communication by using the word Occlude, inst

    • by 4D6963 ( 933028 )

      Don't ask "word geeks", do like "word geeks", open up a fucking dictionary.

      http://en.wiktionary.org/wiki/occult

  • ping (Score:1, Offtopic)

    by Hognoxious ( 631665 )
    I wonder what the ping times are like?
  • First: What is the purpose of 24 hour communications? If you need SOS messaging, signal recovery, or a simple heartbeat, use the sun as the point-of-reference.
    Second: A fleet of solar communications satellites could provide a solar GPS system.
    Third: These satellites could use Solar Propulsion and "hover" at a fixed distance from adjacent satellites. Solar sails could serve as a foundation for power generation (focused beam) and for data reception.

    Downsides: the sun is a noisy place for communications, as

  • Comment removed based on user account deletion
  • continuous-thrusting

    We found that a pair of relay satellites would only have to switch on their thrusters for about 90 days out of every 2.13-year period

    I'm confused. Isn't 90days/(2.13years*days/year) 1?

  • Just off the top of my head, how about this:
    a set of say, four to six, relay satellites placed at the forward and trailing Lagrange points on Venus's solar orbit and the other two placed in Earth's solar Lagrange points.

    Line of site is closer to straight line and as others have pointed out it would give us pretty much unrestricted communication to any point in the solar system. There may be some tech issues with this but wouldn't this or a some variant work better than having relay sat.s in powered orbits
  • This is a job for Venus Equilateral [wikipedia.org]!

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