Neptune is *really* far away

By Phil Plait | September 19, 2011 10:30 am

Mike Brown is an astronomer, specifically one who studies Kuiper Belt Objects, those giant frozen iceballs that haunt the solar system out past Neptune.

In fact, Neptune’s biggest moon Triton has a lot of characteristics similar KBOs — it may be one captured by Neptune — so observing it gives an interesting opportunity for a compare-and-contrast study. So this past weekend Mike was using the Keck telescope in Hawaii to observe Triton along with its (adoptive?) parent planet, and took this fantastic image of the pair:

[Click to poseidenate.]

This false-color image shows the two worlds in the infrared, specifically at a wavelength of about 1.5 microns, twice what the human eye can see. Methane strongly absorbs this color of light, so where Neptune (in the upper left) looks dark you’re seeing lots of methane clouds, and where it’s bright there are clouds higher up, above the methane. Triton is in the lower right, and is bright because it’s covered in ice which is highly reflective.

Now this is all very pretty and interesting and sciencey, but if you know me at all you know there’s more to this story.

Mike tweeted about the image, and I oohed and ahhhed at it, of course. But then he tweeted again, saying he was also observing Jupiter’s moon Europa, but it was too bright to get good images using the monster 10-meter Keck telescope. It "saturated the detector" which is astronomer-speak for "overexposed".

That’s funny, I thought. Neptune looks fine in the image, and the random noisy grain in it makes it clear Mike wasn’t anywhere near saturating the image. Now I know Europa is closer to the Earth, so it should look brighter, but geez, it’s a moon, and a lot smaller than Neptune. How could it be too bright to image?

It turns out my all–too–human and all–too–miserable sense of scale has failed me again. Math to the rescue!


Reflections on reflection

The brightness of an object we see in the solar system depends on a lot of factors, but mostly on three: how big it is, how reflective it is, and how far it is from us and the Sun. The first is obvious: a bigger object should look brighter, since it reflects more light. The same goes for the second; something made of ice is shinier and more reflective than something made of soot, so two objects the same size but with different reflectivities (what astronomers call albedo) will not be the same brightness.

The last bit is little tricky though. Sure, something farther away should look dimmer. A car headlight up close is brighter than one farther away. Normally, that means an object’s brightness drops as the square of the distance — move it twice as far away and it appears 1/4th as bright, move it 10 times farther away and its brightness drops by 100x.

But planets and moons are reflecting sunlight, and the farther they are from the Sun, the dimmer it looks too, and the less light they catch. So not only do they drop in brightness as the square of their distance from us, but also by the square of their distance from the Sun. That drops their light terribly rapidly for remote objects in the solar system.

So let’s put this all together.


Math hysteria

Neptune is 50,000 kilometers across, and Europa is 3100. Since the amount of light they reflect depends on their area, and area goes as diameter squared, Europa reflects (3100 / 50,000)2 = 0.004 times as much light as Neptune.

But, in visible light at least, Neptune reflects 29% of the light it receives, while icy Europa reflects 67%. That ratio is 2.3, meaning Europa is more than twice as reflective as Neptune.

What about distance? Right now, Neptune is about 4.5 billion kilometers from the Sun, and 4.35 billion from the Earth. Europa is 800 million km from the Sun and 650 million from the Earth. That means Europa receives (4.5 billion / 800 million)2 = 32 times more light from the Sun than Neptune does. It’s also closer to us, so distance alone gives Europa a leg up to the tune of (4.35 billion / 650 million)2 = 45 times.

Now we can put these together to see how much brighter Europa really should be from Earth.

( Europa’s brightness / Neptune’s brightness ) = 0.004 x 2.3 x 32 x 45 = 13.

So Europa should appear about 13 times as bright as Neptune to us on Earth. As it happens, Neptune is at about magnitude 8 right now (magnitudes are how astronomers measure brightness, and a star 1 magnitude brighter than another is actually about 2.5 times as bright), and Europa at about 5.2. That’s a factor of 13, so my math worked out just right!

