[math-fun] Maps from earthshine?
I'm always interested in how much can be figured out from how little. The recent gravitational wave observation, and the reconstruction of its source, is a perfect example. Earthshine is the illumination of the dark part of the Moon by the Earth. How bright it is depends on the phase of the Earth as seen from the Moon, how much of the illuminated part of the Earth that's visible from the Moon is cloud-covered, how much is ice-covered, how much is cloud-free ice-free land, and how much is cloud-free ice-free ocean. Also, its color depends on how what's doing the reflecting (clouds, ice, water, desert land, vegetation, etc.). My question is how good a map of the Earth it would be possible to construct from careful measurements of earthshine from one location on Earth. Assume its brightness can be accurately measured even in the daytime (or explain why it can't be). Note that the Moon's latitude as well as its longitude varies considerably, so it doesn't always have an equatorial view. Decades of observations can be combined so as to average out the clouds and concentrate on long-term features. I'm envisioning an alternate history in which photometry, advanced math, and computers were developed before world travel. (And in fact, the nature of earthshine was understood long before Columbus.) Also, a hypothetical skeptic who wonders if other continents really exist as depicted on maps, and only trusts his own observations, given that computers, telescopes, and photometers are cheaper than world travel. (One final aside on moonlight and gravitational waves: Has anyone else noticed that the peak flux of the gravitational wave event, GW150914, on Earth was seven times the flux of the light of the full Moon? If it was visible light, you could not only have seen it, but could have read by its light. LIGO isn't really very sensitive!)
Sounds a lot like http://graphics.stanford.edu/papers/dual_photography/ On Sun, Feb 21, 2016 at 12:59 PM, Keith F. Lynch <kfl@keithlynch.net> wrote:
I'm always interested in how much can be figured out from how little. The recent gravitational wave observation, and the reconstruction of its source, is a perfect example.
Earthshine is the illumination of the dark part of the Moon by the Earth. How bright it is depends on the phase of the Earth as seen from the Moon, how much of the illuminated part of the Earth that's visible from the Moon is cloud-covered, how much is ice-covered, how much is cloud-free ice-free land, and how much is cloud-free ice-free ocean. Also, its color depends on how what's doing the reflecting (clouds, ice, water, desert land, vegetation, etc.).
My question is how good a map of the Earth it would be possible to construct from careful measurements of earthshine from one location on Earth. Assume its brightness can be accurately measured even in the daytime (or explain why it can't be). Note that the Moon's latitude as well as its longitude varies considerably, so it doesn't always have an equatorial view. Decades of observations can be combined so as to average out the clouds and concentrate on long-term features.
I'm envisioning an alternate history in which photometry, advanced math, and computers were developed before world travel. (And in fact, the nature of earthshine was understood long before Columbus.) Also, a hypothetical skeptic who wonders if other continents really exist as depicted on maps, and only trusts his own observations, given that computers, telescopes, and photometers are cheaper than world travel.
(One final aside on moonlight and gravitational waves: Has anyone else noticed that the peak flux of the gravitational wave event, GW150914, on Earth was seven times the flux of the light of the full Moon? If it was visible light, you could not only have seen it, but could have read by its light. LIGO isn't really very sensitive!)
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-- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
https://www.youtube.com/watch?v=p5_tpq5ejFQ On Mon, Feb 22, 2016 at 10:42 AM, Mike Stay <metaweta@gmail.com> wrote:
Sounds a lot like http://graphics.stanford.edu/papers/dual_photography/
On Sun, Feb 21, 2016 at 12:59 PM, Keith F. Lynch <kfl@keithlynch.net> wrote:
I'm always interested in how much can be figured out from how little. The recent gravitational wave observation, and the reconstruction of its source, is a perfect example.
Earthshine is the illumination of the dark part of the Moon by the Earth. How bright it is depends on the phase of the Earth as seen from the Moon, how much of the illuminated part of the Earth that's visible from the Moon is cloud-covered, how much is ice-covered, how much is cloud-free ice-free land, and how much is cloud-free ice-free ocean. Also, its color depends on how what's doing the reflecting (clouds, ice, water, desert land, vegetation, etc.).
My question is how good a map of the Earth it would be possible to construct from careful measurements of earthshine from one location on Earth. Assume its brightness can be accurately measured even in the daytime (or explain why it can't be). Note that the Moon's latitude as well as its longitude varies considerably, so it doesn't always have an equatorial view. Decades of observations can be combined so as to average out the clouds and concentrate on long-term features.
