Discussion > An experimental demo of GHE.
okay, we need to quantify the average Watts/m2 of LW incoming solar radiation, and compare it to the 'back radiation' figure from the GHG. But I would suggest the incoming LW from daylight solar is significantly more than the total from the atmosphere. I have never ever felt my hand warm by placing under a passing cloud.
An interesting proposition, a few points to consider:
Any detector won't be able to tell the difference between a LW photon that 'got through' the atmosphere from the sun, and one which came from the earth and was bounced back. There is no physical difference between them.
This is why when they measure downward longwave radiation, they do it at night, so we can be sure that we're only getting stuff that's been bounced back from the atmosphere.
As for your guess that back-radiation would be dwarfed by LW from the sun, again, since most of the direct LW is scattered by GHGs on the way down, it's difficult to separate the two, during the day. But by subtracting the night time signal from the day time one, you would get a rough idea of the extra coming from the sun. Sorry, I can't locate a graph, but it has been proved to my satisfaction. From memory, it's about 320 W/m^2 back radiation as against 340 W/m^2 solar insolation, something like that.
As for your further assertion that you never got warm holding your hand under a cloud, this unfortunately shows the shortcomings of anecdotal evidence. This experiment has been done many times, most interestingly by Dr Spence - see graph
TheBigYinJames
It's got nothing to do with path length through the atmosphere.
I am fully aware of the angle of incidence issue - as I said in my first comment (page 7) and rep[eated above:
..even when you angle your skin to be perpendicular to the Sun, so you should be receiving the same Watts/m2 as someone sleeping by a pool in the tropics.... So I would suggest it must be the increased path length, for both LW and SW. What else could it be?
Unfortunately, the amount of LW in general insolation is small anyway. The extra number of photons GHGs manage to get rid of is dwarfed by photons coming from the ground. This is because the ground 'converts' SW photons into LW photons, so the total number of LW photons bouncing around is dominated by this effect rather than the little bit of LW directly from the sun.
But you said the warmth you feel on your skin is from this LW IR! So the Sun's LW component is of significant magnitude to feel as warmth, even in Scotland for 9 months of the year (when it isn't cloudy of course). I can't say that I have ever felt any comparable intensity of IR from any object on the ground or indeed from any part of the sky after the sun has gone down. And neither have I noticed any of my cameras' infra-red autofocus systems failing as as result of incident IR, yet as soon as I point a camera in the general direction of the Sun it can't focus for peanuts.
lapogus
lapogus
. So I would suggest it must be the increased path length, for both LW and SW. What else could it be?
Your skin can only 'feel' LW as a temperature. SW in the visible range bounces off us (we're reflective) SW in the near UV passes through our skin (but not our mitochondrial DNA, unfortunately) but we don't 'feel' it (this is why you can get sunburned in cloudy weather even when you feel cool). SW UV in more dangerous bands has been stripped out by Ozone so is not present.
So you can only 'feel' LW radiation as a heat ray. When you angle your hand to be perpendicular to the sun, you are getting a full blast of SW (do your eyes detect it being any duller in sunlight in winter? of course not.) But in those frequencies you can 'feel' with your temperature nerve ends, there IS a reduction due to increased path length, due to GH gases absorbing LW.
TheBigYinJames
BigYin - thanks for the link to Dr Spencer's graph, which I had never seen before and is very useful. I note the night-time warming (compared with ambient air temperature) of the plate is about 1.5F over 2 hours, coincident with the mid level clouds passing over, and don't have any problem with that, but maintain that such a low level of incident IR would not be enough to feel on bare skin, even in windless conditions with a cold ambient air temperature, so I suggest my anecdotal observation holds up fine. I also note that Dr Spencers' plate temperature goes off the scale and surpasses the ambient air temperature during daytime. Again this suggests that incoming solar IR is much greater magnitude than back radiation from GHGs.
I have never been able to get my head around the 320Wm-2 figure for background radiation, thinking there is no way that could be right, given that it is almost a third of the total 1000Wm-2 insolance received at ground level from the midday sun. So I remain sceptical of this 320W/m2, and even more so now as I have just read on wikipedia (sorry) that the IR component of sunlight is actually about 527W/m2. (incident daylight 445W/m2 and UV 32W/m2).
lapogus
there IS a reduction due to increased path length, due to GH gases absorbing LW.
