# The Naked Scientists Forum

### Author Topic: how big?  (Read 2750 times)

#### sunbaked

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##### how big?
« on: 04/01/2014 01:31:49 »
How big would a sattelite need to be in Low earth orbit (approx 250 miles) to appear to be the size of a postage stamp to the naked eye?

#### CliffordK

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##### Re: how big?
« Reply #1 on: 04/01/2014 05:20:58 »
Hmmm....  how big is a postage stamp?

The moon is about 30 arcminutes, or about 1/2 degree of the sky.

SOH, CAH TOA....

So, for a triangle,

Tan(0.5 degree) = X / 250 miles

X = 250 miles * Tan ((0.5/360)* 3.14*2) radians)

X = about 2 miles in diameter.  (approximating an isosceles triangle with a right triangle for small values of θ).

At 250 miles, your satellite would also circle the Earth in about an hour and a half, so it would pass through your field of view in a matter of minutes.  Depending on the orbit you put it in, it may be in the shade during the night and not very bright, and it may be difficult to design it to be visible over a broad area during the day.
« Last Edit: 04/01/2014 05:24:46 by CliffordK »

#### RD

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##### Re: how big?
« Reply #2 on: 04/01/2014 07:09:49 »
Apparently the shape of the ISS is just visible with a modest telescope ...

http://www.space.com/23903-international-space-station-moon-photo.html

The ISS is the speck on the left that looks like a gnat.
« Last Edit: 04/01/2014 07:16:01 by RD »

#### sunbaked

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##### Re: how big?
« Reply #3 on: 05/01/2014 01:40:29 »
CliffordK, thanks for the answer....

This may be off topic? As it relates to visibility, earth orbit, and other such issues it seems like the right place to continue..  if not I hope an admin will direct me to a suitable alternate forum...  nevertheless...

So the real question is, can a satellite be successfully built that could act as a "billboard" in space?

Requirements:

• A large programmable screen
• Visible to the naked eye daytime or nighttime.

Thoughts:

• Designed to unfold (2 miles is awfully big)?  Built in multiple pieces?
• Use LEDs. Bright enough?
• Use Clusters of Red Green and Blue LEDs. Or use RGB LEDs?
• Solar Panel powered
• Weight issues?
• Obviously a slower orbit would allow for better ground view time (but geostationary is much higher right? meaning a MUCH larger satellite needed for visibility)

What do you think are some of the technical issues surrounding a concept like this?

#### RD

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##### Re: how big?
« Reply #4 on: 05/01/2014 01:54:49 »
So the real question is, can a satellite be successfully built that could act as a "billboard" in space?

• Designed to unfold (2 miles is awfully big)?  Built in multiple pieces?

What do you think are some of the technical issues surrounding a concept like this?

similar to this infeasible idea ... http://en.wikipedia.org/wiki/Space_sunshade#Cloud_of_small_spacecraft_near_L1

#### CliffordK

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##### Re: how big?
« Reply #5 on: 05/01/2014 02:50:00 »
Ok,
Thinking of your triangles.
If you cut the distance in half, you also cut the radius in half, or the area a factor of 4 (the square).  So, if you placed it at 125 miles, the object would appear two to four times as big depending on how you measure it, or would take a quarter the material to build for the same size.  Unfortunately the lower orbits are less stable.

Perhaps you could make a thin film LED or active LCD, but you would still be much thicker and heavier than the typical Mylar spacecraft sheeting.  Add to it some kind of solar absorption/storage/emission system, and you likely would be very heavy.

How much info could you transmit if written on the face of a full moon?  Especially if traveling from horizon to horizon in a few minutes?  One word?  A corporate symbol like a yellow "M" or Mercedes Star?  Perhaps the image of a hamburger?

Competing with the sun would be difficult, and would require a larger collector than your emitter, or a narrow focal range, so fewer people would see your display for a shorter period of time.

Choosing an orbit would be complicated.  If you orbited the equator at 250 miles elevation, people in the USA and UK would never see it.  In fact, it may only be visible to a band about twice the altitude, or 500 miles or so, and obviously only traveling overhead for those directly under it.  Could you design an orbit to cross over a single spot on every pass?  Or, would it precess so that it crosses over the entire globe briefly once a day?

Here we get a lot of clouds during the winter, and relatively long days during the summer.

I agree with RD, you would up with an extremely expensive system, with minimal benefit.  Consider the International Space Station microscopic tiny compared to what you are wanting to build, and cost \$150 Billion dollars.

#### evan_au

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##### Re: how big?
« Reply #6 on: 05/01/2014 03:55:38 »
There are challenges around getting enough light out of LEDs to be visible on the ground, getting enough solar cells to power the LEDs, and storing this electricity so the electricity can be delivered during the "night" part of the orbit, which will last about 40 minutes for a 250-mile high orbit.
It may be better to make the satellite out of reflective mylar, and have it reflect sunlight down to the ground, which provides high visibility during the daytime and pre-dawn/post-sunset period (but it doesn't work during the total night, unless you can reflect moonlight). Sort of like one of those reflective data projectors, on a huge scale. Each pixel would need to be a hundred square meters...

