Starship Asterisk*

MarkBour wrote: ↑Wed Jan 16, 2019 12:48 am

neufer wrote: ↑Sun Jan 13, 2019 9:40 pm The operation of a 1D mirror is essentially the "square root"
of the operation of a 2D mirror (= a 180º rotation).

30 years ago I coauthored a paper on "square root" F(0.5, z) operations:
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"Functional Powers near a Fixed Point"
by Lawrence J. Crone and Arthur C. Neuendorffer,
_Journal of Mathematical Analysis and Applications_,
Vol.132, No.2 June 1988.

Abstract: It is proved that if a function F(z) is analytic in a neighborhood of a fixed point z₀, and if 0 < ¦F′(z₀)¦ < 1, then there exists a family of related functions F(p, z), each defined in a neighborhood of z₀, which act as functional powers of F(z). In particular, F(0, z) = z, F(1, z) = F(z), and F(p, F(q, z)) = F(p + q, z). It is further demonstrated that the family of functions F(p, z) is identical with the set of nonconstant analytic functions with fixed point z₀ which commute with F(z).
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Not quite sure I follow your 1D/2D terminology, but I gather you're just labeling the number of times the light changes direction. Then, sure, one can view the twice-reflected transformation as the product of two single-reflection transforms. (Although when used in its usual configuration, I'd say a single-plane mirror's transform, when squared, would result in the identity transform.)

MarkBour wrote: ↑Wed Jan 16, 2019 12:48 am
Interesting paper abstract. Are these functions of the complex plane (locally analytic there)?

neufer wrote: ↑Sun Jan 13, 2019 9:40 pm The operation of a 1D mirror is essentially the "square root"
of the operation of a 2D mirror (= a 180º rotation).

30 years ago I coauthored a paper on "square root" F(0.5, z) operations:
--------------------------------------------------------------------------
"Functional Powers near a Fixed Point"
by Lawrence J. Crone and Arthur C. Neuendorffer,
_Journal of Mathematical Analysis and Applications_,
Vol.132, No.2 June 1988.

Abstract: It is proved that if a function F(z) is analytic in a neighborhood of a fixed point z₀, and if 0 < ¦F′(z₀)¦ < 1, then there exists a family of related functions F(p, z), each defined in a neighborhood of z₀, which act as functional powers of F(z). In particular, F(0, z) = z, F(1, z) = F(z), and F(p, F(q, z)) = F(p + q, z). It is further demonstrated that the family of functions F(p, z) is identical with the set of nonconstant analytic functions with fixed point z₀ which commute with F(z).
-------------------------------------------------------------

MarkBour wrote: ↑Sun Jan 13, 2019 6:21 am
When I first saw this, the term "non-reversing mirror" made perfect sense for what such a mirror does. Because I know that we tend to view a mirror reflection as a sort of "reversal", based on the way we think about it all. But upon further reflection (sorry) it seems that regular mirrors are actually the non-reversing ones, and it would be more appropriate to call these double mirrors "reversing mirrors". I guess this is kind of a subtle issue in human psychology, and that most people would disagree with me here. If you rotate these mirrors 90 degrees and see yourself standing upside down in the image, however, then I think the majority of folks would be in agreement with me. But I'm sure the terminology is too entrenched, to try to overturn it, anyway. I see that these doubly-reflecting arrangements are also called "flip mirrors". I could go for that term as the one I much prefer.

https://www.etymonline.com/word/reverse#etymonline_v_29895 wrote:
reverse (adj.) c. 1300, from Old French revers "reverse, cross, opposite" (13c.), from Latin reversus, past participle of revertere "turn back, turn about, come back, return" (see revert). Reverse angle in film-making is from 1934. Reverse discrimination is attested from 1962, American English.

reverse (v.) early 14c. (transitive), "change, alter;" early 15c. (intransitive), "go backward," from Old French reverser "reverse, turn around; roll, turn up" (12c.), from Late Latin reversare "turn about, turn back," frequentative of Latin revertere.

reverse (n.) mid-14c., "opposite or contrary" (of something), from reverse (adj.) or from Old French Related: revers "the opposite, reverse." Meaning "a defeat, a change of fortune" is from 1520s; meaning "back side of a coin" is from 1620s. Of gear-shifts in motor cars, from 1875. As a type of sports play (originally rugby) it is recorded from 1921.

neufer wrote: ↑Fri Jan 11, 2019 6:20 pm

https://en.wikipedia.org/wiki/Non-reversing_mirror wrote: <<A non-reversing mirror (sometimes referred to as a flip mirror) is a mirror that presents its subject as it would be seen from the mirror.>>

MarkBour wrote: ↑Fri Jan 11, 2019 5:44 pm
(I had never even heard of corner reflector prisms before this -- they're pretty neat optics.)

https://en.wikipedia.org/wiki/Non-reversing_mirror wrote:

Comparison of reflections of a pen in an ordinary mirror (left) and two perpendicular mirrors forming the first type of non-reversing mirror (right). The latter also illustrates the unsightly line in the middle if measures are not taken to minimise it.