So increased CO2 will reflect more of the 445W/m2 incoming solar IR then? If we are to accept the IPCC's "we are all going to die by tea-time" thesis due to CO2's alleged radiative properties, the fundamental question is whether the magnitude of IR reflected by the atmosphere (from the land and oceans) exceeds the proportion of incoming IR from the Sun reflected to space. I remain to be convinced that the climate scientists have got all of this right.
lapogus
Big Yin, Roger, RKS
If you folks arrange a dinner to talk over an experiment or your theories I would very much like to attend. I would not contribute much but I would really like to absorb the interplay ^.^
My email should be available on my profile but anyway it is entium@clara.co.uk
Dung
Well, you're all welcome at the next oxford pub do (whenever that will be), or there's a thing in London on 4th Feb where there's a chance to get together afterwards.
Angle of incidence. It seems to me that a spectrum reading of direct overhead (equator, equinox, Atacama for the H2O content, but anywhere during the day would do) and a simultaneous reading at 60degrees to the vertical would show the effect of doubling GHG, and mostly CO2. I'm thinking much could be cleared up by looking at the two spectra. Am I deluded? How about every angle for 90degrees? Incoming should vary, reflected should be constant, no? If you could get a satellite to look at it from the other side, and a solar spectrum above most of the atmosphere, even better.
And no, I haven't been away, I have been keeping shut up, more of a challenge than one might think.
rhoda
There comes a point where I'm just repeating myself :) Either I'm deluded, or you are all idiots, or I'm just explaining it badly. I know you're not idiots, and I'm pretty sure I'm not deluded, so I have to assume I'm just bad at explaining it :/
Instead of going over it again, I'll relate a piece of anecdotal history.
Around 500 BC, separately the Persians and the Native Americans of the New World discovered a way to make ice during the summer. They would dig a long narrow hole in the ground, and on a clear night would pour a foot of streamwater into the hole. Even in mid-summer, the water would freeze as long as it was a clear night.
Now, I can explain how you can make ice during the summer using this technique with reference to IR back radiation. I cannot, for the life of me (please try) explain how a pressure-based model of air temperature can explain it. Something to ponder.
As for the dinner, I have a vision of us all turning up in 19th century top hats and pocket watches.
TheBigYinJames
BigYin, yes, I have seen ice form in June in Scotland, midsummer to be precise, about 2000 feet up one of mountains at the head of Glen Lyon. It was about 2 in the morning, on a south facing slope, and the air temperature was not below zero, or did not feel it. It was actually very odd, as there were many other wet bits of the path and very shallow puddles which had not frozen. I suspect the water which froze was coming very cold spring, and the loss of IR to the sky in that spot was just enough to start the phase change. I can think of no other (non-paranormal) explanation. (iirc Hamish Brown describes a very odd phenomenon in one of his hillwalking books, when a child's wet boot almost instantly froze when standing on a particular spot on a mountain, but then quickly thawed as soon as the child moved his foot off this spot).
With regard to the Persians and Indians, I have heard of this before but can't remember the details. I suspect it was a deep hole/trench, and the ground was still very cold from the previous winter, which cooled the water enough such that it didn't take much outward radiation before it began to freeze. I'd like to see a reference to this for more details, or better still the process replicated today. But none of this answers my questions - I don't dispute that matter loses thermal energy though emission of IR radiation - but I don't think this loss is anywhere the 320W/m2 as the alarmists suggest.
With respect, I don't think that it is just that you are explaining it badly. Let's recap here; in your response to RKS and his plain English explanation of N&Z (which I thought was excellent and a great summary), you argued that the atmosphere was transparent to solar energy, but you now accept that it is not. When I pointed out that it can't be 100% transparent as the Sun has very little warmth in northern latitudes due to the increased atmospheric path length, which implies some loss to absorption and reflection, you said that this was only the IR component, and UV will get through. But UV is also evidently absorbed and reflected. And it turns out that contrary to your assertion that IR is an insignificant component of the solar spectrum, and that incoming photons were vastly outnumbered by those outgoing, the incoming IR component of solar energy is about 500W/m2, and greater than Trenberth's claimed 320W/m2 IR from back radiation. Thus I suggest that any extra anthropogenic CO2 will likely just reflect more incoming IR than outgoing IR, and result in net cooling of global average temperatures. Your ice anecdote does not address the questions I raise, and does not inspire confidence that your dismissal of N&Z was well founded. While I accept that my analysis is very simple and is likely fundamentally flawed, it would be good to know where.
lapogus
lapogus, you're determined to drag me back into this aren't you?