One point: I used the albedo in visible light, but the two objects may have very different reflectivities in the infrared. In fact, I mentioned Neptune has lots of IR-absorbing methane in it, so in reality its albedo in the IR is probably much lower. So it appears even fainter, lending yet more credence to the idea that while Neptune was faint enough to be seen easily using the Keck telescope, Europa might blast it out.


Are we there yet?

Which (finally!) brings me to my main point. Europa is dinky. I mean, it’s about the size of our moon, so it’s a fair-sized world and all, but compared to Neptune it’s pretty small. But because it’s close, it’s a whole lot easier to see.

When I think of the outer solar system, I tend to lump all the planets in my head. Jupiter (Europa’s home planet), Saturn, Uranus, Neptune… sure, they’re far away, but I think of them all just as being "far". But Neptune is nearly seven times farther away from us than Europa!

That’s a seriously long way off. The spacecraft Juno will take five years to get to Jupiter, so even that planet’s a fair distance. Of course, Juno will orbit Jupiter, so it needs to match speeds with the planet so it can be captured. That lengthens the time of its journey. But even the New Horizons probe, which is screaming through the outer solar system at high speed, will take nearly nine years to cross Neptune’s orbit.

Geez.

So there you go. A tweet, some math, and boom! The solar system suddenly swells seven sizes inside my head.

And I’ll end by noting that with a decent pair of binoculars you can see Jupiter’s moon Europa shortly after sunset, when the planet rises in the east. Neptune is up as well, and again with good binocs or a small telescope (and a good star chart, try Google) you can spot it pretty handily. The last planet wasn’t discovered until 1846, but now we know where it is… and we can point big telescopes at it, like Mike Brown does, and learn about objects even farther away.


Related posts:

New Horizons is a long way away
Home, from the start of a long, lng journey
Happy birthday, Neptune!
Jupiter rolls into view

CATEGORIZED UNDER: Astronomy, Cool stuff, Pretty pictures

Comments (56)

  1. Nicias

    I think you may have missed a factor there. Since Keck resolves both objects as extended sources, you actually care about brightness per angular area. If you just care about angular surface brightness, that adds another factor for their relative sizes in the sky. That factor is their absolute areas (which you already had, but in the other direction) and their relative distances squared. (which you already had, also in the other direction.) This means we should just get: 2.3 x 32 = 74.

  2. Mark M

    Phill,
    I think my head is about to explode.

    Thank you :)

  3. Messier Tidy Upper

    Ah, Crimson Neptune which “Pluto-killer” caught red-handed! Reminds me of :

    “Will all great Neptune’s Oceans wash this blood from my hand? No, rather this my hand would the multitudinous seas incarnadine making the green one, red!”

    – MacBeth, Thane of Cawdor, after the murder of his King Duncan of Scotland.

    To quote, possibly mis-quote (?), from memory my very favourite line of all Shakespeare’s plays.

    Turning all of planet Neptune red – yep, that’s be a lot of blood alright! ;-)

    (“Who would’ve thought the old man had so much blood in him! Out! Out! Dammned spot!”)*

    Or, of course, a different infra-red perspective & camera. ;-)

    Spectacular image there of a marvellous ice giant world and its strange largest moon. Thanks BA & Mike Brown. :-)

    ————–

    * Lady Macbeth, the sleep-walking murderous queen who gave us all “the milk of Human kindness” in her speech demanding Hecate remove that stuff from her. Yes I’m a big Shakespeare fan even if I can’t read the original Klingon!

  4. AJKamper

    Gotta say, considering Europa was discovered in, what, 1512 by the first person we know of to point a telescope at the skies, and it took another 330 years to discover Neptune, I’m not incredibly surprised by the idea that Europa is so much brighter..

  5. @ ^ AJKamper :

    Curiously enough, Galileo Galilei saw Europa along with the other three Galilean moons together with Neptune although he probably mistook our solar systems other blue planet for a star. Recent studies suggest Galileo may have actually suspected Neptune’s planetary status but not confirmed or published it. (Click on my name for source or see space-dot-com article “New Theory: Galileo Discovered Neptune” by Robert Roy Britt published online on the 9th July 2009, Time: 10:40 AM ET.)

