Physics Is A "Troubled Field"? Not As Much as Biomedical Research And Psychology

Image of  artificial CME successfully produced in laboratory experiment in 2016. Is physics a "troubled field"?  Only in the opinions of those who know little or nothing about it.

I confess I was rather mystified on reading the recent reviews of two books by physics superstars: Stephen Hawking ('Brief Answers to the Big Questions') and Martin Rees ('On the Future').    These appeared under the banner 'Serious Doubt On Serious Earth' in the WSJ Review section (p. C12, Oct. 20-21) by John Horgan.  

Horgan, after giving reasonable reviews of each book, then writes:

"Hawking and Mr. Rees recognize science's declining status. They call for better science education to lure more young people into science." 

 Then quoting Hawking:

"The low esteem in which science and scientists are held is having serious consequences."

True, but only in some fields - not all. Case in point, Horgan goes on to note:

 "Both authors fail to mention science's wounds are at least partially self-inflicted. In 2005, statistician John Ioannidis presented evidence that 'most published research findings are wrong'"


Now that is flat out false, and leads the unwary reader to believe all the sciences are publishing error- prone research. In fact,  Joannidis - a meta -researcher- was focused almost exclusively on the credibility of medical research.   

 In effect, his investigations found that much of what biomedical researchers concluded in  their published studies was often misleading, exaggerated or flat wrong. These included studies related to the prescription of antibiotics or blood pressure meds, treatments for back pain, surgery recommended for heart conditions, and advice concerning consumption of fiber and more or less meat.   See e.g.

Dr. John Ioannidis Exposes the Bad Science of Colleagues - The Atlantic

https://www.theatlantic.com/magazine/archive/2010/11/lies-damned-lies.../308269/

The "crisis in replication" as he refers to it is also rampant in psychology. Thus, three years ago in a NY Times report ('Psychology's Fears Confirmed: Rechecked Studies Don't Add Up')   we learned of multiple failures in that discipline including (according to author Benedict Carey):

- A top social psychologist was caught fabricating data, leading to more than 50 retracted papers

- A top journal published a study supporting the existence of ESP that was widely criticized

- The journal Science pulled a paper on the effect of gay canvassers on voters' behavior because of faked data concerns. 

Added to that one also learned (in the same piece)  of a painstaking yearlong effort to reproduce 100 studies published in three leading psychology journals, finding more than half couldn't be validated. According to author Carey (ibid.):

"The vetted studies were considered part of the core knowledge by which psychologist understand the dynamics of personality, relationships, learning and memory"

Note at no point does physics or  its subdisciplines enter into any of this. The beauty of physics is, in fact, its robust quantitative basis which often provides a rigorous cross check on the experiments or observations. (Nearly all of them tied to quantitative models.) Because it isn't merely the outcome of one or more experiments that must be considered, but also the governing quantitative and theoretical dynamic. How can a model be expressed in consistent, quantitative form that gives body to the interpretation of the experimental data? If that quantitative model is defective, then more than likely the whole experimental set up is as well.   So given nearly every physics publication is quantitatively based then there are inherent checks on the model and the capacity for replication.

Take as an example, the astounding replication in the laboratory of an artificial  coronal mass ejection (see top image).  This marked the first time ever solar researchers successfully generated an artificial coronal mass ejection in the laboratory as part of a plasma experiment. The researchers, Ha and Bellan, used a plasma gun in concert with an artificial strapping field to create their own flux ropes in their lab and from these CME-eruptions inside a vacuum chamber.  The strapping field itself  (that field which secures or holds back any emerging flux ropes) had to be carefully computed so that it decayed as a precise function of height. The reason is that the pair needed to generate the most likely instability - called the "torus instability". One self-consistent geometry is shown below as proposed by proposed by DeMoulin and Titov.

Assume then the detailed toroidal structure is initially in equilibrium, what happens to trigger the torus instability? Well, according to one variation proposed by Yuhong Fan, the configuration becomes unstable to an expansion  D R, when the toroidal radius R attains a critical dimension relative to the separation of the charges +q and -q.

Specifically, one will be looking at the decline of the potential field   B _q  with R and when it becomes critically deep.   This is evaluated using a decay index with torus instability occurring when the condition holds:

n = - d ln B _q   / d ln R > 1.5

In respect of their CME -generating experiment, Ha and Bellan would likely have taken these considerations into account to a suitable scale to create their strapping magnetic field that decays with increasing altitude.