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<<A non-reversing mirror (sometimes referred to as a flip mirror) is a mirror that presents its subject as it would be seen from the mirror. A non-reversing mirror can be made by connecting two regular mirrors at their edges at a 90 degree angle. If the join is positioned so that it is vertical, an observer looking into the angle will see a non-reversed image. This can be seen in places such as public toilets when there are two mirrors mounted on walls which meet at right angles. Such an image is visible while looking towards the corner where the two mirrors meet. The problem with this type of non-reversing mirror is that there is usually a line down the middle interrupting the image. However, if first surface mirrors are used, and care is taken to set the angle to exactly 90 degrees, the join can be made almost invisible.>>

MarkBour wrote: ↑Fri Jan 11, 2019 5:44 pm (I had never even heard of corner reflector prisms before this -- they're pretty neat optics. Shows how little I know about this subject, since I get the impression they are in common use for a number of applications.)

neufer wrote: ↑Fri Jan 11, 2019 3:13 pm Shooting lasers with the Moon at zenith has no effect on angular momentum. However, if one only shoots when the Moon is approaching (i.e., from apogee to perigee) then one can slow the Moon until it has the least Energy for its fixed angular momentum (i.e., a circular orbit of radius R_c= 2/[1/apogee + 1/perigee] = 382800 km versus the current semi-major axis of 384400 km. If one only shoots when the Moon is receding (i.e., from perigee to apogee) then one can speed up the Moon until it has the most Energy for its fixed angular momentum (i.e., a parabolic orbit of Perigee = R_c/2 = 191400 km.

Chris Peterson wrote: ↑Fri Jan 11, 2019 5:48 am

MarkBour wrote: ↑Fri Jan 11, 2019 5:23 am I was thinking only of those Apollo reflectors that apparently only will be useful if the Moon is almost exactly overhead (right?)

Why? The reflectors are made up of an array of corner cube prisms. They always reflect light back in the same direction of the incoming light. So it doesn't matter where the Moon is, other than atmospheric extinction possibly being an issue once it gets fairly close to the horizon.

The Apollo program's prisms are recessed into shallow cylinders, so sunlight illuminates them fully only at high noon.

MarkBour wrote: ↑Fri Jan 11, 2019 5:23 am

neufer wrote: ↑Thu Jan 10, 2019 3:54 am

MarkBour wrote: ↑Thu Jan 10, 2019 3:21 am
Aha! So, we're pushing the moon away, Mr. Heisenberg?

• Not necessarily.

If the lasers are pointing to the West then they will impart added angular momentum L_E to the Earth's rotation of
up to: L_E = R_EP_lt/c where R_E = the Earth's radius, P_l is the laser power & t is the duration time of the lasing.

If these laser beams intercept the Moon (and are essentially absorbed)
then the Moon must lose an equal amount of angular momentum (thereby bringing it closer).

Ha! Fascinating point. I was thinking only of those Apollo reflectors that apparently only will be useful if the Moon is almost exactly overhead (right?) But if the lasers are fired at other things, such as the LRO, I guess that can happen in whatever direction. (Well, they can certainly fire whenever they want, but to get any useful data, they'd have to at least hit an appropriately-inclined reflective surface on the object.) I guess folks in multiple nations fire range-finding lasers into space all the time and in all sorts of directions:
https://www.youtube.com/watch?v=u1guaP6e8os

I don't know if they have to know what they're aiming at and if they have to get specific about it, or if they can just aim at a typical metal satellite whenever it passes and assume they'll get a usable reflection. Anyway, if they hit the LRO, they would alter its orbit around the Moon, rather than the Moon's orbit around us.

But back to the Moon. I suppose if they hit it at all times of evening, it would average out to the same as hitting it when it is straight overhead (actually I should be saying "at zenith"). I'm actually thinking that there would be some tendency (for psychosocial reasons) to hit it more often when it is in the East, but maybe not.

But what you're telling me is that I can bring the Moon down, if I shoot at it when it is going down.

MarkBour wrote: ↑Fri Jan 11, 2019 5:23 am I was thinking only of those Apollo reflectors that apparently only will be useful if the Moon is almost exactly overhead (right?)

neufer wrote: ↑Thu Jan 10, 2019 3:54 am

MarkBour wrote: ↑Thu Jan 10, 2019 3:21 am
Aha! So, we're pushing the moon away, Mr. Heisenberg?

