Earth's Shadow (APOD 20 Aug 2008)

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Expand view Topic review: Earth's Shadow (APOD 20 Aug 2008)

Re: Lunar ranging

by Czerno » Wed Sep 24, 2008 2:10 pm

Chris Peterson wrote: Just estimating, but I'd say there's little difference. The beam has lost coherency by the time it gets to the Moon, and the light that reflects back isn't a tight beam at all. It illuminates a large area on the Earth- much larger than the distance the Earth moves during the time-of-flight.
Ah, I see, so twas a false good idea. One more :-(
Be as it may, centimetre to millimetre precision on those absolute distance measurements is fantastic ! Have the results already served as checks against the "theories" that were used previously for the calculation of ephemerids - Brown's, Spenser Jones's - or is it too early ?

thanks, and regards

Re: Lunar ranging

by Chris Peterson » Tue Sep 23, 2008 2:18 pm

Czerno wrote:Re: lunar ranging. Can someone provide a calculated or estimated value for how much higher the intensity of the light received would be (per unit surface) if the detector were near the center of the returning beam ?
Just estimating, but I'd say there's little difference. The beam has lost coherency by the time it gets to the Moon, and the light that reflects back isn't a tight beam at all. It illuminates a large area on the Earth- much larger than the distance the Earth moves during the time-of-flight.[/quote]
Assuming it would be some order of magnitudes higher than the meager count of photons detected at the transmitter site, then why not offset a smaller, lighter telescope to a location at the right distance west of the emittor ?
In any case, the difference is not orders of magnitude. You wouldn't want to make the telescope much smaller, because you still have a weak signal. And keeping track of the exact time difference between the sending an receiving would be more of a challenge using different sites.

AFAIK, the setup in Texas receives plenty of signal for the necessary measurements. Since it isn't signal limited, there would seem to be no advantage in adding another scope, even if the return signal could be stronger someplace else.

Lunar ranging

by Czerno » Tue Sep 23, 2008 7:38 am

Re: lunar ranging. Can someone provide a calculated or estimated value for how much higher the intensity of the light received would be (per unit surface) if the detector were near the center of the returning beam ?

Assuming it would be some order of magnitudes higher than the meager count of photons detected at the transmitter site, then why not offset a smaller, lighter telescope to a location at the right distance west of the emittor ?

Understanding the "right" distance has to be varied, depending primarily on the actual earth-moon distance at the time of the experiment, such a smaller detector could be mobile. Quick mental calculation, knowing that actual eart to moon distance varies by as much as ~ +-10%suggests an 100-200 meter long, east-west oriented track, with its middle point some 2.5km west from the main apparatus (transmitter).

Does this scheme calculate out, both scientifically and economically or am I grossly wrong ?

--
Czerno

Re: Laser reflections

by henk21cm » Thu Sep 04, 2008 9:06 pm

Chris Peterson wrote: I simply meant that if you made a simple drawing of the 2D case, it should become pretty clear how a retroreflector works. But I can do that:
Image
Thanks Chris, now i see it. During the Apollo flights i heared about these reflectors but i never understood how they worked. In 1969 the internet and Google were not even dreams in the eyes of Darpa, let alone a school boy. That retroreflector riddle nagged me for almost 40 years!
Chris wrote:That's Snell's Law, not Snellius (in spite of the fact that it's named after Snellius).
Sorry, that is a language related item, in my language it is called "De wet van Snellius".
Chris wrote:And you don't need to use it. Retroreflectors made as mirrors have no boundary between different indexes of refraction, so the law doesn't apply.


Just another fact (hollow structure) i did not know. I was thinking of chunks of glass, with perpendicular faces polished on them. And even for the solid structure: the incident angle and the returning angle inside the solid are the same, and since refraction at an interface is invariant under reversion, it does not matter.
Chris wrote:assuming it (correction for air) is actually necessary for lunar ranging.
Interesting remark. It made me wonder and trigger some activity. In the handbook of Chemistry and Physics (52nd edition) on page E204 the refractive index of air is given. At λ=600 nm the refractive index is 1.00028. Lets assume that after 60 km the refractive index is 1. On average (very crude 0th order approximation, the air pressure does not decrease linearly) the refractive index is 1 + 1.5E-4 (= 1+a). The speed of light in the atmosphere is then

v = c/(1+a).

