# Telescope Power

Ian J.
Hi all,

Yet another question (all coming up due to re-examining my novels for rewriting):

Regarding telescopes, how powerful would a telescope have to be to make out a two lane road / highway on our moon, and when (in Earth history) did someone build such a telescope?

I'm not looking for seeing enough detail to make out road markings, but just enough power to make out the route and know that it's artificial.

TIA

## Answers and Replies

Mentor
Looks like a simple plug and chug: http://en.wikipedia.org/wiki/Angular_resolution

$$\Delta l = 1.220 \frac {f\lambda}{D}$$

Assuming 5 meters resolution, distance of 300000 km and 562 nm light I got 40 meters diameter. Can be I am completely off.

Ian J.
Many thanks, I didn't even know what it would have been called as a subject, so that wikipedia article sets me off in the right direction by the look of it. If your calculation is correct, then I'm in the clear with detail visibility. The 'people' looking won't be anywhere near 40m, and they'll be dealing with two atmospheres in the way of them too (their world, and for my story, one for the moon they're observing).

Ian J.
According to the Wikipedia article, that equation seems to be for microscopes. As a non-scientist, I have trouble understanding equations, but the article seems to suggest that the equation below it would be for 'small sensors imaging a subject at infinity'?

I have to apologize in advance as I don't understand the various symbols properly, and I have no knowledge of how to use the tex markup language to put the equation here instead of directing readers to the article:

http://en.wikipedia.org/wiki/Angular_resolution#Explanation

It's the third equation in the section 'Explanation'.

Mentor
As far as I can tell in the end the difference is just in the constant factor, so the ballpark is most likely OK.

Staff Emeritus
Regarding telescopes, how powerful would a telescope have to be to make out a two lane road / highway on our moon, and when (in Earth history) did someone build such a telescope?

I'm not looking for seeing enough detail to make out road markings, but just enough power to make out the route and know that it's artificial.
That depends on what you mean by "see".

What is the albedo of your moon compared to the albedo of the roadway? For example, one wouldn't need to resolve down to five meters to see long straight lines on the Moon if our Moon had some white cement five meter wide roadways on it.

Ian J.
As far as I can tell in the end the difference is just in the constant factor, so the ballpark is most likely OK.

OK, thanks for clarifying. I think I still need to learn more about equations though, and how to post them here, but that's for another time.

That depends on what you mean by "see".

What is the albedo of your moon compared to the albedo of the roadway? For example, one wouldn't need to resolve down to five meters to see long straight lines on the Moon if our Moon had some white cement five meter wide roadways on it.

The moon in question would have a variable colouring for the landmass, some parts vegetation, others desert, still others rock of varying colours. I suppose roadways would vary much as they do here on Earth, so could be light coloured concrete through to dark tarmac. I think the telescope technology of the viewing people would be quite primitive, perhaps similar to the kind of telescopes that were being developed during the late 17th century during the enlightenment.

Mentor
Good point by D H, I took the question rather literally.

Try Google Earth - start at say 400 km and scroll slowly through the land and see if anything looks artificial - straight lines for example. You will be surprised in how many places we are easily visible from the space. Surprisingly, it is especially true over deserts.

Plus, during the night lights will tell everything. Thing is the original question was not about detection, but about telescope...

Ian J.
A bit of clarification regarding why I asked the question. I have a society on Moon One, that is not advanced technologically, who are looking at Moon Two which is populated by a society on the verge of manned exploration of other moons. The amount Moon One can see, and what they can make of it, will have an effect on how their society views Moon Two and what it harbours in the way of life. If they can understand the lights and surface details as to have been made by sentient beings, then that is very different to if all they can see is a few patches of lights at night, and maybe grey discolouration of those areas during the day. So the detail level, the Angular Resolution, of their few telescopes becomes quite important, from a story telling point of view.

Mentor
I can confirm Borek's calculations (for telescopes, the focal distance has to be replaced with the distance of the object).
Seeing a road is easier, as mentioned. A 17th-century telescope is not sufficient, but you won't need the E-ELT (under construction, 42m diameter).

The angular resolution limit of the eye is ~1mm at 1m, but you can easily see a hair (~100µm diameter) from a distance of much more than a meter. I guess a telescope with a diameter of .5m to 1m is sufficient, even with naked human (!) eyes instead of a camera. That would correspond to the late 18th century.

If your civilization uses lights at night, you don't need a telescope at all. The pattern alone shows this is life, much more than roads do.

Staff Emeritus
I may be wrong here but I don't think you necessarily need a physical telescope but could do with an array of interferometers dispersed over the same area?

Staff Emeritus
I may be wrong here but I don't think you necessarily need a physical telescope but could do with an array of interferometers dispersed over the same area?

Correct, but that technology did not exist in the late 17th century (Ian J.'s posited time frame civilization level for his Moon One).

