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Space Science

Antique Fridge Could Keep Venus Rover Cool 229

Posted by ScuttleMonkey
from the hot-old-tech dept.
Hugh Pickens writes "In the 1970s and 80s, several probes landed on Venus and returned data from the surface but they all expired less than 2 hours after landing because of Venus' tremendous heat. It's hard to keep a rover functioning when temperatures of 450 C are hot enough to melt lead but NASA researchers have designed a refrigeration system that might be able to keep a robotic rover going for as long as 50 Earth days using a reverse Stirling engine. NASA has not committed to a Venus rover mission, but a 2003 National Academies of Science study recommended that high priority be given to a robot mission to investigate the Venusian surface helping to answer such questions as why Venus ended up so different from Earth and if the changes have taken place relatively recently."
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Antique Fridge Could Keep Venus Rover Cool

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  • No problem. (Score:5, Funny)

    by dozer (30790) on Monday November 12, 2007 @07:19PM (#21329777)
    I've got an easier solution. Don't make the robot out of lead.
    • What will you solder the electronics with? Or what will you make them from for that matter?
      • Dude, no one uses lead for soldering any more.* Get with the times. [wikipedia.org]

        * Except, ironically, NASA and the like, due to the tin whisker panic.**

        ** All the evidence I've seen is that tin whiskers are 99% a non-issue panic. The Wikipedia entry is definitely not NPOV with its inflammatory list of "nuclear power plant, satellites in orbit, aircraft in flight, and implanted medical pacemakers" for places that failures have been seen due to the phenomenon.
        • Re: (Score:3, Funny)

          by s20451 (410424)
          All the evidence I've seen is that tin whiskers are 99% a non-issue panic.

          Given that there are at least 100 nuclear reactors in the world, I'm not exactly reassured.
        • Re: (Score:3, Insightful)

          by mangu (126918)
          The Wikipedia entry is definitely not NPOV with its inflammatory list of "nuclear power plant, satellites in orbit, aircraft in flight, and implanted medical pacemakers" for places that failures have been seen due to the phenomenon


          Would you consider it more NPOV if they stated that aunt Hilda's radio also failed because of tin whiskers? I don't think it's necessary to add irrelevant cases just to make it "neutral".

          • Re: (Score:3, Insightful)

            by SydShamino (547793)
            Would you consider it more NPOV if they stated that aunt Hilda's radio also failed because of tin whiskers? I don't think it's necessary to add irrelevant cases just to make it "neutral".

            No, I don't think additional minor issues should be added. I think the examples included should be backed up by citation or removed. In this case, only the nuclear power plant has a citation, so the second sentence should be deleted entirely.
            • The trouble is afaict only failures in places like nuke plants tend to get analised rigorously enough to diagnose this sort of thing.

              There are so many possible causes of failure in electronics and there is so little reporting of how long equipment lasts and how it fails that drawing meaningfull conclusions on whether this is having a significant effect on the lifetime of consumer electronics is difficult to measure.

        • by cmowire (254489)
          Well, do you tear down your failed electronics to see why it failed? I don't, I just junk the sucker.

          Could be tons and tons of tin whisker failures. Well, might be in the future, now that all of the lead-based electronics are gone.
      • Lead solder substitutes might not be cheap (I honestly have no idea if they are or not) but I'll be damned if launching a rover to any planet is supposed to be cheap.
        • I wasn't referring to the price, I was trying to say that making a robot out of components that won't melt is not possible as AFAIK semiconductors fail much below 450C, and so will any sort of solder I heard of.
  • i've always said (Score:5, Interesting)

    by circletimessquare (444983) <circletimessquare AT gmail DOT com> on Monday November 12, 2007 @07:26PM (#21329837) Homepage Journal
    venus is a better terraforming candidate than mars. oh sure, if you want to get somewhere as quickly as possible that is vaguely hospitable to settlement, mars beats venus hands down

    but if you want to talk about recreating earthlike conditions (water, temperature, gravity, atmospheric density), i think it would easier (easier, not easy) to precipitate out venus' atmosphere than to bulk up mars'. and if you stood on venus right now, you would weigh roughly the same. big bonus right there

    where is all the water going to come from? how the heck do you thin out the venusian atmosphere to earth-like densities? i don't know. but however you do it, it's an easier starting scenario than mars