I don't dispute that matter loses thermal energy though emission of IR radiation - but I don't think this loss is anywhere the 320W/m2 as the alarmists suggest.
Total energy lost has to be equal to total energy received over time. Ordinary GHE theory says it's mostly IR with a bit of convection. N&Z seem to be saying it's almost all convection with a negligable IR component. So as I summarized in my original post, we're arguing about the relative amounts of convection vs IR radiation. RKS then contradicted me by saying that insolation acting on non GHG was the cause. This wasn't 'clear' or 'plain English' - this was plain wrong - insolation, at SW or LW or anywhere on its Planck curve, has virtually zero affect on O2 and N2 molecules.
you argued that the atmosphere was transparent to solar energy, but you now accept that it is not.
I said it was transparet to shortwave. I always accepted that it was not TOTALLY transparent to ALL solar energy, my main argument is that it is not transparent to LW, which is also a (small) component of solar insolation. One of my early graphs to rhoda showed the actual plank curve of solar radiation at sea level, and it has chunks and bites out of it all over the place. But compared with the LW part of the curve, the SW part is almost intact. Almost all SW gets through, quite a lot of LW doesn't. This contradicts nothing I've said.
When I pointed out that it can't be 100% transparent as the Sun has very little warmth in northern latitudes due to the increased atmospheric path length, which implies some loss to absorption and reflection, you said that this was only the IR component, and UV will get through.
The sun does have very little warmth in high lattitudes because of increasd path length because it is the LW component which is being blocked by the extra pth length. With your hand perpendicular to the sun, the SW portion is at full power, you're getting as much SW as you were at the equator. You can't feel it, because you can't 'feel' SW, you can only feel LW which IS being blocked by GHGs.
UV is only a small part of shortwave radiation (about 10%) and most of it is absorbed by a layer of ozone right at the edge of the stratosphere. It's not uniformly distributed throughout the atmosphere, so extra path length does not have an appreciable effect. In the service of accurancy, it will not be a zero effect, but it will be negligable. You can consider UV absorption by Ozone as part of the 'albedo' effect - to be deducted from solar insolation before it gets to the ground. SO it doesn't matter if the atmopshere is thicker or not, it's gone already.
Most shortwave gets through just dandy. Just because your hand can't feel it, doesn't mean it's not there, it just means the LW is not there. I don't see how I can explain it any simpler. If SW radiation was reduced by a thicker atmopshere, the sun would appear less bright in winter. This is patently not true. (I await you contradicting me on this one, at which point I throw up my hands and admit defeat)
And it turns out that contrary to your assertion that IR is an insignificant component of the solar spectrum, and that incoming photons were vastly outnumbered by those outgoing, the incoming IR component of solar energy is about 500W/m2, and greater than Trenberth's claimed 320W/m2 IR from back radiation.
Where did you get that 500 W/m^2 from? The solar flux averaged over just the sunlit half of the Earth's surface is about 680 W/m^2. That's ALL OF IT. The IR portion of that is small, even if it's as large as 10%, that's only 68 W/m^2. Even if it's out by a factor of two, there is no way you can get the IR component to get to 500. I think Trenberth estimated it in the 70s somewhere.
So I don't know where you are getting your figures from, but I would recommend looking again.
TheBigYinJames
lso with a spinning globe with heating to one side - the mean temperature would be the same at whatever rate of rotation. Slow it down, the hot side gets hotter - the dark side gets colder, speed it up, the hot side gets less hot - the dark side gets less cold - the mean temperature remains the same. again, why would it not?
Interesting discussion!
Jan 6, 2013 at 9:33 AM | Registered RKS
...why would it not?
Here's my take on why it would not.
If the rotation is slower, the temperature rises to higher values (as you point out). Since radiation is proportional to T^4, the energy re-radiated to space is more than proportional to the increase in temperature. So, with higher peak temperatuures, the total energy radiated to space will be greater.
So, since more energy is being discarded, the mean heat in the surface will be less and the mean temperature will be lower.
Does that make sense?
Jan 6, 2013 at 12:11 PM | Martin A>>>>>>
Martin.
I've Been in touch with Ned Nikolov regarding the Lunar/Bare Earth mean temperature Question and thought I'd show you the conversation below. He's been working on this for some time so I presume He's taken your argument into account:-
"Interesting problem Ned.
I said that if the Lunar mean temperature was 197K that that should also apply to the Earth.