The time needed for a pulse of light to cross the atmosphere is:

Δt = H/v = (H/c)(1+a) = Δt_{0} + Δt_{extra}

The extra time needed due to the atmosphere is

Δt_{extra} = Ha/c => 60 * 1.5E-4 / 3E5 ≈ 30 ns.

30 ns is about 9 m in length. So neglecting the atmosphere is not an option, if you want to find something like 38 mm.

I found an empirical relation by Edien for the refractive index on page 5 of http://www.feanor.com/laser_principles.pdf, but i have serious doubts about the size of the Δn correction in its equation (5). According to the sensitivity 0.0039 in stead of 0.057 in the exponent is more likely. I can't trace down the original article by Edien.

Re: Laser reflections

by Chris Peterson » Thu Sep 04, 2008 3:03 am

henk21cm wrote:It is not my intention to be rude, but the phrase "It is simple to see" is synonymous with "the author did not bother to elaborate, after three weeks of intensive calculations the result can be found".
I simply meant that if you made a simple drawing of the 2D case, it should become pretty clear how a retroreflector works. But I can do that:

Image

I've drawn two rays, and you can see that each exits at the same angle it enters, because at each reflection the entry and exit angle is the same. In general, for a ray that strikes the first surface at an angle theta with respect to that surface, it reflects at angle theta from that surface. It strikes the next surface at angle 90 - theta, and therefore reflects at angle 90 - theta. Since the second surface is rotated 90° with respect to the first, the total reflection angle is 180 - theta; that is, a 180° reflection.
By the way, Snellius law is involved, since a retroreflector has a boundary between the material it is made of and the vacuum between earth and moon.
That's Snell's Law, not Snellius (in spite of the fact that it's named after Snellius). And you don't need to use it. Retroreflectors made as mirrors have no boundary between different indexes of refraction, so the law doesn't apply. Retroreflectors made as prisms do show refraction, but if you apply Snell's law you'll see that the entrance and exit refraction cancel out, so again you can just consider the system as reflective.
Using IR one might be able to excite the rotational bands of CO2. Lets send out a pulse of light. It travels through roughly 60 km of atmosphere. Reflection is likely proportional to the atmospheric pressure (the more atoms, the more reflection). So during the first 0.4 ms a sharply decreasing reflection pulse is recorded. Assuming that the probability per atom for reflection is constant, it is possible to derive some sort of distribution for the pressure. Assuming that the speed of light as function of pressure is known, from the reflection curve during the first 0.4 ms the extra time delay (with respect to vacuum) can be deduced. Is that what you mean?
That might be one approach. The method I was referring to depends on the knowledge of the height that the fluorescent species is found, and looking at the time of flight. I'm sure there are many methods that can be used for characterizing the atmosphere, assuming it is actually necessary for lunar ranging.

Re: Laser reflections

by henk21cm » Wed Sep 03, 2008 8:52 pm

G'day Chris,
Chris Peterson wrote:It's simple to see why it works if you first consider the 2D case.
The only rule you need is that the angle of incidence equals the angle of reflection. Snell's law deals with refraction, which isn't involved here.
It is not my intention to be rude, but the phrase "It is simple to see" is synonymous with "the author did not bother to elaborate, after three weeks of intensive calculations the result can be found". Additionally "Typical results are shown in the graph" should be read as "These are the best results". "The sample was accidentally strained" should be read as "It dropped on the floor". Nevertheless i'll do my best. By the way, Snellius law is involved, since a retroreflector has a boundary between the material it is made of and the vacuum between earth and moon. As far as the reflections are concerned, indeed angle of reflection is equal to the incident angle.
Chris wrote:The laser stimulates certain atoms in the atmosphere (such as sodium) to fluoresce. By picking of part of the return signal and passing it through the appropriate filters, this can be detected. By measuring the timing precisely, some characteristics of the atmosphere can be determined. I don't know how critical this is, as the passage through the atmosphere is very short. A simple model of density may be all that's required to reach the point where something else is limiting accuracy.
Using IR one might be able to excite the rotational bands of CO2. Lets send out a pulse of light. It travels through roughly 60 km of atmosphere. Reflection is likely proportional to the atmospheric pressure (the more atoms, the more reflection). So during the first 0.4 ms a sharply decreasing reflection pulse is recorded. Assuming that the probability per atom for reflection is constant, it is possible to derive some sort of distribution for the pressure. Assuming that the speed of light as function of pressure is known, from the reflection curve during the first 0.4 ms the extra time delay (with respect to vacuum) can be deduced. Is that what you mean?

by NoelC » Wed Sep 03, 2008 8:04 pm

Regarding the Moon orbiting the Earth...