The point here is that the replication basis of the model as well as the demonstration could easily be checked for self-consistency and adherence to the physical principles. 

Incredibly, despite this, we are informed by Horgan :

"But physics, which should serve as the bedrock of science, is in some respects the most troubled field of all. ...Over the last few decades it has become increasingly disconnected from empiircal evidence."

He then makes the mistake of citing the "proponents of string and multiverse"  conjectures - which of course grab most of the highlights in the corporate press.   But what about the Parker Solar Probe launched Aug. 12 which will provide us new and hitherto imagery and insights into the dynamic nature of our nearest star?  He doesn't mention that space mission at all. Nor the fantastic discoveries of hundreds of exoplanets by the Kepler telescope.

Nor the recent huge success of the Cassini -Huygens mission to Saturn.

Cassini-Huygens changed the game when it found complex hydrocarbons on Saturn’s ocean moons, hinted at hydrothermal vents on Enceladus, and revealed a cycle of liquid methane on Titan. The bottom line is, ocean worlds encapsulated by ice are now more propitious targets in the broader search for life beyond Earth.

If Horgan would have also taken the time and trouble to peruse recent issues of Physics Today he'd have born witness to dozens of new,  empirically validated discoveries, which seldom make the news like string theory or multiverse conjectures.  These have included:

'Isotope Measurements Help Pin Down The Ancient Rise Of Oxygen' (June, p. 16)

'First direct views of attosecond electron-nuclear coupling' (p. 17)

QED experiment detects two distinct photons simultaneously resonant with an optical cavity  (and with one of two electronic transitions of the same atom)  (August, p. 14)

'Use of Xenon isotopes to track volatile recycling in Earth's mantle' (October, p. 14)

'Acoustic metasurface creates quiet locations in a room' (August, p. 18)

Granted, none of these are especially 'sexy'  or exotic but all give the lie to Horgan's claim that physics has somehow become unmoored from empirical evidence.  The error made by Horgan? Focusing too much on the attention -headline grabbing stuff as opposed to the more prosaic but equally important findings.

Because of this selective attention he also commits the logical error of fallacy of composition:  attributing to the whole a characteristic or property that only applies to a part. Hence, concluding erroneously all of physics is somehow "troubled" because he perceives certain deficiencies in two exotic areas.  (Which he also egregiously describes as "modern physics" when string theory and multiverse concepts are only a part, and a very speculative part at that.)

Never mind, Horgan's 'Debby Downer' take, there is plenty in modern science- and certainly in physics-  to enlist and attract the best minds, and fuel their continued curiosity. 

Carrying Out Your Own Exoplanet And Variable Star Observations

The recent news (ASTRONOMY, digital version) that a college senior, not even a grad student, discovered four new exoplanets should not be surprising. If one has the right equipment and techniques this is not a biggie.  Indeed, as an associated article in the print issue of the magazine (July, p. 62) notes:

"With advances in CCD imaging and the development of supporting software, amateurs can now produce exoplanet observations of sufficient quality that professionals can use them to supplement their own studies."

The basic principle at work is elementary to grasp and illustrated by the two graphics shown. In the top image the exoplanet passes in front of its parent star producing a dip in the light curve over a defined interval t2 - t1.    Below, we see a specific example in the case of Wasp -12b for January 6, 2016. The light curve dip is readily visible over an interval t2 - t1 = 2h 50 m. approximately. The assorted dots lining the light curve represent different observations.

In the case of variable stars, it isn't even necessary to have elaborate equipment to do a respectable plot of a light curve. You need only good eyes, good star charts (with magnitudes shown) and the ability to compare the (estimated)  brightness of the target star  with the known magnitudes of those comparison stars in the vicinity.

In effect, one is undertaking basic differential photometry invoking the same basic principle used to make exoplanet observations, and deriving light curves from those.  A student in Barbados (below)was among the first to do a variable star light curve on the island nearly forty years ago.

Over a period of two and a half weeks (17 Julian Days) Stephen Hinds patiently compared brightnesses of the target star Zeta Geminorum with nearby comparison stars to arrive at the light curve shown below:
















Thereby he was able to arrive at the maximum magnitude (+3.7) and the minimum (+4.2) with a period of approximately 10 days.   The same sort of technique can be used to estimate exoplanet brightness changes compared to surrounding stars, except that the naked eye will not be enough and one will need at least a good telescope to do the comparisons, using a CCD detector.

But for the average person, just doing a variable star light curve can be interesting enough and provides the opportunity to do real astronomy, such as done by the American Association of Variable Star Observers (AAVSO).