• Not necessarily.

If the lasers are pointing to the West then they will impart added angular momentum L_E to the Earth's rotation of
up to: L_E = R_EP_lt/c where R_E = the Earth's radius, P_l is the laser power & t is the duration time of the lasing.

If these laser beams intercept the Moon (and are essentially absorbed)
then the Moon must lose an equal amount of angular momentum (thereby bringing it closer).

MarkBour wrote: ↑Thu Jan 10, 2019 3:21 am
Aha! So, we're pushing the moon away, Mr. Heisenberg?

• Not necessarily.

neufer wrote: ↑Mon Jan 07, 2019 2:45 pm

Laser Ranging Facility at at NASA's Goddard Space Flight Center in Greenbelt, Md

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Chris Peterson wrote: ↑Mon Jan 07, 2019 5:17 pm
The laser launch telescope is a 40 cm refractor (acting as a 20x beam expander) with a 97.7% throughput. That telescope is baffled and coated with a light absorbing material. So I'm guessing we're not seeing any scattered light from the optical train at all. Most likely, the telescope and dome structures are simply illuminated by the primary atmospheric scatter. I'm not sure if that would be visible to our eyes or not, but it's not in the least surprising it would be captured by an exposure long enough to record this much depth in the sky field.

Chris Peterson wrote: ↑Mon Jan 07, 2019 5:17 pm
The laser launch telescope is a 40 cm refractor (acting as a 20x beam expander) with a 97.7% throughput. That telescope is baffled and coated with a light absorbing material. So I'm guessing we're not seeing any scattered light from the optical train at all. Most likely, the telescope and dome structures are simply illuminated by the primary atmospheric scatter. I'm not sure if that would be visible to our eyes or not, but it's not in the least surprising it would be captured by an exposure long enough to record this much depth in the sky field.

https://www.eso.org/public/teles-instr/paranal-observatory/vlt/vlt-instr/4lgsf/ wrote:

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<<April 2016 saw the arrival of four new stars above the Paranal skies. After years of development, ESO has completed the installation of the 4 Laser Guide Star Facility or 4LGSF, a new subsystem of the Adaptive Optics Facility (AOF) at the Very Large Telescope (VLT).

The 4LGSF complements the Laser Guide Star Facility (LGSF). Instead of one laser, the 4LGSF sends four laser beams into the skies to produce four artificial stars by exciting sodium atoms located in the atmosphere at an altitude of 90 kilometres. Each laser delivers 22 watts of power — about 4000 times the maximum allowed for a laser pointer — in a beam with a diameter of 30 centimetres.

Lasers can excite sodium atoms in the mesosphere, which is located 90–110 kilometres above the Earth’s surface. The fluorescent light that is emitted by the sodium atoms and collected by the telescope is affected by the atmosphere in the same way as the light emitted by real stars is. So, the fluorescent light from the sodium atoms can be used by the adaptive optics system to measure and compensate for the distortions introduced by the atmosphere.

ESO and several European institutes and industries, including TOPTICA, Germany; TNO, the Netherlands; MPB Communications, Canada; Optec, Italy; Astrel, Italy; and Laseroptik, Germany and INAF–Osservatorio di Roma, have made significant contributions to the project. The new 4LGSF is based on several new technologies. One of these is fibre Raman laser technology, which was developed by ESO and transferred to industry, resulting in a Raman fibre amplifier laser that is lighter, more rugged, and represents a breakthrough in size and stability.

All the operations at the 4LGSF will follow a protocol to avoid any risk to aircraft. The laser system is equipped with an automatic aircraft avoidance system that shuts down the lasers if an aircraft ventures too close to the beams.>>

alter-ego wrote: ↑Mon Jan 07, 2019 4:35 am

Guest2 wrote: ↑Sun Jan 06, 2019 11:06 pm There should be acknowledgement this is a FAKE image (or at least that it's enhanced. )
Laser beams are invisible unless reflected off smoke dust fog or some other particulates.
The light shining on the dome doors is obviously faked.

Second, since these LGS lasers have a Gaussian (continuous) intensity distribution, scattering within the optical tube assembly will occur at some level from one or multiple mirrors. I suspect that what we see is primary or secondary scattering at the exit aperture of that launch tube.

geckzilla wrote: ↑Mon Jan 07, 2019 7:45 am

Guest2 wrote: ↑Sun Jan 06, 2019 11:06 pm There should be acknowledgement this is a FAKE image (or at least that it's enhanced. )
Laser beams are invisible unless reflected off smoke dust fog or some other particulates.
The light shining on the dome doors is obviously faked.

you are not the only person to call one of these laser images fake
it happens every time one gets posted to APOD
but you are still wrong.

starsurfer wrote: ↑Mon Jan 07, 2019 11:20 am
First there was fake news and now there's fake APODs?