    Neptune, like Ouranos (or as it is less well known, 34 Tauri in the Flamstead naming system), was also actually seen – and charted – but mistaken for a star several times before it was discovered as a “new” planet by a number of astronomers.

  6. Calli Arcale

    AJKamper — it gets a little more interesting if you consider that Galileo actually *did* see Neptune, with the same sort of equipment he was using to view Europa. He just didn’t realize what he saw at the time — he recorded the observation (which is how later astronomers were able to work backwards and figure out what he’d seen) but was never able to confirm it because poor weather confounded further observations until Neptune had moved sufficiently that he was unable to recover it.

  7. Tophe

    What about their differences in emission (blackbody radiation)? Europa is about 110 K and Neptune’s atmosphere is only about 55 K.

  8. Jeff

    good illustration of the inverse square law of light, I’ll have to show that example to the students. These inverse square things drop off really rapidly, only exceeded by dipole fields that drop off even faster, inverse cube.

  9. I think Nicias makes a very good point here: the brightness ratio as seen through your binoculars, when they’re unresolved sources, is a very different thing than their likelihood of saturating the Keck detectors, where it’s the flux per pixel that matters, and the objects are resolved. But is Europa resolved by Keck? It’s only about half an arcsecond across according to my rough calculation. That might be near the atmospheric limit. Neptune is more like 2 or 3 arcsec so it’s certainly resolved.

    I’m getting a little confused by these numbers, though, since if Neptune’s angular size is ~5 times more then shouldn’t that be a factor of ~25 for the binoculars answer, so it should be more like 74/25 = 3 instead of the 13 you computed?

  10. Europa is about 1.3 arc second in diameter, not 0.5 arc seconds – and is resolvable into a disk with telescopes as small as 25cm diameter, although it does take a larger telescope to resolve any detail on Europa, but that’s mainly because it does not have a lot of contrasty features.

    Io is only about 20% larger in diameter and it shows surface detail in telescopes as small as 20cm diameter.

    So there’s no question that Europa would be easily resolved in a telescope like Keck, it’s only about a factor 2 smaller in angular diameter than Neptune, and since the image above shows much, much finer detail there’s really no doubt.

  11. tjm220

    … and we can point big telescopes at it, like Mike Briwn does, and learn about objects even farther away.

    Who is Mike Briwn again?

  12. Tbird49er

    Wow, never thought of some of those points.

  13. Chew

    This website shows the Solar System drawn to scale: http://www.phrenopolis.com/perspective/solarsystem/

    Scroll right.

  14. Simon C.

    Since these images are in the infrared, I believe calculating the effective brightness of Neptune is a little more complicated than that. You already mentioned that methane absorbs a LOT of light in its atmosphere, but there is also some infrared >emitted< by Neptune itself. Since Neptune is quite massive, there has to be some internal heating that adds to its brightness in these wavelengths. Since Europa and Triton are much less massive, their internal heating is clearly negligible compared to the light they reflect.

    I specialize in sub-millimeter astronomy (star formation in molecular clouds) and not infrared planetary astronomy, so I don't really know if that additional effect is important or not. Only math can tell us! Anyway, that would be an interesting problem to solve (if I had some time)!

  15. DennyMo

    BA just gave me another entry for my list of “words least likely to mean what they look like they should mean”: albedo. I read “albedo”, but “albino” and “libido” keep jostling it for position.

    For those of you not keeping track (and why would you?), last week’s entry was “prurient”…

    Between posts like this one and my ongoing reading of “Death From The Skies”, I’m learning that not only is there a lot of astromony stuff I don’t know, I hadn’t really scratched the surface of stuff I thought I knew.

  16. pumpkinpie

    Europa is magnitude 5.2–isn’t that within naked eye limit? I have never heard of Europa being visible without optical aid. Is that because it’s so close to Jupiter that it gets washed out?