An excellent test subject currently visible is the Algol-type variable Beta Lyrae.  The interested observer using differential brightness comparisons ought to be able to generate its light curve, e.g.


Showing a magnitude change from +4.4 to +3.3. over the period indicated (the full orbital period is 12.94 days)

For those with a good Schmidt-Casegrain telescope (e.g. 11" aperture) and a CCD camera it's possible to actually go into exoplanet observations - and post results online as part of the Exoplanet Transit Database, e.g.

http://var2.astro.cz/ETD

Whether you go for the basic project of variable star light curve assembly, or exoplanet transits, one thing in common is the importance of  models. In all cases bear in mind the difference between the observed data and what a purported model predicts  is the measure of 'goodness of fit'.

For those who'd just like to do a light curve on Beta Lyrae the map below may be useful, showing the position of Vega in relation to the "Northern Cross" (Cygnus):


Section of star chart to locate Beta Lyrae. Print out the map, and using a flashlight- hold it upside down facing north - to locate the Northern Cross first. The very bright star Vega will be to the W-SW of the Cross and the star Deneb.

Beta Lyrae is the star at the lower left corner of the parallelogram for Lyra.

WSJ: UFOs Don't Exist Because "No One's Seeing Them On Smart Phones" Not Quite!

Today we go from an April Fool's spoof (yesterday's post) to actual written remarks about UFO non-existence in a Wall Street Journal piece. It is always embarrassing when someone or other writes a book, or makes an assertion in the media, that very soon after is upended. Ask author and former State Dept. staffer Francis Fukayama about that after he wrote his tome, 'The End Of History', then had to swallow his proclamations whole after 9/11 and "history" suddenly got revived -  on radically different terms.

IN a similar way it seems WSJ author Steven Poole ('Secret History', Jan. 16-17 p. C10) as well as the author he was reviewing (John Higgs, 'Stranger Than We Can Imagine') allowed their hubris to run ahead of reality and word craft. Basically, the duo came to the same conclusion that - hey - UFOs never existed in the first place, and were merely the projection of our fears and desires.

Not quite. The UFO I observed in North Miami back in 1962 was definitely no projection, having been also observed by a dozen others. As recounted in one of my first blog posts (Dec. 4, 2007) it  appeared "as a brilliant orange disc, at least the same diameter as a full Moon, moving rapidly from north to south. It hovered for two to three seconds...before darting away."

As a seasoned sky observer, even at the age of 16, I was able to quickly eliminate all known man-made or natural objects from consideration. The exceptional luminous and dynamical behavior allowed this. Nevertheless, to this day I am not prepared to pinpoint a specific hypothesis in any dogmatic sense, though up until recently I have gravitated toward an operational craft of unknown propulsion and design. Certainly, no man-made craft I'd ever seen did what this object did. A next day Miami Herald report that an "unknown" was spotted near Miami International Airport imparted an even more valid frame of reference, especially that it was "traveling at over 400 mph".

Then there was the most cited case from Edward U. Condon's 'Scientific Study of Unidentified Flying Objects', the case from McMinnville Oregon (see image) which I'd already explicated in some detail based on two of the researchers' findings, see e.g.

http://brane-space.blogspot.com/2014/04/yes-scientific-analysis-of-ufos-is.html

Included within that discussion is the original definition of UFO given by Prof. J. Allen Hynek, astronomer at Northwestern University, from his book, UFOs- A Scientific Inquiry:

“A UFO is the reported perception of an object or light seen in the sky, the appearance, trajectory and general dynamic behavior of which do not suggest a logical, conventional explanation and which is not only mystifying to the original percipients but remains unidentified, after close scrutiny of all available evidence by persons who are technically capable of making a common sense identification, if one were possible.”

Given Hynek's definition, the logical explanation for why fewer UFOs are being reported is that more people are better educated to discern what they are seeing in the night skies. In other words, they no longer mistake Venus or Jupiter at their brightest or the occasional artificial satellite for a UFO.

It is not, as Poole implies, because they no longer exist. Actually, his exact words are as follows:

"If UFOs really were infesting our airspace there would be plenty of crowdsourced evidence"

This is taken to be because "we all have smart phones now".