    • Re: (Score:2, Informative)

      by calebt3 (1098475)
      Isn't Venus outside Sol's habitable zone? (the region around a star where liquid water is possible)
    • Re:i've always said (Score:4, Informative)

      by evanbd (210358) on Monday November 12, 2007 @07:46PM (#21330033)

      Well, in terraforming terms, finding stuff to make up the Martian atmosphere probably isn't that hard. There are significant CO2 ice caps, and there may be significant water available with modest effort. CO2 plus plants gives you O2. Also, there is some good evidence to suggest that the icecaps' existence is bistable -- that is, if you could mostly evaporate them, the additional greenhouse effect would warm the planet enough to finish the job and keep it that way.

      Basically, the problem of terraforming is to find resources that are already available in almost the form you want, and find some way to leverage your input effort. You don't want to have to process every single megaton of atmosphere you want to add / remove. It's far easier to (for example) dust carbon black on the poles and add a few orbiting mirrors.

      Of course, the only reference I have handy is Zubrin's The Case for Mars which is a bit dated but (I think) still basically correct. The details may well have changed thanks to newer lander data.

      • Re:i've always said (Score:5, Interesting)

        by schnikies79 (788746) on Monday November 12, 2007 @08:07PM (#21330199)
        Isn't the problem with mars a lack of a magnetic field which allows the solar wind to strip away the atmosphere? I don't see how we could jump-start a magnetic field, so whats the point of even trying to rebuild the atmosphere if it's all going to blow away?

        How about the lack of gravity? Can you build atmospheric pressure comparable to earth with lower gravity?

        I saw Zurbin give a talk at my Univ a couple years ago and was going to ask him about it, but I forgot.
        • by Tim C (15259)

          Can you build atmospheric pressure comparable to earth with lower gravity?
          Probably. I wouldn't bet too much on necessarily being able to breathe the atmosphere though.
        • Re: (Score:3, Informative)

          by QuantumG (50515)
          Yes, but it takes thousands of years for the solar wind to blow away the atmosphere. If we one day have the ability to make the atmosphere of Mars suitable for human habitation then surely we will also have the ability to maintain the atmosphere over such a long time period.

        • We should move that atmosphere from Venus to Mars.
        • Isn't the problem with mars a lack of a magnetic field which allows the solar wind to strip away the atmosphere? I don't see how we could jump-start a magnetic field, so whats the point of even trying to rebuild the atmosphere if it's all going to blow away?

          it takes several million years for a sizable atmosphere to be sufficiently eroded without a magnetic field. We don't need to jump start the entire magnetic field on the planet, just create an artificial one- like say a *ton* of orbiting satillites usin

      • it is easier to destroy than it is to create

        so with atmospheric density, it is easier to start some sort of process that would precipiate mass out of venus's atmosphere than it would be to bulk up mars somehow (and can mars' gravity hold the density?)

        as for oxygen, i forgot about that (duh! ;-)

        but getting oxygen (and water) in sufficient quantities is equally hard and daunting for mars or venus. venus has hydrogen and oxygen locked up just as much as mars does, and will require some chemical/ atomic manipul
        • I wonder how much Venus would cool if we simply dropped a couple hundred nukes on the surface. It would surely cool it by a few degrees, although I doubt it would cool it to anywhere close to comfortable temperatures.
          • by Rakishi (759894)
            Well one idea for quickly thermoforming venus is to drop comets on it, broken up before impact to impact all their energy into the atmosphere. The idea being that the simplest method to get rid of the atmosphere is to simply blow it into space. Sadly it seems that the energy required would be quite a lot, as in you'd need to hit the planet with a lot of comets or whatever other space junk you find.
          • > I wonder how much Venus would cool if we simply dropped a couple hundred nukes on the
            > surface. It would surely cool it by a few degrees...