I was challenged that due to different speeds of rotation, and with radiation being proportional to T^4, The more slowly revolving body receiving more radiation would radiate proportionally more to space, resulting in a lower mean temperature.
This left me a bit stumped as I cannot see the flaw in the argument.
Can you help please."
"In our paper, we discuss (among other things) the effect of rotation on the mean surface temperature of a planet. The short answer is this: rotational speed (or more accurately termed the spin rate) can only affect the diurnal temperature amplitude (with the latter decreasing with spin rate), but cannot impact the mean temperature. A factor that has a significant impact on the mean temperature, however, is the fraction of absorbed solar flux stored in regolith as heat during the day that gets released at night giving the night side a higher temperature than expected from cosmic background radiation alone. This surface heat storage fraction depends only on legolith thermal conductivity, which in turn is a function regolith bulk density and the air pressure. In the absence of air (as in the case of the Moon), this thermal conductivity is very low. That's because air pressure is the most important factor controlling it .... Long story short - the Moon is the perfect airless equivalent of Earth, which means that the thermal effect of Earth's atmosphere (i.e. the Greenhouse Effect) must be evaluated against Moon's mean surface temperature. Hence, Earth's GE = 287.6K - 197.3K = 90.3K.
- Ned "
That's as up to date as I can get until the paper is published.
RKS
Was just about to comment on that rotation thing. I think it makes a difference, and here is my chain of thought. Say there was no rotation, and the conduction component is small. Then we have half the planet in the sun, all the time. The other half is in the shade. IMHO the whole of the nightside will radiate down to 0K or space background tem, which is, what, 2K. On the hot side, the very hottest point, central on the no-longer-existing equator, will get the full power of the sun. So, four times the usually quoted average, 1344 watts all day long. Four times at T^4 gives root two times the normally quoted 279K average (wikipedia, discounting albedo), Thats just under 400K. That's the hottest bit. Everything else is at some temp less than that, the lowest temp beng 2K. Mean of 494K and 2K is 203K. In fact, because I lost the ability to integrate the minute I left school, the true figure is somewhat less. So the special case of rotation being zero gives a result far lower than the rotating figure normally accepted.
My explanation is that the normally derived figure expects to radiate over the whole sphere. The stationary planet does not do that, effectively as soon as the nightside reaches zero it stops radiating and invalidates the assumption. It will do this to a lesser extent with slow rotation. Presumably with very fast rotation the whole surface will tend to a temperature, and that is the only time the usual method comes out right.
(Or have I just written a load of rubbish? I truly don't know. Wouldn't be surprised though.)
rhoda
RKS,
An elegant reply from Ned Nikolov. I really like the way he explains things.
I am dreading Paul Dennis coming back and confirming his discrepency between analytical and numerical integrations, because it means I would have to do it myself. With my poor programming skills this would take many hours. I wonder if N&Z have ever looked at this, and if so, have they got some code available? I do not wish to pester Ned in his work, but perhaps you could ask him, if you think appropriate?
I have also been thinking about your experiment. My latest idea is that the ceiling is the uninsulated undersurface of an otherwise heavily insulated LN2 tank. And I still think the walls should be mirrors, but at the moment that is based upon intuition. It would be nice if others would join in with this discussion.
Now - back to the day job.
Roger Longstaff
Delete ' Mean of 494K and 2K is 203K.' substitute mean of 394K and 2K is 198K. Which is not far off that moon temp, is it?
rhoda
Jan 7, 2013 at 2:00 PM | rhoda>>>>
Rhoda.
I think Ned had dealt with the problem of a non rotating airless globe in the passage below where he discusses the low storage properties of regolith on an airless body. You need to see his paper to see how he derives mean temperature for a sphere and which Richard and Paul are playing with at present. And Ned does nor differentiate between a slowly rotaing Moon and a comparatively fast rotating Earth. [which of course is relevant to the effect of GHE on Earth]
"A factor that has a significant impact on the mean temperature, however, is the fraction of absorbed solar flux stored in regolith as heat during the day that gets released at night giving the night side a higher temperature than expected from cosmic background radiation alone. This surface heat storage fraction depends only on regolith thermal conductivity, which in turn is a function regolith bulk density and the air pressure. In the absence of air"
RKS
I have also been thinking about your experiment. My latest idea is that the ceiling is the uninsulated undersurface of an otherwise heavily insulated LN2 tank. And I still think the walls should be mirrors, but at the moment that is based upon intuition. It would be nice if others would join in with this discussion.