Not to detract from the APOD that started all this, but I did an animation of a number of lunar still images taken at intervals of several seconds... I find viewing it helps make the rotation of the moon around the Earth seem more real. Note that the crescent moon eclipses a star at one point, then some thin clouds blow through.

There's a little bit of wobble in the sequence; that's my fault for not getting the frames perfectly aligned. Sorry about that.

Note that the part of the moon you can see mostly in this image is illuminated by earthshine.

Image

-Noel

Re: Laser reflections

by Chris Peterson » Wed Sep 03, 2008 4:31 am

henk21cm wrote:In the wiki i can read that it differs from a plane mirror. It is a constellation of three perpendicular perfectly flat reflecting planes. The reason (proof or explanation) why for any incident angle the light is reflected in the same direction, is missing. I guess its a matter of repetative application of Snellius law.
It's simple to see why it works if you first consider the 2D case. The only rule you need is that the angle of incidence equals the angle of reflection. Snell's law deals with refraction, which isn't involved here.
Regarding the ever changing path (different heights above the horizon) of the laser through the earths atmosphere
you wrote:This has to be compensated for. I believe the current method involves measuring scatter and fluorescence from the beam in the atmosphere to determine the path characteristics.
First of all there is refraction, which means that the atmospheric pressure influences the speed of light and so the apparent distance between moon and earth. (The actual deviation as caused by refraction is not the key issue). As far a i understand scatter is mainly caused by microscopic airborne particles, next to Rayleigh scatter. The reason for fluorescence i do not understand. If you could be so kind to elucidate that aspect, it would be appreciated.
The laser stimulates certain atoms in the atmosphere (such as sodium) to fluoresce. By picking of part of the return signal and passing it through the appropriate filters, this can be detected. By measuring the timing precisely, some characteristics of the atmosphere can be determined. I don't know how critical this is, as the passage through the atmosphere is very short. A simple model of density may be all that's required to reach the point where something else is limiting accuracy.

Re: Laser reflections

by henk21cm » Tue Sep 02, 2008 8:38 pm

Chris Peterson wrote:The reflectors are arrays of corner prisms, aka retroreflectors. These cannot help but to send reflected light back along the same path it entered on.
In the wiki i can read that it differs from a plane mirror. It is a constellation of three perpendicular perfectly flat reflecting planes. The reason (proof or explanation) why for any incident angle the light is reflected in the same direction, is missing. I guess its a matter of repetative application of Snellius law.

Regarding the ever changing path (different heights above the horizon) of the laser through the earths atmosphere
you wrote:This has to be compensated for. I believe the current method involves measuring scatter and fluorescence from the beam in the atmosphere to determine the path characteristics.
First of all there is refraction, which means that the atmospheric pressure influences the speed of light and so the apparent distance between moon and earth. (The actual deviation as caused by refraction is not the key issue). As far a i understand scatter is mainly caused by microscopic airborne particles, next to Rayleigh scatter. The reason for fluorescence i do not understand. If you could be so kind to elucidate that aspect, it would be appreciated.
Second is a geometrical aspect: the location of the observer on earth is varying. A rather precise description of the geoide (the shape of the surface of the earth) is needed, since a simple sphere is too inaccurate.

Regarding DIY experiments
you wrote: It would be difficult. Even using large mirrors (several meters) to collimate the beam, the laser pattern is kilometers across by the time it reaches the Moon.
A mirror of several meters is far beyond amateur equipment: i must forget it.
neufer wrote:The part of the project I worked on (in 1968) was the corner reflectors:
A linearly polarized laser beam into the reflector comes back out the way it came in but...it comes out elliptically polarized. (This does not pose much of a problem however.)
So the detector must be of the non-polarized type. And again one loses some sensitivity.