Ian J.
A bit more clarification: Moon One's society, while having a few telescopes that equate to 17th century-ish capability, is not otherwise as advanced, at least not in all ways. Their understanding isn't the same as ours and without clear detail they might tend to see the lights as some kind of natural phenomena rather than sentient made. If their telescopes could resolve enough detail, then they'd be 'observing' a new piece of knowledge and would have to learn to interpret that.

Staff Emeritus
I think by focusing on roads you are missing the forest for the trees. Humanity has altered 80% of the land surface of the Earth, at least to some extent. We have significantly altered a smaller but still very significant percentage. We have replaced vast forests with fields and cities. We have made deserts bloom. Those large scale changes would be visible to the naked eye from your Moon One.

Most of those changes occurred in the last 2000 years, with the more significant changes in the last 500 years. The most dramatic change would be what your Moon One inhabitants see on the dark side of Moon Two. They would see this:

This would have been a very recent development in the history of your Moon One's inhabitants observations of Moon Two. Two hundred years ago they would have seen darkness across the face of the dark side of Moon Two. 150 years ago they would have started seeing some feeble lights. They would have seen an explosion of light starting seventy or so years ago, or whenever your Moon Two started using electricity.

They would also see that the places with the greatest nighttime lighting are exactly the places where the landscape has changed the most.

Ian J.
I see your points today's level of knowledge, but to an unenlightened mind such things might not be so obviously explained. I am under the impression that the naked eye wouldn't show enough level of detail, just patches of change to the environment in daylight, and light areas at night. Even with the telescopes they have, it might not be enough to be sure of the reasons for the changes, though they might be beginning to suspect and posit the sentient life argument for the changes.

Staff Emeritus
The image I showed is easily within the reach of what a late 17th century telescope could see from a distance of 300,000 km. That image might be within reach of what can be seen with the naked eye.

Ian J.
I'm not disagreeing with you on that. The problem I have is how an unenlightened mind (that of pre 1600 Earth) would interpret the image. That's not to do with telescopes as such, but more about social science and how people would try to understand what was going on without the knowledge we have today. I have a feeling that that's a question for a different science area, maybe social science, rather than for this thread.

Mentor
Well, where is the point in seeing roads as lines without detail in daylight, if you see them clearly at night?

If moon one has telescopes, it has roads and some sort of artificial light - probably by burning organic things. They would see the same concept on moon two, just on a much more massive scale.

Ian J.
It's difficult to explain why, but I just don't feel that the people of Moon One have enough information or understanding, even with what appear to be faint, straight lines of light, to easily presume that it's obviously the result of the development of roads by a developed, sentient society.

I'm open to having my mind changed, but I think it'll take some serious and careful arguments to convince me.
The basic question of how much detail would be visible through a 17th century telescope has been answered, and I'd like to thank all those who have responded as it's very useful information. However, I don't want to waste anyone's time here more as I feel it's not a physics matter now, but one of opinion (and speculation) about how a pre-enlightenment people might interpret what they see.

Staff Emeritus
People believes that groves on the surface of Mars (seen through early telescopes) were giant canals built by a society trying to irrigate a growing desert. I agree with the points others have made that the spread of lights would be an obvious example to people that societies were developing. Maybe not all people but scholars who study the lights, chart them and compare them to records wouldn't have to make much of a leap to see it was a sign of civilisation.

Mentor
Unless there were some religious reasons or taboo that would not allow this kind of conclusions. But then it is hard to imagine one society/culture/nation inhabiting the whole planet, so probably opinions on the source of these lights/lines/shapes would vary from place to place.

Gold Member
I think creatures would always, in a sort of semi paranoid way, attribute observed changes to intellegent otherwordly influences. That is, if they were intelligent enough to have the obsession that everything had to have a meaning or explainable cause. If they were oblivious to the sky by nature, or just stupid, then they might not jump to any conclusions.

Mentor
It just occurred to me - the other world, if well seen, could be a source of religion. It could be a Heaven/Hell, place where gods/angels/ghosts/daemons live, whatever.

Ian J.
Maybe. I think that they would tend to see one of two possibilities:

1. Natural - Looking at the night image with the lights that DH posted, I could see them thinking it might be some kind of natural occurrence, maybe lava in pools and running along rock fissures.

2. Supernatural - The lights perhaps could be the souls of the departed, shining down on their descendents, or maybe some kind of angels or something. Admittedly as the lights would have appeared relatively recently in their time, it would have to be a new interpretation.

The issue of sentience isn't by any means out of the question. In the middle ages, in Europe, I believe there was often talk of 'dog headed men' living beyond the edge of the known world in lands as yet largely unvisited. It says something about pre-enlightenment thinking that that same interpretation could often be applied by distinctly separate societies to each other!

I am currently inclined still towards the general population interpreting it as one of the two above (depending on their specific culture, as Borek mentions), with the, at that point, very small group of astronomers and their very few telescopes beginning to question the general beliefs and speculating that it could be intelligence driven.