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.

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

I may never fully recover!

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.

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

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?

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.

Hmmm…

“Equals” is an interesting and powerful math concept.

“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.

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.

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.

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.

Math to the rescue!

Yay!

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

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.

(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!)

[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.

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.

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.

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