Uh, yes, many of us do (I don't) but we use them mostly for selfies and some other forms of navel gazing and grazing (or 'sexting' in the case of misguided teens).  But I'd warrant very few have them trained on the heavens - so why the hell would they see anything? The UFO I spotted along with about a dozen others in FLA was visible for barely 4-5 seconds at most. And, if you didn't look up, you'd have missed it completely (as dozens of others did). Since there are 360 degrees of open sky visible in azimuth on any given night (90 degrees in altitude), and a person-  by biological construction - doesn't have the eyes of a fly, it is doubtful he can see all those sky areas at once. That means he is bound to miss something if not looking at the exact area where a UFO manifests.

But my point here is it is folly to make the argument Poole does that just because millions or billions have smart phones they'd have faithfully captured any objects that are truly unidentified - like the McMinnville object or what I witnessed in 1962. Again, no instrument of any sophistication is any use unless it is specifically trained on where the alleged phenomenon is.

Let's also concede time is a factor in these teen years of the 21st century and you can't compare the time pressures now with the much slower pace in 1962. That left us more time to gaze at the starry skies and was one reason I became involved in astronomy and later astrophysics in the first place. Back then there were no computers, no cell phones, no video games, and the TV had basically three networks which only stayed on until about midnight. The radio was our main entertainment (usually WQAM in Miami was most popular) and the telephone the primary instrument for teens to communicate. (Unless your parents had to use it, and generally there was only one phone per home).

The point again is that back then it would be far more plausible to see something in the sky  -known or unknown  - because people took the time to LOOK there, since there were few other activities competing for one's time!

Another remark by Poole is also somewhat comical:

"Flying saucers now look a little parochial beside the routine discovery of exoplanets."

But exoplanets are still not validated to be actual abodes where humans (or sentient aliens) can live, a point he conveniently omits. In addition, most laymen haven't the foggiest notion of how exoplanets are actually detected, so yeah ..they'd seem more exotic. As for "flying saucers" - Poole here reverts to the most popular, debased usage, i.e. "UFO" equals "alien spacecraft."   which as we saw Hynek's UFO definition disallows. In other words, once you use the term "flying saucer" you are no longer writing about UFOs, but an identified entity adhering to a specific hypothesis of origin..

He ends his take by writing:

"UFOs were once the future they are now just a part of the history of our desires and fears."

Again, wrong. So long as there is a visible, accessible sky and there are people who know little about it, i.e. can't even distinguish a planet from a star, from a satellite, there will be UFOs - because people will not have reached the level of observational sophistication to make determinations. What Hynek and I mean by "UFO" Poole is thinking "flying saucer" and little green men.

What we really need, as opposed to fancying ourselves such a superior breed in outlook that we're beyond inquiry into UFOs, is to develop means and methods that might finally uncover what has attracted curiosity - not just over one century - but many.

Solar physicist Peter Sturrock has perhaps contributed the most in this sphere via his  (2000) book: The UFO Enigma: A new Review of the Physical Evidence, Warner Books. The book is an outgrowth of the findings of a scientific panel formed to provide an evidentiary consensus for what would constitute: a) acceptable physical evidence for UFOs - especially in train with the extraterrestrial hypothesis and b) how that evidence might be obtained. None of the panel members were lightweights, and most had serious backgrounds in either astrophysics or plasma physics. Left unsaid too, is that most who "roll their eyes" harken from the less quantitative sciences, like psychology, sociology or anthropology. 

Also left unsaid is that most astronomers and astrophysicists take the UFO phenomenon far more seriously than the corporate mainstream media would have you believe.

Reports of UFOs, as Sturrock indicates, can be at least subjected to statistical tests (e.g. z-test, chi-squared)  against a stated null hypothesis: e.g. that the phenomenon is as likely to be caused by random meteorological or other agents as artificial craft from "another world".

In terms of a comprehensive scientific process of investigation, Sturrock notes the following aspects are all of use (pp. 94-95):

 i) Mechanical – A continuous or brief mechanical pressure distorts the soil, and this can be measured by a penetration instrument.

ii) Thermal – Measurement of the quantity of water in the soil as compared to other nearby control samples, allows determination of the amount of energy required to reduce the water content to that level.

iii) Magnetic: Some soils have a high magnetic remanence. In this case it is useful to examine the magnetic pattern of the soil with the help of magnetometers either in situ, or in a laboratory.

iv) Radioactive residue: Soil samples can be analyzed either in situ, of in the lab using recovered samples.

v) Physico-chemical: Samples from the trace region and control samples (recovered far from trace region) can be analyzed for molecular, atomic and isotopic composition.