What would Donald Trump think?

Guest2 wrote: ↑Sun Jan 06, 2019 11:06 pm There should be acknowledgement this is a FAKE image (or at least that it's enhanced. )
Laser beams are invisible unless reflected off smoke dust fog or some other particulates.
The light shining on the dome doors is obviously faked.

https://www.nasa.gov/multimedia/imagegallery/image_feature_1768.html wrote:

Image Credit: NASA

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Observe the Moon
Sept. 28, 2010

<<This photograph shows the Laser Ranging Facility at the Geophysical and Astronomical Observatory at NASA's Goddard Space Flight Center in Greenbelt, Md. The observatory helps NASA keep track of orbiting satellites. In this image, the lower of the two green beams is from the Lunar Reconnaissance Orbiter's dedicated tracker. The other laser originates from another ground system at the facility. Both beams are pointed at the moon - specifically at LRO in orbit around the moon.>>

https://www.skyandtelescope.com/astronomy-news/pesky-problems-for-lunar-reflectors/ wrote:

A powerful laser illuminates a spot of high thin clouds on its way to the totally eclipsed Moon in December 2010. The target was a bank of retroreflectors left on the Sea of Tranquility by Apollo 11 astronauts. Jack Dembicky / Apache Point Observatory

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Pesky Problems for Lunar Reflectors
By: Kelly Beatty | February 21, 2014

<<Astronomers back on Earth periodically fire lasers at these suitcase-size banks of reflectors to determine where the Moon is in its orbit and, specifically, precisely how far it is from Earth. Initially, the laser ranging was good to an accuracy of about 15 cm, 100 times better than any previous method.

But in recent years the accuracy has gotten down to nearly 1 mm, thanks to an effort led by Thomas Murphy (University of California, San Diego) using the 3.5-m reflector at Apache Point Observatory in New Mexico. (Amusingly, Murphy has named the effort the "Apache Point Observatory Lunar Laser-ranging Operation," or APOLLO.) Moreover, thanks to Lunar Reconnaisance Orbiter's images of the long-lost Lunokhod 1 rover (spotted by Russian scientists, by the way), the count of available reflector sites on the Moon now stands at five.

Some years ago, Murphy and his colleagues noticed that the laser pulses were coming back to Earth weaker than expected. "Each shot sends about 10¹⁷ [100 quadrillion] photons toward the Moon, and in good conditions we detect about one return photon per shot," the team noted in an article published in Icarus. That's only about a tenth of what should be coming back, leading to suspicion that a microscopic veneer of lunar dust has coated (or abraded) about half the area of the exposed optical surfaces.

But something else is causing weak returns, and the dropoff gets particularly bad (by another factor of 10) around full Moon. In Icarus, Murphy and his team surmised that the problem is due to distortions in the optics due to heat from the Sun. The Apollo program's prisms are recessed into shallow cylinders, so sunlight illuminates them fully only at high noon — that is, around the time of full Moon. The thermal effect is much worse for the Lunokhod arrays — they can't be used at all during the lunar day.

One way to confirm this hypothesis would be to monitor the reflectors' performance during a total lunar eclipse. The rapid plunge into shadow, Murphy reasoned, should allow the optics to cool and relax. Some earlier observations during eclipses already hinted that solar heating was indeed the culprit, but Apache Point was clouded out during lunar eclipses in 2007 and 2008.

Fortunately, clear skies prevailed during the total lunar eclipse of December 21, 2010, and for 5½ hours the team bounced laser pulses off three Apollo reflector arrays and a fourth on Lunophod 1. Sure enough, the efficiency immediately improved, as Murphy and others report in the March 1st issue of Icarus. Interestingly, none of the laser pulses fired at Lunokhod 1 during the eclipse resulted in detections. However, as the team comments, "In general, the Lunokhod arrays are more susceptible to thermal disruptions than the Apollo arrays, so the lack of returns from Lunokhod 1 during the eclipse is not entirely surprising.">>

Guest2 wrote: ↑Sun Jan 06, 2019 11:06 pm There should be acknowledgement this is a FAKE image (or at least that it's enhanced. )
Laser beams are invisible unless reflected off smoke dust fog or some other particulates.
The light shining on the dome doors is obviously faked.

Guest2 wrote: ↑Sun Jan 06, 2019 11:06 pm There should be acknowledgement this is a FAKE image (or at least that it's enhanced. )
Laser beams are invisible unless reflected off smoke dust fog or some other particulates.
The light shining on the dome doors is obviously faked.