# How big will a space billboard have to be to be visible?

So recently there's been the news story about how SpaceX is launching a billboard to space (space billboards are an approximately bi-annual occurrence). This "billboard" is a cubesat that will just display ads on a livestream of Earth, similar to what NASA was doing with HDEV. However, what people are imagining is a billboard, visible from orbit on the ground.

Ignoring the fact it's already illegal, to do what they're imagining feels to me like a borderline physical impossible, simply because of how big the billboard would have to be; the ISS is basically a point source and it's the size of a football field. Writing out even just visible plain text feels like it would be hard.

So how big would a space billboard have to be? (and is it reasonably possible to construct one?)

• As a suggestion, read Watch this Space from Arthur C. Clarke's Venture to the Moon from 1956. You wouldn't build a physical billboard. It'd be cheaper and easier to "skywrite" the advertisement.
– JRE
Aug 10 '21 at 6:54
• I think a fleet of satellites flying in (relative) formation that can maneuver to be the 'pixels' of an image is way more practical than one big satellite Aug 10 '21 at 12:31
• What about a bunch of tiny cubesats and launch them from a parent vessel in such a way that they reenter together, and for a brief moment produce a corporate logo as they burn up? If they are made out of different materials you could even possibly have a bit of color in the logo Aug 10 '21 at 13:21
• @Innovine You mean like this/ spaceflightnow.com/2019/11/28/… Aug 10 '21 at 13:45
• Don't give Richard Branson any more ideas! Aug 10 '21 at 17:38

Suppose we start with @SE-stopfiringthegoodguys's answer of 1000 km orbit but instead of making it solid and darkly and diffusely reflective like the Moon (albedo only 0.15-ish)

what if it produced its own light like a billboard?

For reference, the full moon is about magnitude -13 and the earthshine from the part we can see via reflected light from Earth is about magnitude -3.

But not to be outdone by the Moon let's stick with a brightness of -13.

Per How to make a green LED as visually bright as a 0 magnitude star? in Physics SE, I got that an object that appeared to be 0 magnitude in green light should illuminate the Earth with about $$2.1 \times10^{-9} \ W/m^2$$.

If it is roughly uniform over a cone with a half-width of 10°, then the LED produces $$0.7 \ W/Sr$$, or $$0.7/r^2 \ W/m^2$$ at a distance of $$r$$ meters.

That means I would have to move my 100 mA, 30% eQE 555nm LED with a 10° half-angle 18 kilometers away for it to look roughly as bright a 0 visual magnitude star!

At a bias of say 3 volts, our LED needs 0.3 watts to be 0 magnitude at 18 km with a half-angle of 10°.

To be -13 mag at 1000 km over a 30° half-angle would then need about 500 megawatts.

It's hard to compete with astronomical objects. Stick with shiny things if you want a big solid billboard.

But if you can live with "a thousand points of light" then consider a group of LED-bearing cubesats.

At 450 km each satellite can shine as a 0 magnitude star over a 10° half-angle using only 7.5 watts which is a perfectly reasonable power load for a well designed and built 3U cubesat with solar panels and batteries to maintain much of the time.

If your "flock" of cubesats can communicate with each other or better yet see each other, then they can "fly" in formation like an LED drone show, which has a lot of pluses over a flat, static and boring billboard.

Screenshots from Biggest drone display ever! - Guinness World Records (click for larger)

• Even those large half-angles, at an altitude of 1000km, are only enough to be seen from small areas of the surface, so to cover all of Europe or all of the US would need another the equivalent of a few large power stations in orbit Aug 10 '21 at 15:27
• @ChrisH that's precisely the point of that section, and the reason I proposed the alternative "thousand points of light" 0 magnitude star-like cubesat constellation. Envelope-back calculation suggests only about 7 watts average power for a 10° half-angle. There is room for optimization, but it's still going to be a lot less glamorous than a 9 kilometer wide billboard, and a lot more achievable near term.
– uhoh
Aug 10 '21 at 15:31
• Yes, after running the numbers because the angles felt too big, I felt a footnote was in order Aug 10 '21 at 15:33
• Why bother powering LEDs? Why not just reflect sunlight, like the ISS or some of the SpaceX sats do? Aug 10 '21 at 16:05
• @jcaron it's a good question and if you post it as such there will probably be a few answers since there have been many attempts.
– uhoh
Aug 10 '21 at 17:22

An object already in the sky that clearly has a cultural impact is the Moon. We can use it as a benchmark for how large a space billboard has to be.

While the angular diameter of the Moon isn't too large, it is enough to make out some details, so a billboard of similar apparent size would be sufficient for displaying a logo, which I would say is enough to be an efficient advertisement if well designed.

To avoid atmospheric drag, the billboard probably has to be as high as a 1000km orbit, which would place it 384 times closer than the Moon, and thus require a diameter 384 times smaller, 9km wide.

This would rule out pretty much any construction method that requires a non-trivial thickness. What's left then are foils.

With tested solar sail materials, that's at least 250-500 tonnes for just the foil alone, neglecting any support structure. This could perhaps be reduced slightly by using holes and voids in the foil as part of the logo design, but this would nevertheless be one of the largest construction projects ever undertaken in space.

• I fully expect a large faceless multinational corporation to fund it anyway. Aug 10 '21 at 14:20
• I suppose you could imagine a smaller billboard in a lower orbit as well. The higher drag would mean that it wouldn't stay up as long, but it would be cheaper. And I could imagine that a Space Billboard™ would lose its effectiveness as an advertising gimmick once everyone had got used to its existence. ("Hey, remember that orbiting Pepsi logo they put up a few years back? Did you know that you can still see it at night?") Aug 10 '21 at 14:52
• @MichaelSeifert Yeah, but if you keep making it smaller and closer, at some point, it's just a blimp, or a plane with a banner behind it - we already have those... Aug 10 '21 at 20:27
• If you drop it down to a 250-km orbit, it only needs to be 2.25 km across, with a mass of 15-30 tonnes. A Falcon Heavy could launch a pair of those billboards into low Earth orbit.
– Mark
Aug 10 '21 at 21:19
• @uhoh, the cost of 30 seconds of advertising time on the Super Bowl broadcast is around \$5 million. I'm sure there are plenty of companies that would be willing to pay five times that for an orbital ad.
– Mark
Aug 12 '21 at 0:07