I'm envisioning an alternate history in which photometry, advanced math, and computers were developed before world travel. (And in fact, the nature of earthshine was understood long before Columbus.) Also, a hypothetical skeptic who wonders if other continents really exist as depicted on maps, and only trusts his own observations, given that computers, telescopes, and photometers are cheaper than world travel.
(One final aside on moonlight and gravitational waves: Has anyone else noticed that the peak flux of the gravitational wave event, GW150914, on Earth was seven times the flux of the light of the full Moon? If it was visible light, you could not only have seen it, but could have read by its light. LIGO isn't really very sensitive!)
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
-- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
Far more moondane: Did any ancients figure out the angles of the Earth-Sun-Moon triangle from carefully observing the lunar crescent? --reg On 2016-02-21 12:59, Keith F. Lynch wrote:
I'm always interested in how much can be figured out from how little. The recent gravitational wave observation, and the reconstruction of its source, is a perfect example.
Earthshine is the illumination of the dark part of the Moon by the Earth. How bright it is depends on the phase of the Earth as seen from the Moon, how much of the illuminated part of the Earth that's visible from the Moon is cloud-covered, how much is ice-covered, how much is cloud-free ice-free land, and how much is cloud-free ice-free ocean. Also, its color depends on how what's doing the reflecting (clouds, ice, water, desert land, vegetation, etc.).
My question is how good a map of the Earth it would be possible to construct from careful measurements of earthshine from one location on Earth. Assume its brightness can be accurately measured even in the daytime (or explain why it can't be). Note that the Moon's latitude as well as its longitude varies considerably, so it doesn't always have an equatorial view. Decades of observations can be combined so as to average out the clouds and concentrate on long-term features.
I'm envisioning an alternate history in which photometry, advanced math, and computers were developed before world travel. (And in fact, the nature of earthshine was understood long before Columbus.) Also, a hypothetical skeptic who wonders if other continents really exist as depicted on maps, and only trusts his own observations, given that computers, telescopes, and photometers are cheaper than world travel.
(One final aside on moonlight and gravitational waves: Has anyone else noticed that the peak flux of the gravitational wave event, GW150914, on Earth was seven times the flux of the light of the full Moon? If it was visible light, you could not only have seen it, but could have read by its light. LIGO isn't really very sensitive!)
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https://en.wikipedia.org/wiki/On_the_Sizes_and_Distances_(Aristarchus) On Mon, Feb 22, 2016 at 11:32 AM, rwg <rwg@sdf.org> wrote:
Far more moondane: Did any ancients figure out the angles of the Earth-Sun-Moon triangle from carefully observing the lunar crescent? --reg
On 2016-02-21 12:59, Keith F. Lynch wrote:
I'm always interested in how much can be figured out from how little. The recent gravitational wave observation, and the reconstruction of its source, is a perfect example.
Earthshine is the illumination of the dark part of the Moon by the Earth. How bright it is depends on the phase of the Earth as seen from the Moon, how much of the illuminated part of the Earth that's visible from the Moon is cloud-covered, how much is ice-covered, how much is cloud-free ice-free land, and how much is cloud-free ice-free ocean. Also, its color depends on how what's doing the reflecting (clouds, ice, water, desert land, vegetation, etc.).
My question is how good a map of the Earth it would be possible to construct from careful measurements of earthshine from one location on Earth. Assume its brightness can be accurately measured even in the daytime (or explain why it can't be). Note that the Moon's latitude as well as its longitude varies considerably, so it doesn't always have an equatorial view. Decades of observations can be combined so as to average out the clouds and concentrate on long-term features.
I'm envisioning an alternate history in which photometry, advanced math, and computers were developed before world travel. (And in fact, the nature of earthshine was understood long before Columbus.) Also, a hypothetical skeptic who wonders if other continents really exist as depicted on maps, and only trusts his own observations, given that computers, telescopes, and photometers are cheaper than world travel.
(One final aside on moonlight and gravitational waves: Has anyone else noticed that the peak flux of the gravitational wave event, GW150914, on Earth was seven times the flux of the light of the full Moon? If it was visible light, you could not only have seen it, but could have read by its light. LIGO isn't really very sensitive!)