            More likely a few hundredths of a degree, but why do you think that would cool it at all?
            • by joggle (594025)
              For the same reason it would cool earth's atmosphere, by blocking more sunlight (ie, global dimming). If enough dirt is kicked up high into the atmosphere it may block more light than the clouds by themselves, thus reflecting some of the sun's energy before getting trapped by greenhouse gas.
        • by CorSci81 (1007499)
          Actually, Mars has lost a significant amount of hydrogen (as has Venus, but not as severely) and most of the surface rocks are highly oxidized. Really, you'd need to add back some hydrogen to make Mars really work. And as far as the radiation goes, Earth's atmosphere (and also Venus's) do a LOT to stop radiation. Sure it doesn't get all of it, but astronauts on the space station are getting a much higher radiation dose than you and I down at ground level.
      • Re: (Score:3, Interesting)

        by inviolet (797804)

        Well, in terraforming terms, finding stuff to make up the Martian atmosphere probably isn't that hard. There are significant CO2 ice caps, and there may be significant water available with modest effort. CO2 plus plants gives you O2. Also, there is some good evidence to suggest that the icecaps' existence is bistable -- that is, if you could mostly evaporate them, the additional greenhouse effect would warm the planet enough to finish the job and keep it that way.

        Eh... better to leave Mars alone. It will

    • Re: (Score:3, Funny)

      by jimbojw (1010949)

      but however you do it, it's an easier starting scenario than mars
      That's ridiculous - everyone knows that as soon as Quaid activates the turbidium reactor, Mars' atmosphere will fill out nicely.
    • Re:i've always said (Score:5, Interesting)

      by Average_Joe_Sixpack (534373) on Monday November 12, 2007 @08:03PM (#21330167)
      i don't know. but however you do it, it's an easier starting scenario than mars

      Probably not due to the 243 day rotation.
      • by Daimanta (1140543)
        But it has GREAT all night parties!
      • and you get wicked weather at the night/ day interface, a blistering midday, and a chilling midnight. but it won't be as wicked a change as on mercury, because the atmosphere will conduct some heat (little, yes, but some is better than none)

        and even with day length considered, venus is still ahead of mars, considering all the other variables, mars comes out a worse prospect still

        but you are correct to point out that day length is a big impediment, i forgot to address that
        • Worse than blistering mid-day... a boiling midday. Though the silver lining is that the 240 day rotational period is the sidereal day. The solar day is closer to 120 days.

          The truth is that neither Mars nor Venus are good candidates for "terraforming," but Mars is far more viable for settlement.
      • by Tumbleweed (3706) *
        Probably not due to the 243 day rotation.

        And the vampires thought Barrow, Alaska was a great place to vacation...
    • venus is a better terraforming candidate than mars. oh sure, if you want to get somewhere as quickly as possible that is vaguely hospitable to settlement, mars beats venus hands down

      but if you want to talk about recreating earthlike conditions (water, temperature, gravity, atmospheric density), i think it would easier (easier, not easy) to precipitate out venus' atmosphere than to bulk up mars'.

      In some magical universe where you can safely sequester the billions of tons of carbon that will have to

      • Re: (Score:3, Interesting)

        by CorSci81 (1007499)
        Well, Earth has managed to safely sequester billions of tons of carbon. We have just as much of it as Venus, ours just happens to be locked up in nifty things like carbonate rocks. Venus could have carbonate rocks too if we could just get it a little cooler and get some water back on the surface to help with erosion. Just at present the reaction goes the wrong way and you have CaCO3 + SiO2 -> CaSiO3 + CO2, so there aren't a lot of carbonate rocks laying about. In terms of atmospheric composition if y
        • All very true - and all having nothing to do with what I wrote. Removing the CO2 from Venus's atmosphere is a Hard Problem.
          • by CorSci81 (1007499)

            No, really, I was answering you. If you take what I wrote earlier and extrapolate you can see one possible (albeit slow) solution. And no one said terraforming was going to be easy or practical, it's just not technically impossible.

            If you can manage to cool Venus's atmosphere sufficiently (with say a giant sunshade in orbit at the Lagrange point, but you can use your imagination) for carbonate rocks to form the chemistry does the work for you. Venus has a nearly identical chemical makeup to the Earth, s

    • Re: (Score:3, Informative)

      by Loke the Dog (1054294)
      They both lack magnetic fields which makes long term terraforming pointless which means we can just drop the whole idea.
      • there are many ways to block radiation

        but obviously, you are correct to point out this is a major impediment. but beggars can't be choosers. i don't see any other small rocky orbs close by to consider. mercury is way worse, and the gas giants are, well, gas giants, and their moons are too cold
      • by Tumbleweed (3706) *
        The technology required to terraform another planet will probably come along about the same time as making our own planetary-scale magnetic fields. I'll worry about it if we actually get to the point of being able to terraform and *can't* make a huge magnetic field. We should probably speed up the rotation of Venus while we're at it.