Now - back to the day job.
Jan 7, 2013 at 2:19 PM | Roger Longstaff>>>>>
As the experiment idea, as with any other proposed experiments on this thread, has interested so few contributors I wonder if it's worth creating a new thread for my throw away idea.
I think it might have legs if enough people put in their ideas but, unlike Tallbloke where people seem more willing to collaborate, BH discussion often ends up with a pissing contest.
RKS
Delete ' Mean of 494K and 2K is 203K.' substitute mean of 394K and 2K is 198K. Which is not far off that moon temp, is it?
Jan 7, 2013 at 2:25 PM | rhoda>>>>
Our posts seem to have crossed there.
It does seem as if Ned Nikolov's description is correct there with such a close result.
RKS
I haven't had a chance to build a model in Mathematica and carry out an analytical solution to the Grey Body problem yet Roger. So no further comment yet except to say there is some discrepancy in Ned's paper that is at Tallbloke's site. Here he has indicated differing limits of integration between 0 and 2*pi for one variable and between -1 and 1 (is that cos theta (latitude)?) but then the next line indicates integration between 0 and 1.
I've had a look at the 2012 lunar paper based on the Diviner equatorial measurements. The position of zero energy flux is some depth below the surface (10's of cm). As Ned points out the incident solar energy is partitioned between outgoing radiation and thermal diffusion below the lunar surface. Interestingly the dominant transport vector is radiation between grains but this is an aside. The key issue is the temperature at depth is 240K. If one accounts for the change in albedo with incidence angle as noted by N&Z then this temperature is what one computes for the S-B grey body temperature at the equator.
I probably won't look at the integration again until the weekend. If one is going to ask N&Z a question it is when they calculated their grey body temperature did they use average insolation over a lunar day, or instantaneous insolation. i.e. one can divide the moon up into a series of small circle 'washers' parallel to the lunar equator and estimate the average insolation and therefore average temperature of the edge of each washer and integrate this way and work out an average. That was the way I did it. On the other hand one can estimate the instantaneous solar radiation, and temperature at each point on the surface using polar co-ordinates and determine the average. My hunch is both methods will produce different results because of the T^4 issue.
The question is which is the right method. Using the average insolation does seem to give the temperature of the region at which there is zero energy flux on a diurnal basis and feels intuitively correct to me but I need to think about it some more.
Paul Dennis
Re that rotation thing. A static model has limits both high and low. Whether (and how much) the various temps reach their limits MUST affect the average. If both up and down were unlimited no doubt the rotation speed wouldn't matter. But where cold side can reach and maintain zero(ish) all over, but warm side can only reach peak SB temp at the centre of the illuminated portion, there is more down than up in it. And in my estimation, static is no more a special case for an exception than having rotation rate equal R where R is anything. I'm assuming that conduction is not a factor, of course. Heat is not noted for conducting much through long distances in rock.
rhoda
Big Yin, Roger and other pro "back radiation" posters.
Can I ask you to critique an experiment by Berthold Klein that I pasted near the top of page 2 of this discussion?
I described it as being by Nahle at the time which was incorrect.
Dung
Going back to Dung two days ago:
AR3 included a reference to the "fact" that effect of CO2 (and other greenhouse gases) was logarithmic. This has since been swept under the the politically correct carpet and has disappeared.
I'm not convinced this has been swept under a politically correct carpet and I'm not sure Martin A's 'answer' yesterday afternoon, taken from SoD in April, should be considered the last word as far as the original source, because didn't a man called Svante Arrhenius write this in 1896:
if the quantity of carbonic acid [H2CO3] increases in geometric progression, the augmentation of the temperature will increase nearly in arithmetic progression
I don't claim to understand the development of the concept of the GHE, and how scientists became convinced of it since then, despite known flaws in Arrhenius, but that's the origin of the logarithmic claim at least, based on a simple theoretical model, as Martin A said he'd originally expected.
Moving forward over a hundred years, in July 2010 Stefan Rahmstorf on RealClimate cited Wally Broekner (1975) as saying
The response of the global temperature to the atmospheric CO2 content is not linear. As the CO2 content of the atmosphere rises, the absorption of infrared radiation will “saturate” over an ever greater portion of the band. Rasool and Schneider point out that the temperature increases as the logarithm of the atmospheric CO2 concentration.
and went on to comment:
Based on this logarithmic relationship (still valid today) Broecker assumes a climate sensitivity of 0.3ºC warming for each 10% increase in CO2 concentration, which amounts to 2.2ºC warming for CO2 doubling.