_______________________________________________
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-- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
From this reference
http://www.aei.mpg.de/~schutz/download/lectures/AzoresCosmology/Schutz.Azore... the flux (power per unit area) carried by a gravitational wave of frequency f and strain h is F = (pi/4) (c^3/G) f^2 h^2 = (3.2 mW/m^2) (h / 1e-22)^2 (f / 1 kHz)^2. At the peak of the recently detected wave, h = 1e-21, f = 100 Hz, so that F[peak] = 3.2 mW/m^2. Note that strain is dimensionless. Unlike the situation in an elastic solid, the gravitational wave flux is necessarily frequency dependent, since a static strain is merely the use of a different scale for the x, y, and z axes, and this is just flat space. The constant c^3 / G = (3e8 m s^-1)^3 / (6.67e-11 kg^-1 m^3 s^-2) = 4.05e35 W m^-2 Hz^-2. Since general relativity is classical, Planck's constant can't appear, and the constant must be constructed from G and c only. If the frequency dependence were any power of f other than f^2, this would not be possible. About 2% of the Sun's luminosity is emitted as neutrinos. That's 20 mW/m^2 at Earth. -- Gene From: Keith F. Lynch <kfl@KeithLynch.net> To: math-fun@mailman.xmission.com Sent: Sunday, February 21, 2016 12:59 PM Subject: [math-fun] Maps from earthshine? (One final aside on moonlight and gravitational waves: Has anyone else noticed that the peak flux of the gravitational wave event, GW150914, on Earth was seven times the flux of the light of the full Moon? If it was visible light, you could not only have seen it, but could have read by its light. LIGO isn't really very sensitive!)
Resubmitting this post to correct an error. The solar neutrino flux at Earth is 20 W/m^2, not 20 W/m^2.Nimble fingered Pacher Christoph pointed this out to me before I could post the correction myself. -- Gene From: Eugene Salamin <gene_salamin@yahoo.com> To: math-fun <math-fun@mailman.xmission.com> Sent: Monday, February 22, 2016 4:00 PM Subject: Re: [math-fun] Maps from earthshine?
From this reference
http://www.aei.mpg.de/~schutz/download/lectures/AzoresCosmology/Schutz.Azore... the flux (power per unit area) carried by a gravitational wave of frequency f and strain h is F = (pi/4) (c^3/G) f^2 h^2 = (3.2 mW/m^2) (h / 1e-22)^2 (f / 1 kHz)^2. At the peak of the recently detected wave, h = 1e-21, f = 100 Hz, so that F[peak] = 3.2 mW/m^2. Note that strain is dimensionless. Unlike the situation in an elastic solid, the gravitational wave flux is necessarily frequency dependent, since a static strain is merely the use of a different scale for the x, y, and z axes, and this is just flat space. The constant c^3 / G = (3e8 m s^-1)^3 / (6.67e-11 kg^-1 m^3 s^-2) = 4.05e35 W m^-2 Hz^-2. Since general relativity is classical, Planck's constant can't appear, and the constant must be constructed from G and c only. If the frequency dependence were any power of f other than f^2, this would not be possible. About 2% of the Sun's luminosity is emitted as neutrinos. That's 20 W/m^2 at Earth. -- Gene From: Keith F. Lynch <kfl@KeithLynch.net> To: math-fun@mailman.xmission.com Sent: Sunday, February 21, 2016 12:59 PM Subject: [math-fun] Maps from earthshine? (One final aside on moonlight and gravitational waves: Has anyone else noticed that the peak flux of the gravitational wave event, GW150914, on Earth was seven times the flux of the light of the full Moon? If it was visible light, you could not only have seen it, but could have read by its light. LIGO isn't really very sensitive!)
Um, how does 20 W/m^2 differ from 20 W/m^2 ? —Dan
On Feb 22, 2016, at 4:11 PM, Eugene Salamin via math-fun <math-fun@mailman.xmission.com> wrote:
Resubmitting this post to correct an error. The solar neutrino flux at Earth is 20 W/m^2, not 20 W/m^2.Nimble fingered Pacher Christoph pointed this out to me before I could post the correction myself.
Oh, I screwed up again. It's 20 W/m^2, not 20 mW/m^2. I'm sorry to be wasting everyone's time over this. -- Gene From: Dan Asimov <asimov@msri.org> To: Eugene Salamin <gene_salamin@yahoo.com>; math-fun <math-fun@mailman.xmission.com> Sent: Monday, February 22, 2016 4:33 PM Subject: Re: [math-fun] Maps from earthshine? Um, how does 20 W/m^2 differ from 20 W/m^2 ? —Dan
On Feb 22, 2016, at 4:11 PM, Eugene Salamin via math-fun <math-fun@mailman.xmission.com> wrote:
Resubmitting this post to correct an error. The solar neutrino flux at Earth is 20 W/m^2, not 20 W/m^2.Nimble fingered Pacher Christoph pointed this out to me before I could post the correction myself.
participants (5)
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Dan Asimov -
Eugene Salamin -
Keith F. Lynch -
Mike Stay -
rwg