  17. Dragonchild

    @4. AJKamper –
    To follow up on Messier Tidy Upper (more to clarify for lurkers), brightness is probably only part of the story. Lots of stars were discovered with the invention of telescopes, and Neptune would look like any blue star — a point of light. But Mercury also looks like a dot and was considered a planet all along. The other parts? Apparent path and apparent magnitude. The idea of a planet as “wandering star” predates the discovery that they’re part of our solar system; among early astronomers, it was Mercury’s motion across the sky that set it apart from the stars. Neptune is so far away that it moves very slowly and isn’t visible to the naked eye. They didn’t have blink comparators back in Galileo’s day. So you’d look one night and discover (and chart) a faint blue star; look at the same spot a month later and it’d be gone. (Galileo actually didn’t lose it, but rather unluckily caught it just as it was going retrograde.) Apparently it was charted and lost several times until its theoretical orbit was calculated based on its influence on Uranus. I’d imagine some charts needed a Tidy Upper after they’d sorted out the Messier.

  18. Pete Jackson

    What is that tiny object about 3/4 of the way out to Triton on the poseidenated version? Not likely Nereid since it orbits much further out, unless we see it by chance passing in front or behind Neptune. Too far out to be Proteus, so it’s most likely a background star.

  19. Jon Hanford

    Keck should have no problem seeing detail on Europa (d=3138km). Keck IR imagery of Io (d=3642km) using adaptive-optics looks great: http://scienceblogs.com/SETI/Im_forBlog-lg.jpg

  20. Simon Green

    @Pete: Cosmic ray strike?

  21. Bulwersator

    I found this great video: http://www.youtube.com/watch?v=GJIs8h-Si6o&feature=watch_response . Unfortunately there multiple things modified to make Universe cool in Hollywod style (density of asteroid field from Star Wars etc). Is it possible for somebody here to find somewhere similar simulation, based on real data? Or static map on scale of 5000 ly?

  22. Screamin Chicken

    Area is function of radius squared, not diameter squared! But since you’re taking the ratio your mistake doesn’t matter…

  23. Chris

    and area goes as diameter squared,
    Area = pi*radius^2
    Phil!!!

    @13 pumpkin pie
    Yes Europa is technically visible unaided but Jupiter is way to bright. It is possible if you get behind a flagpole and stand far enough away to block out Jupiter you may be able to see it. I’ve never tried it because where I live you can’t see dimmer than mag 4. Another fun thing it to take your digital camera, assuming it has night sky setting, zoom in on Jupiter (If you have >10x the better), let it integrate for a minute and you’ll see jupiter and the satellites.

  24. TStein

    What I want to know is how does someone get Keck time when they did not bother to calculate ahead of time whether or not it would saturate the image? I have a hard time believing that the average albedo of Europa in the near infrared isn’t well known. I don’t mean to insult BA’s friend; I am sure there is a reasonable explanation. It just seems weird to me.

  25. Screamin Chicken (25), Chris (26): So you’re saying area does not scale as diameter squared? Are you sure you want to argue that?

    To make it more clear: if I double the diameter of a circle, what happens to the area?

  26. George

    Nice Phil,

    This is a nice example of the inverse 4th power (inverse square squared) that applies to all illuminated bodies.

    Here is another surprising result along this same line: Jupiter, if moved to about 10,000 AU, IIRC, would disapear from the HST since it would become < 31 in mag. Considering some exoplanets have actually been observed directly, it is a surprising fact.

    [Of course, IR scopes can see Jupiter at this distance and considerably further.]

  27. Resolution like this withstanding, I contend that Neptune and Uranus look better in a pair of 10x50s… wider field of view means that one can see where they have been. ;)

  28. Kappy

    @Pete Jackson I’d actually guess that it’s a hot pixel. If you look at some of the images Mike Brown posted today of Uranus, he mentions hot pixels in a few instances (basically pixels on the imager that were over exposed so they appear fully white).

  29. ozprof

    BA, you have your maths mixed again. Area does not increase by DIAMETER squared, but by RADIUS squared.

  30. ozprof (32) see comment 28 above.