Even if only photographic (or video) imagery is available, numerous physical analyses can be applied (cf. p. 178-179), such as attending to:

Basic film properties (to see if the profile is compatible with the imagery obtained)

i) Measurement of the diameter of the film’s crystals
ii) Obtaining the Modulation Transfer Curve (plot of response vs. spatial frequency)
iii) Obtaining spectral sensitivity curve (log of sensitivity vs. wavelength in nm)

Image Analysis:

i) Linear measurements made on an enlarged print – in tandem with elevation angles made using a surveyor’s transit of the location and objects in the vicinity (buildings, Mountains etc)

ii) Micro-densitometry scans: e.g. using the Joyce Loebl Recording Micro-densitometer to ascertain variations in optical density in the print. The result is obtained as a scan through the disc image (of the UFO for example)

iii) Black and white enlargements on different wavelength sensitive papers: Comparison between UFO (disk) images on panchromatic and blue-green paper may show features visible in one, that are not evident in the other (cf. Fig. 25-7, p. 185, with dome on disk visible on panchromatic image (a) not visible on blue-green sensitive paper (b).

iv) Computer-based contrast enhancement: e.g. digitize negatives using a scanning densitometer. Comparisons of enhancements using various filters (e.g. blue, green, orange, etc. ) show differential detail that must be accounted for. (E.g. Figs. 25-9, 25-10, and 25-11 on pages 188-89).

Digital enhancements may include high-reverse contrast images of the disk itself, e.g. Fig 25-20 on page 207 of Sturrock, which discloses the left side of the particular disk is not a circular extension of the rest of disk – but is rather flattened to some unknown extent.

All of the above are eminently doable in terms of available modern  technology. All that's required is the right confluence of circumstances - that is, an encounter or proximate sighting of a UFO which allows all or most of the preceding to be applied.

Sturrock's book, to be sure, is not an easy read for the layman. But for those- say in the "soft" sciences - who think or believe that the "UFO" is the province of mental misfits, 20th century parochialism or those inhabiting "La-La land" it delivers an excellent wake up call. Alas, most of those would -be skeptics likely would not be able to navigate even the most rudimentary chapters.

Whether the WSJ's Poole falls into this category is another thing, but his column reference to UFOs being a "parochial" phenomenon and an anomaly of 20th century history and paranoia is not designed to inspire confidence.

Is Kepler 452b Really A "Cousin" Of Earth?

Artist's depiction of relative sizes of Earth and Kepler 452 b (right)

NASA's Kepler space telescope has been on a veritable planet-finding binge with thousands of exoplanets discovered the past 6 years. Now, the latest addition announced is named Kepler 452b and has been described as "a cousin of Earth" and even "Earth 2.0". (Several other worlds have also briefly held that label until a better candidate appeared.)

Kepler was launched in 2009 and has nearly 5,000 potential exoplanets to its credit — worlds beyond our solar system..  Boulder-based Ball Aerospace & Technologies Corp. built Kepler for NASA and still runs its operations in space, with support from the Laboratory for Atmospheric and Space Physics at the University of Colorado.

Why is Kepler 452 b being described as a "cousin of Earth"? For one thing its star has the same spectral class (G2) as the Sun. Second, it's at about the same distance that Earth is from the Sun. As one investigator put it: this is now the nearest system found to an Earth-Sun system.

Some of the other comparisons made are as follows:

Age:

Earth at 3.5 billion years old vs. Kepler 452b at 6 billion years old

Length of Year:

Earth 365 days, vs. Kepler 452b at 385 days (given its 5% further away from its sun)

Gravity:

Earth value = 1 g or 9.8 m/s/s  =  9.8 N/kg

Kepler 452b: 19.5 m/s/s  = 19.5  N/kg

Since it is 60% larger by volume and with 5 times more mass, so we use the equation:

g = G M / r²


So here: r =   5R  (where R is Earth's radius or 6.4 x 10 ⁶   m)

And M =  5 M _E  where  M _E     =   6.0 x 10 ²⁴   kg

Bear in mind weight w = mg

The individual mass times the acceleration of gravity.

So if one has a mass of 100 kg then his weight on Earth will be:

w = m g = 100 kg (9.8 N/ kg) =  980 N

And on Kepler 452 b:

w = m g = 100 kg (19.5 N/ kg) =  1950 N

For those who opt for English- British units, a 100 pound woman on Earth would weigh nearly 200 pounds on Kepler 452b

The latter difference in terms of g is important, so we can't simply think - as some have - of just colonizing Kepler 452b one day without calculating the consequences.