        And by that time, I expect we'll be able to download our consciousnesses into artificial bodies, so we could probably live in just about any physical environment, anyway.

        Still,
    • if you want to talk about recreating earthlike conditions (water, temperature, gravity, atmospheric density)

      Unfortunately, the rotation of Venus is ridiculously slow, that would create a problem, not only for human work cycles but, much worse, for managing temperature.

      Suppose they create some kind of shield between Venus and the sun, for instance with a swarm of thin foil satellites. The surface temperature would fall down to bearable levels, perhaps to the point of solidifying the CO2, which would make th

      • by mbone (558574)
        The length of day isn't really a problem.

        Venus had a habitable climate for billions of years. If you get the CO2 out of the air and back into the rocks, like on Earth, it could again, long length of
        day or not. BTW, there are lots of people who live in arctic areas with roughly similar day / night distributions.

        However, if you really needed to, you could hit the planet with a carefully aimed ice rich asteroid or (better yet) a comet. This would both add water and change the spin, in principle to whatever yo
        • by Smidge204 (605297)
          Length of day IS a problem. more specifically, the length of NIGHT that goes along with it. During the "day" you would have the hot sun beating down constantly, and during the "night" you have the icy cold blackness of space into which all your heat radiates into.

          Temperature swings would be a bitch.

          Right now, the planet has a nice thick blanket of CO2 and dust to keep the warmth in and solar radiation out, so the temperature swings aren't that bad. We would need to strip that blanket off if we ever want to
    • The real truth is all the other inner planets suck as terraforming cannidates. Mars is realitively benign compared to Venus. Its the high content of sulfuric acid that would hamper terraforming. Shifting the orbit to Earth orbit might help with the greenhousing and it might be possible to blast away part of the atmosphere but removing large amounts of sulfuric acid is going to be trickier. The concentrations are high enough to erode mountains on Venus. Mars may lack a dense atmosphere and has low gravity bu
      • > The real truth is all the other inner planets suck as terraforming cannidates.

        Earth seems like a fairly promising candidate. Just get rid of the humans...

        > ...rings like in Ringworld are superior since spinning them can reproduce the effects of
        > gravity. Make one the diameter of the Earth and add a wall the height of our atmosphere
        > and spin it and you effectively have a planet.

        Bit of a materials problem there.
    • You can't just precipiate it out... I remember reading in (I think) some Carl Sagan book long ago, that if we did so, they'd end up with a layer of charcoal a few feet deep, plus around a hundred atmospheres of pure oxygen. Someone lights a match, and you're back to square one.

      His best analysis was that we'd have to blow the atmosphere off by hitting the planet with asteroids. Not exactly as easy feat.
      • by Cadallin (863437)
        Ga Zuh? "His best analysis was that we'd have to blow the atmosphere off by hitting the planet with asteroids. Not exactly as easy feat."

        How exactly is that NOT easy? At least in any context where you're seriously discussing terraforming planets, striking the targets with planetoids is as easy as it gets. All you have to do is go out and identify likely sized asteroids (we're well on our way to doing that, with various catalogs of solar system objects), and then move them in to place using well place

      • and this is why: considering terraforming venus, mars, or any planet, you are already in a realm of technological futurism that is impossible. so, when you say it is impossible to keep an oxygen rich atmosphere off of willing chemical kindling, well, who is to say there wouldn't be some sort of technology by then that could dampen that effect

        i mean, in a way, you and sagan are describing the earth: lots of oxygen, lots of kindling. as san diego proved a few weeks ago, that's a problem. and yet the earth mai
    • by geobeck (924637)

      venus is a better terraforming candidate than mars.

      True. In fact, we're doing our best to reverse-terraform Earth to be more like Venus every day.