  31. Oops – I was going to add last night but forgot to that another source for the info. in comment #5 re : Galileo seeing Neptune and also Ouranos being 34 Tauri is Patrick Moore’s book ‘New Guide to the Planets’, published by Sidgwick & Jackson, 1993.

    PS. Click on my name to view AggManUK’s excellent youtube clip about Neptune – he’s got a great one on Triton too. :-)

  32. Messier Tidy Upper

    @21. Pete Jackson :

    What is that tiny object about 3/4 of the way out to Triton on the poseidenated version? Not likely Nereid since it orbits much further out, unless we see it by chance passing in front or behind Neptune. Too far out to be Proteus, so it’s most likely a background star.

    Well Neptune has many more moons than just Proteus as I’m sure you know.

    See :

    http://en.wikipedia.org/wiki/Moons_of_Neptune

    which names and describes all thirteen of them : Triton, Nereid, Naiad, Thalassa, Despina, Galatea, Proteus, Halimede, Sao, Psamathe, Laomedeia, and Neso.

    Not that I’m saying the object you’re talking about there is one of those necessarily.

    For AggManUK’s Triton video see :

    http://www.youtube.com/user/AggManUK#p/u/9/wriUZ8J0Ofw

    whilst this :

    http://kencroswell.com/NeptuneOcean.html

    article by Ken Croswell explains how how Neptune may one day live up to it’s watery name. :-)

  33. kroosing

    Thanks Phil!

    You should do this more often. This is quite comprehensible math for most people if they just put their heads to it a bit, while it’s easy to skip for those who don’t want it.

    And it packs a lot of practical info which, if you’d look for it, would take considerable time to collect.

    This mathofobia becomes silly, a daft instinctive attitude, and reacting to it a caricature.

  34. See :

    [wikipedia Moons_of_Neptune page.]

    which names and describes all thirteen of them : Triton, Nereid, Naiad, Thalassa, Despina, Galatea, Proteus, Halimede, Sao, Psamathe, Laomedeia, and Neso.

    Sorry Larissa – you’re a Neptunean moon as well which I breifly forgot.

    I love the names of the outer moons of Neptune – and the other gas giants too. Grandiose mythic names for small chunks of ice and makes them sound almost magical places. :-)

    It’s funny – and kinda neat too – how so many of the moons are common female names too – Larissa (Neptune), Miranda, Ariel, Ophelia, Cordelia, Juliet, Belinda, Rosalind, Bianca & Margaret (Ouranos), Phoebe, Pandora, Helene (Saturn), Elara, Leda, Himalia, (Jupiter) plus Luna and Selena from Earth’s Moon! ;-)

    (Click on my name for source.)

    Guess it comes from the myths and astronomical naming conventions but still ..neat. :-)

  35. Of course, thinking moonlet names I believe one of Pluto’s moons was named for a US baseball team or vice-versa – Nyx! ;-)

    (Am I recalling right that there’s a baseball team called the New York Knixs or something like that? We play cricket over here instead!)

  36. MadScientist

    I’m always amazed by how well these huge telescopes resolve Neptune. I remember helping a buddy with photometry on Neptune with an 18″ reflector; at the time I would never have imagined seeing the sort of resolution that the Keck’s got (of course it helps to have all that extra light to spread around the larger image too).

  37. Messier Tidy Upper wrote:

    Am I recalling right that there’s a baseball team called the New York Knixs or something like that?

    Sir, first a preface: As always, your clarifications of any of BA’s ambiguities are most welcome.

    The Knixs, or New York Knickerbockers, are a round ball team.

  38. Sort of knew this without it being spelled out.

    You can see the moons of jupiter very clearly through a five inch telescope (my trusty meade) in Sydney with suburban lights.

    The Sydney Observatory telescope (a 16 inch meade) makes neptune look pretty unexciting and its moon a genuine dot.

    Even in a dark-sky place Neptune is not that interesting through my 5 inch telescope… and the moons of jupiter are fascinating – you can see shadows and eclipses and…

    J

  39. Nigel Depledge

    The BA said:

    Math to the rescue!