Re: Laser reflections

by neufer » Thu Aug 21, 2008 10:10 pm

Chris Peterson wrote:
henk21cm wrote:Why is the laser light relefected so preceisely back to earth and not somewhere near the earth?
The reflectors are arrays of corner prisms, aka retroreflectors. These cannot help but to send reflected light back along the same path it entered on.
Of course the moon is moving 1.022 km/s so there is the problem of light aberration (which is different on the way out that it was on the way in); hence, the peak of the return beam misses the earth telescope by about 2 miles. (One can thing of it as the moon giving the reflected photons some angular momentum forward.)

http://en.wikipedia.org/wiki/Aberration_of_light

Re: Laser reflections

by neufer » Thu Aug 21, 2008 9:50 pm

henk21cm wrote:[*]On radio frequencies the Faraday rotation is a real pain in the neck. To overcome this phenomenon, you need to switch to circular polarisation, since the resulting polarisation is all over the place. Are there any problems due to Faraday rotation with these laser pulses? [/list]
The part of the project I worked on (in 1968) was the corner reflectors:

A linearly polarized laser beam into the reflector comes back out the way it came in but...it comes out elliptically polarized. (This does not pose much of a problem however.)

by neufer » Thu Aug 21, 2008 9:41 pm

NoelC wrote:
The moon probably has a liquid core of about 20% of the Moon's radius.
I can only guess that they must see it wobbling or something to infer this.
Probably the lunar "libration" wobble has different dynamics
http://antwrp.gsfc.nasa.gov/apod/ap070602.html
(just as an uncooked egg twisting at the end of a rope will have different dynamics from a hard boiled egg.)
NoelC wrote:
The universal force of gravity is very stable. The experiments have put an upper limit on the change in Newton's gravitational constant G of less than 1 part in 1011 since 1969.
I had no idea there was a concern over whether the force of gravity might be changing over time. I view the concept as ultimately possible, I just didn't realize anyone thought it might be something worth testing. A change of 1 part in 1011 isn't really small potatoes. Do they really think it might be changing near that much? I'd think we'd have no luck at all with missions to the outer solar system if we didn't have gravity nailed down to eleventy seven decimal places... :)
Of course that's 1 part in 10^11 which totally demolishes
Dirac's suggestion of ~ 1 part in 10^10 per year.
http://en.wikipedia.org/wiki/Dirac_larg ... hypothesis
NoelC wrote:
The moon is spiralling away from Earth at a rate of 38 mm per year
Anyone got a good reference for an explanation of why this is? Seems to me if the Moon is dragging the tides around on the Earth, it ought to be losing energy, not gaining it. Is it because the Earth is spinning some 28 times faster than the moon's orbital period? Is the Earth slowing down?
Because the Earth is spinning some 28 times faster than the moon's orbital period the earth's (moon generated) tides actual precede the moon such that these tides are dragging the moon around. The earth thereby looses angular momentum which the moon gains. Days are getting longer.... but then so are months since the moon is flung outward to longer orbits of higher angular momentum.

Re: Laser reflections

by Chris Peterson » Thu Aug 21, 2008 9:22 pm

henk21cm wrote:Why is the laser light relefected so preceisely back to earth and not somewhere near the earth?
The reflectors are arrays of corner prisms, aka retroreflectors. These cannot help but to send reflected light back along the same path it entered on.
How does the ever changing path (different heights above the horizon) of the laser through the earths atmosphere influence the measurements?
This has to be compensated for. I believe the current method involves measuring scatter and fluorescence from the beam in the atmosphere to determine the path characteristics.
From what you describe i guess that one needs rather elaborate equipment to send and receive pulses. Other than moonbounce, as done by radio amateurs on 2m and 70 cm (and 23 cm) is it possible for us, the common amateur astronomer, to send out light pulses to the moon and receive these pulses back?
It would be difficult. Even using large mirrors (several meters) to collimate the beam, the laser pattern is kilometers across by the time it reaches the Moon. Only a tiny fraction is reflected by the retroreflector array. So you need a big telescope and a powerful laser (powerful enough that FAA clearance is required to shine it upwards).