      • we ARE turning our planet into venus

        so, perversely and sadly, if we are going to survive to the point where terraforming venus ever becomes possible, to get to that point, we will have had to master the technology to cool down a hot planet already

        yet another reason venus is a better candidate: a historically inevitable future technological convergence point. we will come to master the technology to cool down a hot planet no matter what, or we won't be around at all
    • The problem with Venus's atmosphere is that there is so damned much of it. In order to get rid of Venus's atmosphere, you need get rid of the mass of something the size of asteroid Vesta. Basically, you need either calcium or something the size of the asteroid Vesta, and gently put it on Venus, and that will precipate the carbon out as calcium carbonate. Or, you could try and find a Vesta sized chunk of hydrogen, and via some chemical wizardry, that will get rid of the carbon dioxide as well and leave wa
      • by lachlan76 (770870)
        If you just dropped a whole lot of calcium on there, you'd end up with calcium sulphate, rather than calcium carbonate, because of the sulphuric acid. So you would probably need even more.
      • Or, you could try and find a Vesta sized chunk of hydrogen, and via some chemical wizardry, that will get rid of the carbon dioxide as well and leave water.

        This, at least, can be had. Saturn would probably be the best place to get it, although lifting it all out of that gravity well would be energetically expensive. You'd probably need fusion power to do it - fuel the reactors from a small amount of the atmospheric hydrogen, and start pumping the rest of it into space.

    • But what about the slow rotation? It takes what, 243 Earth days for Venus to complete one local day? It'd be rather difficult to maintain Earth-like conditions like that.
    • by Iron Sun (227218)
      One big advantage Mars has over Venus in terms of terraforming potential is that Mars' day length is really close to that of the Earth (43 minutes longer, I think). Venus, on the other hand, has a day longer than its year. You would either have to spin up the planet somehow (good luck with that) or else have a series of mirrors and shades at the Venus-Sun Lagrangian points to allow the simulation of a proper day/night cycle. This might lead to the interesting situation where the entire planet shares the sam
  • Isn't it obvious. Venus is Global Warming run amuck. And we're next!
  • Stirling coolers (Score:5, Informative)

    by EaglemanBSA (950534) on Monday November 12, 2007 @07:29PM (#21329881)
    While stirling engines are certainly old, the idea of using them as refrigerators is just recently catching on. Here in sleep Athens, OH a company called Global Cooling is the forefront producer of such devices (and is still hand-making a good number of them).

    The nice little advantage to these coolers is that they operate with very high COP's, and are limited in lower temperature merely by available power and the boiling point of the working gas. In global cooling's case, Helium is typically used, so temperatures down to around 5K are obtainable (at which point the helium liquifies. Yeah. Cold.) Also, control of the device can be very precise, in that instead of a compressor kicking on and off, it operates constantly, quietly, and with good variable control.

    LG is beginning to outfit refrigerators with Stirling pumps because they're so much better than current designs - only problem is they're not mass produced yet. Coleman has a portable unit shown here [coleman.com] that is quite a nice unit, albeit very pricey.

    One of my professors here at school is one of the pioneers of Stirling refrigeration, so I've been exposed to it a lot. If the whole country switched their refrigerators to stirling compressors, California could shut off its power grid and we'd still have a surplus of energy country-wide.
    • Re: (Score:3, Informative)

      in sleep Athens, OH a company called Global Cooling is the forefront producer of such devices (and is still hand-making a good number of them).

      ... and, in fact, Global Cooling licensed their free-piston Stirling engine technology from Sunpower (also of Athens, Ohio), and Sunpower works with NASA Glenn on the Stirling engine development. So they really are the cousins of the Venus engines.

    • If Stirling Coolers are so efficient, why are we not using them to cool our homes & office buildings?
  • by Biff Stu (654099)
    Now that everybody has made the shift to ROHS electronics, who cares if the heat melts lead? They should be able to do it with all COTS parts.
    • by ThePeices (635180)
      it matters because the melting point of lead free solder is well below 400deg C!
  • 1970's refrigerator? (Score:3, Interesting)

    by downix (84795) on Monday November 12, 2007 @07:34PM (#21329941) Homepage
    Sterling's are older than the 70's. I've been tinkering on using a sterling for cooling off an engine block for a few years now (pretty good results too, allowing me to generate electricity from the previously wasted heat).
  • by AnonymousCactus (810364) on Monday November 12, 2007 @07:42PM (#21330003)
    Yeah, an engine, sure: http://en.wikipedia.org/wiki/Image:BetaStirlingTG4web.jpg [wikipedia.org]
  • by kaoshin (110328) on Monday November 12, 2007 @07:48PM (#21330045)
    Yes, but can this device provide adequate cooling for a pair of NVIDIA 8800's in a brutal "room temperature" environment?
  • I would rather put a Stirling-cooled robot rover on Venus than pairs of human feet in the dust of the Moon.