    Yay!

  40. Ivar

    As Nicias and others pointed out, the calculations hold true only for unresolved sources – if it worked this way for resolved sources, you would effectively have solved Olber’s paradox for an infinite eternal homogenous universe. ;)

    Funny thing is, the correct ratio is greater than your 13 – I would have been slightly surprised if a factor of 13 was sufficient to go from grainy images to a saturated sensor. The math would get even more fun, if one was resolved and the other was not, in this particular case the factor would be even greater!

    And the people who kvetch about diameter versus radius, should at least use tau (or whatever you want to call it) rather than pi, as pi is defined by the ratio of the circumference to the diameter, not the radius. They’d still be wrong of course, but would be closer to having a semantic point. Truth is, the area scales with ln(11) times the diameter cubed divided by (e^7) times the radius.

  41. Nigel Depledge

    MTU (37) said:

    so many of the moons are common female names too – Larissa (Neptune), Miranda, Ariel, Ophelia, Cordelia, Juliet, Belinda, Rosalind, Bianca & Margaret (Ouranos), Phoebe, Pandora, Helene (Saturn), Elara, Leda, Himalia, (Jupiter) plus Luna and Selena

    Well, first, I think some of these names are not so common. I’ve never met anyone named Luna (nor encountered in any way except in fiction). I have neither met nor heard of anyone named Elara, Leda, Himalia or Ariel, except in the source work from which the name was taken.

    Second, many of the names might be common names because of the source from which they were taken. So, I’m sure there are people who name their children (or have done in the not-so-distant past) after characters from the works of Shakespeare. And Ouranos’s moons are all named for characters from Shakespeare’s works. Less commonly, there may also be people who have named their children after characters from classical mythology (from whence many of the other satellite names are derived).

    So, I think overall it is not surprising.

  42. BJ

    Dude, you’ve made a math error!!!!11one

    Area of a circle goes as CIRCUMFERENCE squared, not diameter, duhhhh….

    People, seriously, if you’re going to try and correct someone’s math error, be really, really sure that you’re correct. Radius, diameter, and circumference are all related by constant factors; thus, scaling of quantities with one of these factors is the same as scaling with the other two.

    Same thing goes for grammatical errors. You’re not going to effect any changes in anyone’s posting by pointing out errors incorrectly.

  43. Bruce

    Several people (Nicias, Joshua Zucker, Ivar) have this correct – because these are resolved images, surface brightness matters, which is proportional only to the distance to the sun squared; combined with Neptune’s very low near-IR albedo.

    “But is Europa resolved by Keck? It’s only about half an arcsecond across according to my rough calculation.”
    These are images using Keck’s (extremely good) adaptive optics system – the resolution is closer to 0.04 arcseconds.

    Tophe and Simon C ask about thermal emission – this is a short enough infrared wavelength (almost visible) that thermal emission from these cold objects is negligible.

    “What I want to know is how does someone get Keck time when they did not bother to calculate ahead of time whether or not it would saturate the image? ”
    I believe from Mike’s tweet that the science data is fine – I’m guessing he’s using one of the AO-fed spectrographs for the main science goal; these images are just from the acquisition camera that is used to set up the spectrograph data – saturating that is just a mild nuisance.

  44. CB

    A = pi*r^2 = pi*(d/2)^2 = 0.25 * pi * d ^ 2 = 0.25 * (1/pi)*C^2 :)

    Hmmm…

    “Equals” is an interesting and powerful math concept. :)

  45. Poseidenate…classic!

  46. Screamin Chicken

    @28. Phil Plait:
    “Screamin Chicken (25), Chris (26): So you’re saying area does not scale as diameter squared? Are you sure you want to argue that? To make it more clear: if I double the diameter of a circle, what happens to the area?”

    You obviously didn’t read my statement correctly. What I stated is 100% correct. Area is a function of radius squared, NOT diameter squared, but since you’re taking ratios it doesn’t matter. That ratios bit is the same thing as SCALING (and you know it).