by Chris Peterson » Thu Aug 21, 2008 9:13 pm

NoelC wrote:
The moon probably has a liquid core of about 20% of the Moon's radius.
I can only guess that they must see it wobbling or something to infer this.
To be fair, this is not established. There are various well regarded theories about the Moon's core, including little iron or a small, solid iron region.
I had no idea there was a concern over whether the force of gravity might be changing over time.
There is a strong interest in measuring all physical constants to extreme precision in order to determine if they are, indeed, constant. The gravitational constant is one of the hardest to measure, and has only been established to about one part in 10^13. Many physical constants have been determined with much higher accuracy.
The moon is spiralling away from Earth at a rate of 38 mm per year
Anyone got a good reference for an explanation of why this is? Seems to me if the Moon is dragging the tides around on the Earth, it ought to be losing energy, not gaining it. Is it because the Earth is spinning some 28 times faster than the moon's orbital period? Is the Earth slowing down?
The tidal drag is slowing the Earth down. The rotational angular momentum of the Earth is being transferred to orbital angular momentum of the Moon. So the radius of the Moon's orbit increases.

Laser reflections

by henk21cm » Thu Aug 21, 2008 9:03 pm

G'day Art,

You quoted the wiki on the reflectors on the moon. More specifically: the accuracy which was improved to near mm accuracy. That means that the time of flight must be accurate to 10 ps, (100 GHz being 3 mm). The time of flight is about 2.5 s, so a remarkable accuracy. That has rizen a few questions, which i boldly will pose.
  • The space between moon and earth is not empty. Solar wind spoils the pure vacuum. Therefore the speed of light is somewhat slower than in vacuo. What is the magnitude of the correction for non-vacuum conditions? And how do the fluctuations in solar wind influence these measurements?
  • Why is the laser light relefected so preceisely back to earth and not somewhere near the earth? Due to the non constant orbital velocity of the moon in comparison with the constant axial rotational period, the moon shakes her head, so it is virtually impossible to align a mirror that it reflects the light back to earth.
  • How does the ever changing path (different heights above the horizon) of the laser through the earths atmosphere influence the measurements?
  • From what you describe i guess that one needs rather elaborate equipment to send and receive pulses. Other than moonbounce, as done by radio amateurs on 2m and 70 cm (and 23 cm) is it possible for us, the common amateur astronomer, to send out light pulses to the moon and receive these pulses back?
  • On radio frequencies the Faraday rotation is a real pain in the neck. To overcome this phenomenon, you need to switch to circular polarisation, since the resulting polarisation is all over the place. Are there any problems due to Faraday rotation with these laser pulses?

by NoelC » Thu Aug 21, 2008 8:39 pm

Great post, neufer. I learned a thing or two, and you got me a thinkin'...
The moon probably has a liquid core of about 20% of the Moon's radius.
I can only guess that they must see it wobbling or something to infer this.
The universal force of gravity is very stable. The experiments have put an upper limit on the change in Newton's gravitational constant G of less than 1 part in 1011 since 1969.
I had no idea there was a concern over whether the force of gravity might be changing over time. I view the concept as ultimately possible, I just didn't realize anyone thought it might be something worth testing. A change of 1 part in 1011 isn't really small potatoes. Do they really think it might be changing near that much? I'd think we'd have no luck at all with missions to the outer solar system if we didn't have gravity nailed down to eleventy seven decimal places... :)

Oh and lastly...
The moon is spiralling away from Earth at a rate of 38 mm per year
Anyone got a good reference for an explanation of why this is? Seems to me if the Moon is dragging the tides around on the Earth, it ought to be losing energy, not gaining it. Is it because the Earth is spinning some 28 times faster than the moon's orbital period? Is the Earth slowing down?

-Noel

by neufer » Thu Aug 21, 2008 8:19 pm

emc wrote:[Well there we go again... reality dashing the dream of another space artist. "Man's got to know his limitations."
More interesting & successful is a project I was a part of once:
-----------------------------------------------------------
http://en.wikipedia.org/wiki/Lunar_Lase ... Experiment
Lunar Laser Ranging Experiment

<<The ongoing Lunar Laser Ranging Experiment measures the distance between the Earth and the Moon using laser ranging. Lasers on Earth are aimed at retroreflectors previously planted on the Moon and the time delay for the reflected light to return is determined. Since the speed of light is known with very great accuracy, the distance to the moon can be calculated. This distance has been measured with increasing accuracy for more than 35 years.

The distance continually changes for a number of reasons, but averages about 384,467 kilometers (238,897 miles).

The experiment was first made possible by a retroreflector array installed on July 21, 1969, by the crew of the Apollo 11. Two more retroreflector arrays left by the Apollo 14 and Apollo 15 missions have contributed to the experiment.

