The Buzz Aldrin's object. Part I. Distance.

I was challenged to present the odds of the object observed during the Apollo 11 mission to be a SLA panel, travelling in the same direction that the CSM-LM on their way to the moon, and showing a close to constant apparent magnitude (not flashing).

The model below, is a simple but representative model for the panel.



Calculus of the distance of the object to the observers.

The telescope

Postulates
1. The object was observed through the telescope and had a recognizable shape.
2. Lets agree that they were able to use maximum useful magnification.
3. Lets agree that the telescope had a maximum resolution of 1" (1 second of arc).
4. Lets agree that the object was observed in the best scenario, namelly:
4.1 The light had its origin in a source (the sun) directly behind the observer (no angle between the sun-observer-object). This, in fact corresponds to the condition observed in that time frame ( the launch was on the 16th of July of 1969, which corresponds to 2 days after the new moon; because they were scheduled to land on the moon 3 days later (on the 20th), their direction was approximately to the position the moon would be by the 21th (first quarter); their direction of travelling is in good correlation with this postulate).
4.2 The panel presented to the observer its maximum apparent reflective surface (h x w).

Calculus

The distance, considering a 1" maximum resolution, and that it would resolve the two furthest points in the object, is given by the expression:
2 x Pi x L= 1,296,000 x ht or L=206,264 x ht (where L is the distance to the object and ht is the maximum length, which for the purpose below I will consider equal to h).

For a value of h=6.4 m, L= 1,320,090 m (1320 km).

According to Buzz Aldrin they could see ellipses and a bell shape. If we agree that such things would be observed in an object with the same apparent size of Júpiter or slightly higher (seen through a telescope), then with an apparent size of the object, to simplify things, of 60", L=22 km.

Thank you for reading.
Any comments on the model and proposals for postulates are welcome.

To come:
Part 2. apparent magnitude of the object.

a reply to: 2timesOO

Wait, math has a real world purpose..?

Perhaps, then, I should do my infinitesimal calculus homework .. *Sigh*


Anyway .. great work, 2times - I love seeing someone actually taking the time to do their own calculations and draw their own conclusions!

The issue of flashing has fascinated satellite observers for a long time, here is some background: www.satobs.org...

My only query is your assumption about the telescope, which was not a particularly powerful one and had a relatively wide viewing field. Its primary use was in navigation. That is as much information as I have been able to glean from what's available online!

If it helps, this photograph shows a roughly 4 Km swathe of the lunar surface from about 100 up using the sextant telescope (Apollo 12).

www.hq.nasa.gov...

a reply to: onebigmonkey

Well the optical characteristics of a telescope are defined by the aperture and focal distance (well, being a reflector or a refractor, and the quality of the materials used, will have their effect ). The useful maximum magnification will be a function mainly of the aperture. The maximum magnification depends on the focal distance of the eyepiece ... and so will the field of view, depending on the type of eyepiece (how the elements are combined in groups). I guess they had some eyepieces or a zoom eyepiece ... you know ... to have a little fun.
1" resolution is easily obtained with a 70 mm aperture telescope and a good short focal distance eyepiece.
If that's the only query, I'll move on based on those postulates.

Well. by all means continue with your calculations, but any conclusions you draw won't really be valid until your model parameters are reliable.

Here are some links about the 'telescope':

www.hq.nasa.gov...

airandspace.si.edu...

apollo.spaceborn.dk...

a reply to: onebigmonkey

No need, the telescope thing is just a cane (kind of a support), it will be backed up by other physical data (that curiously but not unexpectedly supports very well the analysis made about the telescope observation ...) let's assume that it's the panel and move on ... I already have a first set of probabilities, I will post them tomorrow.

a reply to: DupontDeux

Thanks for your support. You can be sure that it will be an unbiased analysis.

You can get much more testable range estimates from the telescopic observations of SLA panels near the CSM on several Apollo missions. What's stopping you from doing that math?

The exact range from Earth is available on page 200 of

www.jsc.nasa.gov...

where the request "Do you have any idea where the S-IVB is with respect

to us?" occurs shortly after 7/18/69, GET 60:47, CDT 21:09, and the

mission commentary had just given the range as "184,600 nautical miles

from earth," about 212,000 statute miles, speed 2061 mph. The crew

was preparing for sleep after putting the CSM into a passive thermal

roll ["barbecue mode"] of 3 revs per hour, or about 18 deg/minute.





Elsewhere, Aldrin has discussed his role:

mysteriousuniverse.org...



On Apollo 11 in route to the Moon, I observed a light out the window that appeared to be

moving alongside us. There were many explanations of what that could be, other than

another spacecraft from another country or another world – it was either the rocket

we had separated from, or the 4 panels that moved away when we extracted the lander

from the rocket and we were nose to nose with the two spacecraft. So in the close vicinity,

moving away, were 4 panels. And i feel absolutely convinced that we were looking at

the sun reflected off of one of these panels. Which one? I don’t know. So technically,

the definition could be “unidentified.”




We have telescopic observations of moon-bound Apollo spacecraft with

up to four flashing lights within a few tenths of an angular degree -- a few hundred miles at

those ranges. A summary of those observations and images is here:

www.astr.ua.edu... and I attach one image from Apollo-13.





Mike Collins made the observation that he could just barely make out a shape

[that seemed to change] through the CM sextant's small telescope whose technical specs are here:

www.ion.org... and here

fer3.com...

The instrument consisted of two telescopes. The first was a one-power, wide-field scanning telescope,

which was used to locate a star or constellation in space. The second was a 28-power sextant,

which took the actual reading.


The slow barbecue-mode roll would probably allow Collins to watch the flasher cross

the field of view, once he's lined it up to catch it every twenty minutes. Of course, they

could also watch it out a down-sun window. I don't know if the 28-power telescope was

removable from the sextant.



Something with just BARELY resolvable shape would be on the order of 0.01 deg across.

www.quora.com...





There were four SLA panels out there, 6.4 meters tall, about 3 meters wide at the apex,

and if they were at the range others were telescopically observed at on other missions,

they would be subtending visual angles of on the order of 0.001 degrees at about 100 miles out.

With a 28-power scope that puts it slightly above the physiological minimum to detect the existence

of a shape but not resolve it. Not proof, but comforting that it's consistent.



Recall the four panels would be distributed symmetrically around the CSM, but viewing

would only be possible from a shadowed window, so the fact that only one was seen

is not surprising.

a reply to: JimOberg

No need, I'm going to present my results in a few minutes.

originally posted by: 2timesOO
a reply to: JimOberg

No need, I'm going to present my results in a few minutes.

So you don't want anyone to use those telescope images to estimate range?

Seems if you were confident your results are accurate, you'd WANT corroboration from different methods.