    If you had used proper English I wouldn’t have commented at all. You said, “area goes as diameter squared”, which is not clear at all. What does “goes” mean??? Obviously you meant “scales” and not “equals”. You could have just replied saying, “Yes, I meant scale when I said goes” instead of ignoring the rest of my post and saying I’m arguing something that I wasn’t.

    @ 45. BJ:
    “People, seriously, if you’re going to try and correct someone’s math error, be really, really sure that you’re correct. Radius, diameter, and circumference are all related by constant factors; thus, scaling of quantities with one of these factors is the same as scaling with the other two. ”

    Duh! I never said anything different. Phil used the word “goes” which is ambiguous at best. That’s the only thing I had a problem with. And just to be clear I did state that there was nothing wrong with Phil’s math since they do scale.

  47. Screamin Chicken

    And just because I know people will say I’m wrong…yes I know (d/2)^2 is the same as r^2 and some people say that that means area is a function of radius & of diameter & of circumference, but I’m from the school that says a function is of the simplest terms. Since you’re always going to find the radius to get to the area, that’s what it’s a function of, plain and simple (to me). I’ll agree to disagree on this…

  48. Nigel Depledge

    Screamin Chicken (49) said:

    Area is a function of radius squared, NOT diameter squared

    Except CB (47) said:

    A = pi*r^2 = pi*(d/2)^2 = 0.25 * pi * d ^ 2 = [etc.]

    [My bolding]

    So, Screamin Chicken, what exactly are you trying to say? That equations should never be rearranged from their simplest form? Or what?

  49. Isaac

    @ 44. Nigel Depledge:

    I have a cat named Luna, and I know a woman named Ariel. For what it’s worth…

  50. Nigel Depledge

    @ Isaac (52) –

    Curse, you, sir, for blowing my thesis out of the water!!

    Over here in the UK, Ariel is a brand of washing powder, which (I guess) is probably why it is not a very popular girl’s name.

  51. Isaac

    Argh! I’ve been cursed!

    I may never fully recover!

  52. Mike Brown

    Hi world —
    Josh way back on #11 has it right, actually. While it is true that Europa is 7^4=2400 times brighter than Neptune, the images I was taking were well resolved (even Europa, at 1 arcsecond, is [or would have been] well resolved with the adaptive optics at Keck, which can resolve down to ~0.05 arcseconds which, I must say, is one of the most awesome things ever). In this case, resolved means spread out over a number of pixels proportional to angular diameter^2, thus the flux PER PIXEL is down by a factor of angular diameter^2. But the angular diameter is proportional to the (real diameter/distance). So the brightness per pixel, which matters, is only proportional to (the distance ratio)^2 = 7^2=49. Still too much for Keck, though, sadly.

    Another way to think about this is that if we suddenly made Neptune twice the diameter, it would be 4 times brighter in total, but if you were resolving it, the surface would still be just as bright, there would just be 4 times more surface.

    The REAL reason Europa was saturated at Keck though is because astronomers always design these things to look at distant faint galaxies and forget that every once in a while someone will come along and want to look in our neighborhood to check on the whales on Europa.

    Mike

  53. I am facepalming like crazy here to read people saying that area is a function of radius squared but NOT a function of diameter squared. Hmmm, next time I get pulled over for speeding, I’ll just say, “But officer, the law in America only restricts how many miles per hour you can travel. Since my car was clearly travelling in kilometers per hour, I’m innocent!”

    Even Screaming Chicken’s argument that a function must be in its simplest terms falls flat. Pi is no more a fundamental quantity than Pi/4. In fact, some people have suggested making 2Pi the constant (and calling it “Tau”) because it simplifies certain other formulas. Not that that helps here, but my point is that there is nothing special about Pi that privileges it over any other linear scaling of Pi. Hell, what if we lived in a world where the equivalent fundamental constant was called Fnord and had a value of approximately 0.785… would you then be arguing that area was a function of diameter but NOT a function of radius?!

    Sorry, I know you are trying to save face after making a really stupid remark, but better now would be to simply say that you said something silly, you feel silly, and of course you realize that area is a function of diameter.

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