The unmanned Soviet Lunokhod 1 and Lunokhod 2 rovers carried smaller arrays. Reflected signals were initially received from Lunokhod 1, but no return signals have been detected since 1971, at least in part due to some uncertainty in its location on the Moon. Lunokhod 2's array continues to return signals to Earth.

The Apollo 15 array is three times the size of the arrays left by the two earlier Apollo missions. Its size made it the target of three-quarters of the sample measurements taken in the first 25 years of the experiment. Improvements in technology since then have resulted in greater use of the smaller arrays, by sites such as the McDonald Observatory and the OCA Laser-Lune telemetry station affiliated with the Côte d'Azur Observatory.

At the Moon's surface, the beam is only about 6.5 kilometers (four miles) wide and scientists liken the task of aiming the beam to using a rifle to hit a moving dime 3 kilometers (two miles) away. The reflected light is too weak to be seen with the human eye, but under good conditions, one photon will be received every few seconds (they can be identified as originating from the laser because the laser is highly monochromatic). This is one of the most precise distance measurements ever made, and is equivalent to determining the distance between Los Angeles and New York to one hundredth of an inch. As of 2002 work is progressing on increasing the accuracy of the Earth-Moon measurements to near millimeter accuracy.

Some of the findings of this long-term experiment are:

* The moon is spiralling away from Earth at a rate of 38 mm per year.

* The moon probably has a liquid core of about 20% of the Moon's radius.

* The universal force of gravity is very stable. The experiments have put an upper limit on the change in Newton's gravitational constant G of less than 1 part in 1011 since 1969.

* Einstein's theory of gravity (the general theory of relativity) predicts the moon's orbit to within the accuracy of the laser ranging measurements.

Additionally, the accuracy of these experiments has improved historic knowledge of the Moon's orbit enough to permit timing of solar eclipses up to 3,400 years ago.

The presence of reflectors on the Moon has been used to refute claims that the Apollo landings were faked. For example, the figure on the left shows evidence of something very small, located within a few kilometers of where a landing occurred, and which reflects laser light directly back to the source as well as a mirror array.>>
-----------------------------------------------------------

2 b real or ! 2 b real: that's the photoshop question

by henk21cm » Thu Aug 21, 2008 6:45 pm

John Newstead wrote:I am unhappy about the sequencing of the overlaps. How come the fourth image from left in in front of all others if this be a time sequence. Or am I just dumb and the whole composite is Photoshopped?
Yes John, it is photoshopped. In a real multi exposed image parts of the moon would have been overlapping, creating a chaotic image. Another way to see that it is photoshopped: place a ruler over the north poles of the moon. They are not in straight line, neither a curved line.

by emc » Thu Aug 21, 2008 6:14 pm

neufer wrote:
emc wrote:So are you telling me there's no hope of making bunny ears appear in our moon shadow? :(
Maybe if you can get Gort to help out...
----------------------------------------------
Artist Wants to Paint Moon, But Physics May Foil Plan
By Robert Roy Britt Senior Science Writer
posted: 07:00 am ET 10 August 2001
http://www.space.com/scienceastronomy/g ... 810-1.html

<<An artist hoping to recruit millions of laser-pointer owners to "paint the Moon" may instead be disappointed by physics.

...[snipped]">>
Well there we go again... reality dashing the dream of another space artist. "Man's got to know his limitations."

by neufer » Thu Aug 21, 2008 6:01 pm

emc wrote:So are you telling me there's no hope of making bunny ears appear in our moon shadow? :(
Maybe if you can get Gort to help out...
----------------------------------------------
Artist Wants to Paint Moon, But Physics May Foil Plan
By Robert Roy Britt Senior Science Writer
posted: 07:00 am ET 10 August 2001
http://www.space.com/scienceastronomy/g ... 810-1.html

<<An artist hoping to recruit millions of laser-pointer owners to "paint the Moon" may instead be disappointed by physics.

James T. Downey, the artist behind the project, is intent on creating a "collaborative work of celestial art" by illuminating a fleeting red spot on our only natural satellite.

The event, an effort to help people "find the excitement of space," is scheduled for two nights, one in October and another in November. Downey has chosen a target location for the beams on the dark portion of the Moon while it's in its first-quarter. Each attempt would last five minutes. A web site, called "Paint the Moon," has been set up with instructions for where and how to point your laser and why you should participate.

