





4. OK - what would it take to see them?



If we could put different sized telescopes in orbit around the Moon we could accomplish this.



The resolution of a space-based (diffraction-limited) telescope is given by the formula:



resolution (in radian measure) = 1.4 L/D

resolution (in arc seconds) = 1.4 L/D * 180 / π * 3600



Where: L = the wavelength of the light being observed (550 x 10 -9 m for visible light)

m for visible light) D = the diameter of the objective mirror (in metres) We would need a resolution that could see the landers clearly, that's about 0.42 metres (1/10th of the lander size) to make sure we were seeing the lander and not just a big rock.



Using 0.42 metres for "W" and calculating the distance from the Moon for various telescope sizes we get:

D (mm) 100 200 400 800 1600 2400 D (metres) 0.1 0.2 0.4 0.8 1.6 2.4 D (inches) 3.94 7.87 15.75 31.50 62.99 94.49 D (feet) 0.33 0.66 1.31 2.62 5.25 7.87 Maximum

Lunar

Orbit

Distance 54.5 km 109 km 218 km 436 km 873 km 1309 km



In other words, Hubble would have to be in orbit around the Moon at an altitude of 1300 km or less, instead of in orbit around the Earth at about 350 km altitude.









5. OK, so how else do we know that the landers and rovers are there? The astronauts recorded thousands of still images and hours and hours of movies of their descents, their explorations, and their departures - a historical record of the events. There exist movies of the astronauts driving several miles in their Lunar Rovers - something that would have taken the largest building ever constructed on Earth to simulate. There are also movies taken of the ascent stages blasting off from the moon (taken by cameras left behind) which would, of course, have blasted through the roof of any building unless it was also the tallest building ever constructed on Earth.

The moon rocks brought back by the astronauts have been examined by unbiased scientists all over the world and are unquestionably of lunar origin. Even the dust collected from their spacesuits on return was of Lunar origin.

The ALSEP science packages put on the surface by the astronauts radioed back significant amounts of data.

The ALSEP seismometers recorded "moonquakes", and when the astronauts returned to the Command Module they jettisoned the lander's ascent stages and crashed them into the moon and the seismometers recorded these events as well as the crashes of the Saturn IV B stages.

The Apollo 11, 14 and 15 missions left behind "corner reflectors" which astronomers (e.g. McDonald Observatory, Texas) can use to measure the distance between the Earth and the Moon precisely, even today. This has been upgraded recently to the Apache Point Observatory Lunar Laser-ranging Operation. We now know the range from the Moon to Texas within one millimetre.





6. Is there another way to "see them"?



Maybe - here's a challenge to those who are reading this.



The 2-dimensional diagram below shows the orientation of the Lunar Lander(s) on the Moon's surface during a Lunar month. Since the Moon always presents the same face to the Earth (the side the Apollo astronauts landed on), the "top" of the Lunar Landers Descent Stages (the part left on the Moon when the Astronauts left) generally point towards the Earth (i.e. we never see them "sideways"). As the Moon orbits the Earth, each point on the Lunar surface experiences sunrise, noon, sunset and midnight, except that it takes a full month to go through the cycle instead of an Earth day. From "Local Sunset" (at the top of the diagram) to "Local Sunrise" (at the bottom of the diagram) the landing sites are in darkness except for very weak "Earthshine" (i.e. the whole left side of the diagram). However, from Local Sunrise, through Local Noon, to Local Sunset, (the right side of the diagram) the landers are illuminated by bright sunlight at varying angles.



A lot of the Descent Stage was covered in bright gold foil and there might be other polished surfaces that could reflect some sunlight towards the Earth. The reflectivity of the Moon's surface (its albedo) averages 0.12 (i.e. it reflects about 12% of the light hitting it). In order for us to see a flash, the reflective surface on the lander would have to be oriented correctly, and have a reflection coefficient much greater than 12% after 33+ years of sitting on the lunar surface. The angle of these surfaces would have to be as shown in the diagram, but the angle continuously varies from 45° through 0° (flat) and back to 45° over the period from First Quarter Moon to Last Quarter Moon.







The exact coordinates of all landers are well known and are spread across the Moon's Surface.





The actual 3-dimensional reflection angles involved are more complicated than the simplified 2-dimensional diagrams above.

As pointed out by self-confessed New Zealand "space nut" Doug Bennett: the Apollo 15 Lunar Module had a distinct lean on due to one leg being in a crater. We do not know the exact angular tilt of any descent stage on the surface.

the landers are spread across the lunar surface (a sphere) at a range of lunar latitudes from -8.99° S to 26.1° N (only Apollo 11 is situated at the lunar equator). This means that if they point "upwards" on the moon, they actually form an angle with respect to the Earth depending on their actual northerly or southerly latitude.

the Earth is roughly 4 times bigger than the moon, so even at the distance of the moon, your observing position on the Earth affects the angle at which you would see each lander

the moon's orbit is inclined 5.16° with respect to the ecliptic which is tilted 23.4° with respect to the Earth's equator

the moon librates i.e. seems to "nod" up and down while orbiting (a fact that allows us to see a little more of the terrain around the moon's edges than we would if it were perfectly "still")

the moon's orbit precesses and through a complicated set of orbital alignments sometimes seems very "high" in the sky, or very "low" in the sky. As of late 2006, this angle is at its maximum providing some of the lowest (nearest the horizon) Full Moons that Northern Hemisphere observers have seen. All these angular factors contribute at different times, making the actual reflection angles a continuously varying phenomena at each site.