Another problem I have with referring to 452b as a "cousin" of Earth is that we don't even know if it possesses an atmosphere. Although it is certainly at the right distance and has a large enough g-value to retain an atmosphere we don't know: a) if one exists, or (b) - if one does - if its conducive to life as we know it (say Nitrogen and CO2 instead of Nitrogen, Oxygen).

We also don't know what kind of axial tilt, if any, exists. Bear in mind Earth has a tilt of 23.5 degrees which moderates our seasons. Thus, now in northern hemisphere summer,  the temperatures are warm though Earth is further away from the Sun. For Kepler 452b, imagine the same tilt orientation but occurring at orbital perihelion as opposed to near aphelion. Given the central star is 20% warmer than our own Sun (since its luminosity is 10 % greater) according to stats disclosed, that means the temperatures on Kepler 452b would be almost unbearable for humanoid life- even though it's 5% further from its Sun than we are from ours.

All this means that there is as yet too little hard data to really assert Kepler 452b is a legitimate "cousin" of our Earth. By the exterior trappings of distance to its sun, relative size, etc.  the indications are promising-  but still not a slam dunk. It is better to say it is a likely cousin of Earth, provided other factors (such as breathable atmosphere) also turn out to be present.

The Planetary Parade Continues

News of NASA's Kepler's telescope and its planetary findings continues to fascinate many, as more and more Earth-like planets are reported. Most recently, astronomers have reported for the first time the discovery of two Earth-sized planets, one of which (Kepler 20f) is almost the exact same size as Earth, and the other (Kepler 20e) is about 4/5 its radius. The pair were discovered between three much brighter planets orbiting a star designated as Kepler 20 in a solar system 1,000 light year distant. That means its light has taken 1,000 years to reach us and also when Kepler observes these planets now, or their sun, it is seeing them as they were in our year of 1011, when the Inquisition was barely being planned and no printed books yet existed.

On the downside, both planets appear much too hot to expect the emergence of any Earth-type carbon based life, and they may lack water or a normal atmosphere as well. Kepler 20f 's orbit is so near its star that its year lasts only 19.5 days or 0.053 Earth years. Using Kepler's 3rd law this leads to a distance of only about 0.14 AU or 13 million miles. By comparison with our system, the planet Mercury is about 36 million miles from the Sun and parts of its surface are hot enough to melt lead! Meanwhile, Kepler 20e is so close that its period is only 6.1 days or 0.017 yrs. so its distance works out to slightly over 6 mllion miles. Roast much?

Despite the unearthly conditions, Kepler astronomers are still confident that they will eventually detect one or more worlds that have very nearly Earth-like conditions as well as physical properties. After all, the odds are with them. Kepler is designed (see graphic attached) with ultra-sensitive photometers - to detect and analyze the slightest light variations- to look for any planets around 156,000 stars orbiting within 3,000 light years.

As the graphic shows, the craft can determine a number of key parameters, including:

- Planet size (from how much the light of the star dims when the planet passes in front)

we call this the "light curve" during partial eclipse and use it also for binary stars along with radial velocity curves, see e.g.

http://brane-space.blogspot.com/2011/09/solutions-to-intermediate-astronmoy-7.html

- - The size of the planet's orbit - calculated by the interval between dips of light during the "eclipse"

- The planet's temperature, computed from the orbital size (e.g. using semi-major axis a) and the temperature of its star (found from its spectrum)

Say the given planet is found to reflect a certain fraction A of light from its star, and hence must absorb (1- A) and that the "solar constant" of the star (amount of radiation arriving at the planet) is k, then the energy absorbed would be:

E(A) = (1 - A) πR^2 x k/ a^2

where R is the radius and a the mean distance from its star

Setting this equal to the stellar luminosity:

(1 - A) πR^2 x k/ a^2 = 4 π R^2 oT^4

enables one to work out the effective temperature T, where o = 5.67 x 10^-8 Wm^-2 K^-4, the Stefan-Boltzmann constant). Then:

T = {(1 - A) x k/ 4π a^2x o}^¼

- The star's surface temperature, meanwhile, was discussed in a previous blog in conjunction with its luminosity, e.g.

http://brane-space.blogspot.com/2011/09/solutions-to-intermediate-astronomy-9.html


The good news is more than 2,000 so-called exoplanets have been found. The bad news is we are still looking for that specific Earth-type planet that not only possesses similar gravity and size, mass, but also the distance from its star to put it in the 'Goldilocks zone" for life as we know it.