"Inexpensive yet surprisingly powerful laser-pointing devices have become ubiquitous in America," said Downey. "Millions of people own such a device. Laser light stays coherent over vast distances, the beams spreading very little."

Lasers are powerful devices, concentrated bursts of energy that can damage the eye, cut through metal or, theoretically, shoot down enemy missiles. And all at the speed of light. Astronomers use lasers to measure distances between telescopes and even to enhance observations in order to improve resolution of light coming from distant stars. Experiments planted by Apollo astronauts allow scientists to use lasers to more accurately gauge the distance from Earth to the Moon, and even detect moonquakes.

But all technology has its limits. It seems there are not enough people in North America to make Downey's idea work.

"As I suspected, the number required is not millions of people, but more than millions of millions of millions of people," said Donald Umstadter, a laser expert at the Center for Ultrafast Optical Science at the University of Michigan, Ann Arbor.

Umstadter became curious about the project when SPACE.com asked him if it was feasible to illuminate the Moon in this way. He asked one of his graduate students, Chad Vandenbosch, to look into the possibility as a mathematical exercise.

To calculate how many people it would take to successfully make a temporary red spot on the Moon visible from Earth, Vandenbosch estimated several factors. He considered a typical handheld laser pointer's power and how much of the light would be absorbed by Earth's atmosphere, as well as how much of the laser light would be reflected by the Moon vs. how much would be absorbed.

As a premise, he based the calculations on what would be needed to make the spot visible to people in cities, where bright lights would obscure a faint spot that might otherwise be visible in rural locations.

A reader says there's another reason why this won't work.

Vandenbosch said there is a little wiggle room in his calculations due to the estimate of background light.

"The main thing to glean from the calculation is that the divergence of these pointers, due to their small aperture and a basic law of optics governing the diffraction of light, results in a huge diameter beam, and thus very dim beam, by the time it arrives at the Moon," Umstadter said.

Downey, the artist, was intrigued and a bit dismayed when he learned of Vandenbosch's science, but plans to proceed with the artistic attempt nonetheless.

"I knew that it would be a long shot from the start," Downey said. "But success is something that can be measured in a lot of ways. We may not be able to accomplish actually painting the Moon, but still the act of participating in something such as this has value."

In what way?

"If I can get people thinking about the Moon as something they might be able to touch, if I can get science teachers to talk about the physics involved, Moon phases, etc., if I can just help people find the excitement of space as part of the human drama again, then the project will have been a grand success."

Downey also doesn't want to spoil a good party.

"In emails, I hear from people who are planning parties around the event, who become enraptured with the whole notion and tell all their friends," he said. "Of course, I also hear from people who think the entire idea is just plain lunacy, and tell me I should be locked up for spreading such tripe. But hey, art is like that."

Downey came up with the idea as part of a novel he's writing, set 50 years into the future. "A couple of characters are discussing oddball things back at the beginning of the millenium, and this comes up. I thought that it would be fun if someone read my book (assuming I can get it published, of course) and actually tried to organize such an event, thereby having life imitate art.">>

by emc » Thu Aug 21, 2008 5:52 pm

Chris Peterson wrote:
emc wrote:The terminator in this eclipse sense is the edge peak right?
I think so. It's the line between night and day on the Earth. If you were standing there, with the setting (or rising) Sun at your back and the partially eclipsed Moon in front of you, your shadow would be cast on the Moon.
So everything along this edge peak casts a penumbral (low contrast) silhouette? And this can be resolved with a telescope? I think I am following you but the real bunny ears casting a shadow on the moon has me stunned.
Yes, everything along the edge must cast a shadow out into space. Realistically, it would have to be very large- probably mountain range sized- to be detectable at all as a shadow on the Moon. And while it's theoretically true that you could see even small objects silhouetted against the Sun using a telescope from the Moon, in actual practice you have to worry about practical resolution. You won't see a rabbit's silhouette without a telescope with an aperture of hundreds of meters.
Ok - So we won't be making any shadow puppets for the moon... Thanks for helping me understand. It was fun to contemplate. :)