No doubt SoD knows many of his onions but I though this answer was strange and worth a bit more investigation, agreeing as I do with Martin that
In science generally, but particularly with "climate science", it can be enlightening to try to track things back to their origin.
I did consider starting a separate thread for this called "The basic for a logarithmic relationship" but decided against it for now. However, if others agree, I think this is usefully separable.
Richard Drake
Paul, thanks for the update. I think you are asking all of the right questions. In the meantime I will keep my eyes open for any "off the shelf" code that has been verified and could be adapted for this puropose.
Dung, I will certainly have a look at your experiment, as soon as I get time. I probably won't be able to get back before tomorrow at the earliest.
Roger Longstaff
A Tale of Two Planets, Qubi-stat and Qubi-spin
Two strange small planets have been discovered orbiting the Sun, each one at precisely the same distance from the Sun as the other. (Their discovery was inspired by rhoda's Jan 7, 2013 at 4:42 PM comment)
They are cubes of identical sizes; each side of each planet measures 1km by 1km. One of the planets, Qubi-stat , rotates once in its (circular) orbit around the Sun, so that one face is always turned towards the Sun. Its other five faces are in perpetual darkness.
The other cubic planet, Qubi-spin , rotates very fast - its day lasts just a few Earth minutes. Its axis of rotation is perpendicular to the plane of its orbit around the Sun, so that two of its faces are in perpetual darkness. The other four faces are warmed, in rapid succession, by the Sun.
For some as yet unknown reason, it rotates on its axis in 90° jumps, so that only one of its four faces is illuminated at any given instant. (Various hypotheses have been conjectured to account for how angular momentum is conserved.)
The planets are as near to a black body as can be imagined - they absorb all incoming radiation. They are made of a material whose thermal conductivity is low, so that a warm face provides no heat to cooler faces. They have no atmosphere.
First, let us consider Qubi-stat.
The incoming radiation from the Sun at the illuminated surface is 1000W/m2. This means that the illuminated surface has to radiate at this level, for thermal equilibrium.
The Stefan–Boltzmann formula (mks units) says
1000 W/m2 = 5.67 × 10^-8 × T^4
so T^4 = 1.76 × 10^10, giving T = 364K for the temperature of the illuminated face of Qubi-stat. Its other five faces are at 2K, so the arithmetic mean of the temperatures of is faces is
(364 + 2 + 2 + 2 + 2 + 2)/6 = 62.3K
Now consider Qubi-spin.
It spins so fast that each face is virtually in thermal equilibrium, despite only facing the Sun 25% of the time.
The mean incoming radiation on one face is 1000/4 W/m2 = 250W/m2.
So each of the four illuminated faces has to radiate at this level to remain in equilibrium.
Thus, for a face of Qubi-spin, we have from the Stefan–Boltzmann formula
250 W/m2 = 5.67 × 10^-8 × T^4, so T^4 = 4.41 × 10^-9, giving T = 258K for the temperature on each of the four illuminated faces of Qubi-spin. So the arithmetic mean of the temperature of its faces is
(258×4 + 2×2)/6 = 173K
(Note: Qubi-stat is now known also to rotate in 90° jumps in addition to the continuous once-per-orbit rotation. The jumps occur at such long intervals that it was thought not to rotate at all. Thus the behaviour of the two planets is in fact essentially identical, except for their rotation rates.)
I hope I got the calcs right - anyone feel like checking them? I'm time-slicing between other things that demand attention.
__________________________________________________________________
I know that the cubic planets are a bit unlikely, especially one that rotates in 90° jumps, but would you not expect something similar with spherical planets, one rotating very slow and the other rotating fast?
Martin A
However, if others agree, I think this is usefully separable.
Jan 7, 2013 at 6:14 PM | Registered CommenterRichard Drake
Richard, would it make sense to hold off until BH hits a quiet phase? It's diffcult to keep up at present.
Martin A
Mant thanks to all for a facinating weekend. I have been made to think, and I have learned. But I now have to go away to earn a living.... I will try to drop in during the week, but back next weekend. Please keep it up!
rhoda, you sure picked a bad weekend to go on holiday.
RKS - I would really like to see your experiment worked up.
Paul - good luck with your integration. If you can get a different result using numerical techniques it will be a game changer. I would love to visit your labs. My email is roger dot longstaff at live dot co dot uk.
Best to all, R.