    Robotic exploration of our solar system is critically important and will achieve much more than a pair of glass-encased Lunar baby blues.
  • by MichaelCrawford (610140) on Monday November 12, 2007 @08:47PM (#21330501) Homepage Journal
    Back in his day, refrigerators used gaseous ammonia as the refrigerant, which is highly toxic. He was appalled to hear of a whole family being killed by a leaky refrigerator, so he and Leo Szilard invented one [wikipedia.org] that had no moving parts, and thus without the risk of leaky seals.

    Leo Szilard was later instrumental in launching the US' Manhattan Project to build the atomic bomb. It was his idea, but he got Einstein to write the letter to President Roosevelt that convinced him to fund the project.

  • But there's still hope for this planet!
  • designed a refrigeration system that might be able to keep a robotic rover going for as long as 50 Earth days

    Unfortunately, the refrigeration system only lasts 10 days. So the refrigeration system will have a refrigeration system which will make it last for 50 days. Unfortunately, that refrigeration system will only last 10 days. So NASA will construct a refrigeration system refrigeration system refrigeration system, which will make the refrigeration system refrigeration system last 50 days. Unfortunately, THAT refrigeration system will only last 10 days...

  • Welcome! (Score:3, Funny)

    by Tablizer (95088) on Monday November 12, 2007 @10:33PM (#21331407) Homepage Journal
    We at Venus welcome your cool beer-carrying roverlords. We're damned thirsty over here.
  • Why do you need nuclear power onboard when there is all that HEAT around you? Is there no way to convert that to usable energy?
    • by yeremein (678037)
      No. You need a temperature gradient to convert heat into energy.

    • by Boronx (228853)
      Not by itelsef, but if you could create some sort of reservoir of coolness, perhaps with a refrigerator or heat pump, you could run a sterling engine with the temperature difference.
      • Not by itelsef, but if you could create some sort of reservoir of coolness, perhaps with a refrigerator or heat pump, you could run a sterling engine with the temperature difference.

        Seems kind of pointless... energy source X powers a heat pump to maintain a cool region, against which you run a Stirling engine to produce energy output Y. I bet you anything you like that Y X.

  • TFA:

    The researchers say the power to run the Stirling cooler, about 240 watts, would be provided by on-board plutonium batteries, which generate power from the heat of radioactive decay.

    Excuse me while I go slam my head against a wall...
    • by fuzz6y (240555)

      The researchers say the power to run the Stirling cooler, about 240 watts, would be provided by on-board plutonium batteries, which generate power from the heat of radioactive decay.
      Excuse me while I go slam my head against a wall...

      Slam it against a physics textbook instead. Perhaps the second law of thermodynamics will be driven into your brain.

  • Few people on this forum take the time to carefully consider the story of our investigations to date of Venus' exceptionally high temperatures. It is a very interesting story that has incredible ramifications for science to this day. The various probes sent there did not say what NASA wanted to hear, so it was decided that the *assumption* of global energy balance would take priority over the sensor data. And this is how the theory of CO2-based global warming survived one of its first scientific challeng
    • Pseudoscience (Score:4, Insightful)

      by MaDeR (826021) on Tuesday November 13, 2007 @04:18AM (#21333637)
      Funny that many people mistake mythology with factual history... you also think that x-files are documentary, aren't you?

      Your comment is classical pseudoscience tactic: find some problem with actual theories and claim "so my completely ludicrous idiotic shambling on acid must be right!!!!oneone".

      And for rest of universe, I would like to present Velikovsky in all ot his (in)famous glory...

      http://en.wikipedia.org/wiki/Immanuel_Velikovsky [wikipedia.org]

      http://skepdic.com/velikov.html [skepdic.com]

      "report the arrival of Venus into our solar system as a comet-like body within the past 10,000 years"

      No. Venus was to be expelled from Jupiter. And remind me, what comets have anything in common with Venus? Mass? Temperature? Looks? Materials? Orbital parameters?

    • (a) A satellite on the dark side of Venus beamed a light towards Venus and measured how much of that light returned, or (b) A satellite on the light side of Venus simply turned the instrument towards the Sun and then towards Venus, and computed a ratio of the light intensities.

      Or (c): the apparent brightness of the Sun is measured from Earth, the apparent brightness of Venus is measured from Earth, and a simple inverse square law calculation is done.

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