by Chris Peterson » Thu Aug 21, 2008 5:38 pm

emc wrote:The terminator in this eclipse sense is the edge peak right?
I think so. It's the line between night and day on the Earth. If you were standing there, with the setting (or rising) Sun at your back and the partially eclipsed Moon in front of you, your shadow would be cast on the Moon.
So everything along this edge peak casts a penumbral (low contrast) silhouette? And this can be resolved with a telescope? I think I am following you but the real bunny ears casting a shadow on the moon has me stunned.
Yes, everything along the edge must cast a shadow out into space. Realistically, it would have to be very large- probably mountain range sized- to be detectable at all as a shadow on the Moon. And while it's theoretically true that you could see even small objects silhouetted against the Sun using a telescope from the Moon, in actual practice you have to worry about practical resolution. You won't see a rabbit's silhouette without a telescope with an aperture of hundreds of meters.

by emc » Thu Aug 21, 2008 5:25 pm

Chris Peterson wrote:
emc wrote:So are you telling me there's no hope of making bunny ears appear in our moon shadow? Not even with two gigantic space elevator docking/transfer stations?
Even a real bunny standing on the Earth's terminator casts its shadow on the Moon. In the case of a space elevator, the cables would cast shadows, as would the docking station. But the docking station would be too far out for both its and Earth's shadow to be on the Moon at the same time unless greatly foreshortened (that is, with the Earth, Moon, and docking station approaching being in line).

The problem is that the shadows in all these cases are penumbral, so the contrast is low. Imagine you were on the Moon, looking towards the shadow casting structures (possibly with a telescope). You would see them silhouetted against the Sun, but not blocking the Sun completely. In order to get an umbral shadow on the Moon, the occluding object needs to have the same angular size as the Sun- 1/2°. In other words, from the Moon, an object at Earth's distance would have to be Moon-sized: about 3500 km across. While a space elevator is longer than this radially, it is very much narrower in the other direction.
The terminator in this eclipse sense is the edge peak right? So everything along this edge peak casts a penumbral (low contrast) silhouette? And this can be resolved with a telescope? I think I am following you but the real bunny ears casting a shadow on the moon has me stunned.

Could this be an expanded art form taking shadow play to the moon?!

by Chris Peterson » Thu Aug 21, 2008 4:59 pm

emc wrote:So are you telling me there's no hope of making bunny ears appear in our moon shadow? Not even with two gigantic space elevator docking/transfer stations?
Even a real bunny standing on the Earth's terminator casts its shadow on the Moon. In the case of a space elevator, the cables would cast shadows, as would the docking station. But the docking station would be too far out for both its and Earth's shadow to be on the Moon at the same time unless greatly foreshortened (that is, with the Earth, Moon, and docking station approaching being in line).

The problem is that the shadows in all these cases are penumbral, so the contrast is low. Imagine you were on the Moon, looking towards the shadow casting structures (possibly with a telescope). You would see them silhouetted against the Sun, but not blocking the Sun completely. In order to get an umbral shadow on the Moon, the occluding object needs to have the same angular size as the Sun- 1/2°. In other words, from the Moon, an object at Earth's distance would have to be Moon-sized: about 3500 km across. While a space elevator is longer than this radially, it is very much narrower in the other direction.

by emc » Thu Aug 21, 2008 4:41 pm

neufer wrote:
emc wrote:Getting back to this APOD... I have a question... How large and how high would a construction need to be from earth to create a shadow on the moon? According to the earth shadow angle displayed on the moon and the horizon angle displayed in the ISS photos... the structure would need to be many times higher and larger than the ISS to make an impression. Just curious.

http://en.wikipedia.org/wiki/Space_elevator
The problem is that the sun is not a point source of light.

An opaque moon sized object will produce a penumbra
twice the size of the moon at the distance of the moon
but only a small umbral shadow.

On the other hand, the earth's thin (~10km. thick) atmosphere
already produces the dark red "shadow" of a total solar eclipse.

http://antwrp.gsfc.nasa.gov/apod/ap070308.html
http://antwrp.gsfc.nasa.gov/apod/ap070302.html
http://antwrp.gsfc.nasa.gov/apod/ap041030.html
http://antwrp.gsfc.nasa.gov/apod/ap010104.html
Hi Art,

So are you telling me there's no hope of making bunny ears appear in our moon shadow? Not even with two gigantic space elevator docking/transfer stations? :(

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