If someone were to videotape the landing zones continuously over this two-week period, we might see a flash from one or more landers as the sun angle and a piece of the spacecraft line up exactly to reflect sunlight into the observer's camera. The exact timing and angles are not known well enough to predict this. Also, since the Earth is rotating daily "under the Moon" we would need 2 or more cameras spread around the world, trained on the Moon at all times, in order to provide continuous coverage. The cameras would have to spend some time "zoomed in" on each site in turn, so the whole process would take several months (not including "re-takes" due to cloud cover or poor "seeing".





There have been other flashes observed and photographed on the Moon: Leonid meteors

Explosions?

Explosions?

A rogue Meteor?

In 1178, Gervase of Canterbury reported seeing a bright flash on the Moon

Is anyone up to this challenge?







7. The Flags on the Moon



Can we see the American flags planted on the Moon by the U.S. Astronauts?



The answer is Not Even Close!



Take another look at the "Apollo Lunar Lander Orientations during a Lunar Month" diagram above. The flag poles are are more-or-less vertical on the Moon (having been driven in by hand) which means they point generally upwards towards us on the Earth (see the discussion on actual angles above) - except for Apollo 11's - Buzz Aldrin saw the Apollo 11 flag fall over as the ascent stage took off from the Moon. The poles have a diameter hundreds of times smaller than the landers and the nylon flags themselves would be just a thin line, if they still exist at all after being blasted by solar radiation, UV, and sunlight for 33+ years. i.e. they might look something like the diagram on the right below. We would have to be right on top of them to see them, on the other hand, their shadows might be used as a sundial.







Side note - some people, having seen the following picture (or the video) assumed the Earth was on the horizon while the astronauts were on the Moon. This is not the case. The photograph was taken from the orbiting Command Module, circling the Moon. The landing sites were all timed to occur during local "dawn" on the moon about at the location of the Moon's terminator to take advantage of the oblique sun angle (as can be seen above) and slightly cooler temperatures. The Earth, however, was almost directly overhead of the landing sites as can be seen in the large diagram above. Also check the angle of the "corner reflector" in the photo above and you'll see that it is laying almost "flat", i.e. aimed "up" at the Earth from that lander's lunar position.











8. July 17, 2009, Sept 3, 2009, Oct 1, 2009 - Apollo Landing Sites imaged by satellite after almost 40 years!



As I stated above (several years ago), it would take a pretty good telescope in Lunar orbit to be able to resolve the Apollo landing sites.



Well, it's happened. On July 17, the Lunar Reconnaissance Orbiter released its first pictures of the Moon, including most of the Apollo landing sites taken with LROC - the 195mm LRO Cameras from a height of approximately 50km.



See the following links for the story http://www.skyandtelescope.com/news/home/51023977.html

http://www.nasa.gov/mission_pages/LRO/multimedia/lroimages/apollosites.html

http://lroc.sese.asu.edu/news/?archives/76-LROC%C3%A2%E2%82%AC%E2%84%A2s-First-Look-at-the-Apollo-Landing-Sites.html

In September 2011, the LRO site released newer, closer, better photographs of the Apollo sites fro a much lower orbit.

See: http://www.nasa.gov/mission_pages/LRO/news/apollo-sites.html.





The latest LRO images of Apollo landing sites can be found at:

http://www.nasa.gov/mission_pages/apollo/revisited/index.html







For higher resolution photographs of the

Apollo 11 landing site taken on October 1,

2009 see: this link or the link above.



January 6, 2014

For a "flipbook" of LRO images of the

Apollo 11 landing site including the

most recent images, see this link. Apollo 12



Sept 3, 2009 - This image shows the LRO spacecraft's first look at the Apollo 12 landing site.

The Intrepid lunar module descent stage, experiment package (ALSEP) and Surveyor 3

spacecraft are all visible. Astronaut footpaths are marked with unlabeled arrows.

This image is 824 meters (about 900 yards) wide. The top of the image faces North.

Credit: NASA/Goddard Space Flight Center/Arizona State University.



January 6, 2014 For a "flipbook" of LRO images of the Apollo 12 landing site

including the most recent images, see this link.





(magnified view)



January 6, 2014 For a "flipbook" of LRO images of the Apollo 14 landing site

including the most recent images, see this link.







January 6, 2014

For a "flipbook" of LRO images of the

Apollo 15 landing site including the

most recent images, see this link.





January 6, 2014

For a "flipbook" of LRO images of the

Apollo 16 landing site including the

most recent images, see this link.

For higher resolution photographs of the

Apollo 17 landing site see this link or the link above.



January 6, 2014

For a "flipbook" of LRO images of the

Apollo 17 landing site including the

most recent images, see this link.





Finally, if you're reading this page not to learn about angular resolution, but because you have heard something about a "moon landing hoax" then I suggest you visit the following sites:

http://www.clavius.org/

http://science.nasa.gov/headlines/y2001/ast23feb_2.htm

http://www.badastronomy.com/bad/tv/foxapollo.html

http://www.redzero.demon.co.uk/moonhoax/

http://www.squidoo.com/apollo-moon-landing-photos-from-space#module73500051 more pictures of the landing sites

http://dsc.discovery.com/tv/mythbusters/ Even the Mythbusters "totally busted" the urban legend/conspiracy about the Moon landings.