But there is a more fundamental problem - since the invention of TV, almost noone looks up at the sky at night (apart from astronomers, and they will hate this extra source of light pollution!). And very few people look up at the sky during the day, because they don't expect to see anything.

#### CliffordK

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##### Re: how big?
« Reply #7 on: 05/01/2014 06:01:29 »
during the "night" part of the orbit, which will last about 40 minutes for a 250-mile high orbit.
The day time would still be a challenge as at noon, the sun would be behind it.  The moon and some of the planets are barely visible during the day if one is lucky.

Good point that the night for the orbiter is short.  You may do pretty well at night with a phosphor light source, although getting the brightness and detail right might be a challenge.  In advertising, you need something that is "Hey, Look at ME" rather than "Where's Waldo?"

#### sunbaked

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##### Re: how big?
« Reply #8 on: 05/01/2014 08:57:36 »

But there is a more fundamental problem - since the invention of TV, almost noone looks up at the sky at night (apart from astronomers, and they will hate this extra source of light pollution!). And very few people look up at the sky during the day, because they don't expect to see anything.

I agree that people don't regularly look up... but if everyone knew this thing was up there ... I think that in itself would attract regular attention.  Outdoor advertising is often sold on a "potential impression count" i.e.average traffic that passes a billboard each month.  The revenue side could be monstrous.  Think about the cost of a superbowl ad and that's not nearly the number of impressions that a satellite could garner in a single day.

How much info could you transmit if written on the face of a full moon?  Especially if traveling from horizon to horizon in a few minutes?  One word?  A corporate symbol like a yellow "M" or Mercedes Star?  Perhaps the image of a hamburger?.....

.....I agree with RD, you would up with an extremely expensive system, with minimal benefit.  Consider the International Space Station microscopic tiny compared to what you are wanting to build, and cost \$150 Billion dollars.

As for the creative...  International logos would of course make sense... but you could also sell regional brands well in advance since you would safely be able to predict what region it would be flying over at any given date / time.

Considering a 10 year lifespan you'd have over 10 Million 30 second "spots" (there of course would be a loss of some portion of that sellable time due to the orbit naturally passing over oceans with little or no viewership opportunities).  I think one could make a ROI case for a considerable cost.

#### alancalverd

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##### Re: how big?
« Reply #9 on: 05/01/2014 11:08:09 »
Unfortunately it probably isn't all that difficult to do. Commercial 0.5 micron Mylar weighs about 1 g/m^2 so a tonne of the stuff will give you a square kilometer of surface on which to print your logo. If you are happy with 50% visibility, no need for power - sunshine works OK for most billboards.

Deploying the sheet needn't be difficult: it's just a few minutes' spacewalk for four blokes at the corners.

However it is worth reviewing the effectiveness of aerial banner towing. Friends who do it point out that unless you are fairly close to the audience with a really noisy aeroplane, nobody bothers to look up.

#### CliffordK

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##### Re: how big?
« Reply #10 on: 05/01/2014 11:29:00 »
I agree that people don't regularly look up... but if everyone knew this thing was up there ... I think that in itself would attract regular attention.
The novelty would likely wear off after it passes overhead a few times, after which people would likely just ignore it.

However it is worth reviewing the effectiveness of aerial banner towing. Friends who do it point out that unless you are fairly close to the audience with a really noisy aeroplane, nobody bothers to look up.

Unless one is fairly close, they can be quite difficult to read.

#### David Cooper

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##### Re: how big?
« Reply #11 on: 05/01/2014 21:39:52 »
It would maybe be worth putting something that looks as big as the moon up there in order to create more solar eclipses which could occur all over the place with a higher frequency. A momentary eclipse wouldn't be all that great, of course, and it would also fail to darken so much of the sky if it's a lot smaller and closer than the moon, but it would darken a path right down to your eyes and could maybe give you a chance to see something similar to a solar eclipse. To make these eclipses longer than a fraction of a second, you would want to have the thing rotating round another object such that it sometimes moves twice as fast across the sky and sometimes stops for a short time, thereby creating a series of points under its orbit where you could go and stand to see it with the eclipse length maximised. The real issue with this though is how big and far away it would need to be to darken enough of the sky to make it worth doing at all - you need dark sky around it in order to see the sun's atmosphere through it.

#### CliffordK

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##### Re: how big?
« Reply #12 on: 06/01/2014 01:26:17 »
Above I calculated that a lunar (or solar) transit of the ISS is about 2 miles (across the equator) for any spot it is viewed from the ground.

At about 4.7 miles a second, the transit would last just under 1/2 second.

For a 2 mile diameter body, going from a partial eclipse to full, back to partial eclipse would be about 4 miles, or in total it would last for about a second.

And, on Earth, the path that the full eclipse is visible would be extremely narrow.

I'm trying to imagine the orbit that would effectively slow it down.  I'm not sure you could design a LEO orbit so that it would "hover".

In a geostationary orbit, your satellite would appear to hover over the equator, or in a different geosynchronous orbit, it would appear to move north and south.  And the apparent velocity would be greatly reduced.  However, your satellite would need to be about 100 times as large, or about 200 miles in diameter.

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##### Re: how big?
« Reply #12 on: 06/01/2014 01:26:17 »