If you want to see the space station, you only get to see it during sunrise and sunset. But what if a disco strobe light was on it, could you look up and see where it is every ninety seconds,all night?
Would an ordinary disco strobe be bright enough?
It would have been good advertising, a reason for people to look up for the space station. They should have made it flash three times a second. It would have used almost no power. I'm surprised they missed it.
The answer is no, a disco light on the ISS isn't visible to a ground-based observer's naked eye.
This is true both for the literal definition of disco light (a light used in a disco around people) and the slang definition (emergency lights on vehicles), trivially by reversing the issue: what kind of lights does an astronaut on the ISS observe from space while looking down at the Earth? The answer isn't individual car headlights or emergency lights, individual ships on the sea, etc etc etc. Remotely-eye-safe lights, without being pointed at the observer, are not going to be visible across a 400km-ish gap (at minimum; the ISS is further away when at the observer's horizon).
Successful observation from the ISS of specific, targeted lights from the ground has been done! In 2012, 800-million-lumen spotlights and a 1-watt laser (eye danger!!) were spotted from the ISS by Don Petit. The results are recorded:
I agree with the article's interpretation: the dim light is from the laser pointer. The bright light is from the 800-million-lumen spotlights. Both are pointed at the space station. The light you're asking for is supposed to be visible to any observer, not just someone an astronaut is tracking with a spotlight. (800 million lumens is slightly more meager than the lights advertised by Northstar Searchlight Promotions, so that tight beam likely requires around a kilowatt of electric power.)
If you want the light to be about as bright as what we currently see from the ISS, the light has to be about as bright (within an order of magnitude) as the sun seen from Earth. The additional path length added by reflection from ISS is negligible compared to the Earth-Sun distance. The reflectivity of the ISS in visible light is reasonably high. That isn't an unachievable level of light, but it would be terribly inconvenient for anyone on or near the ISS.
A quantitative answer to "how bright would the light have to be," the natural follow-on question can be worked out from the maths done by uhoh regarding orbiting billboards by varying the parameters as appropriate.
Funnily enough, the objections others raised about astronomy are basically trivial since you're only asking for the one source on ISS; the issue with Starlinks is that they're bright AND everywhere, and so observing can't be planned around them. Much less of an issue with only one stupidly-bright source. I maintain my objection that the light shouldn't strobe, though, to avoid the need to update the How to Identify that Light in the Sky chart.
From eoPoportal's FITSat-1 (Fukuoka Institute of Technology CubeSat) / Niwaka
We know that Niwaka or FITSAT-1, an LED-covered 1U cubesat was visible on the ground from LEO. For more on that see Have any satellites had lights visible from Earth besides FITSat-1? as well as this answer to Deep Space Optical Communications (DSOC) - from what distance could a flashlight be detected by a space-based telescope and answers to How can I estimate the optical power that a single-color LED generates?
Also this answer to How big will a space billboard have to be to be visible? links to Physics SE's How to make a green LED as visually bright as a 0 magnitude star? The answer there says a single off-the-shelf lensed 100 mA green LED with a 10 degree half-angle at 18 km would look as bright as a 0 magnitude star (which confirms that the FITSat-1 LED-covered cubesate would have been visible from LEO.)
At say 400 km (ISS overhead pass) we'd need it to be almost 500 times brighter.
That's easy - use fifty 1 Amp lensed LEDs with a 10 degree half-angle! At 3V and 30% quantum efficiency, that would be 500 Watts if run continuously.
But we're talking about a "strobe light". I don't know how short the duty cycle could be before the flashes started appearing significantly dimmer than 0 magnitude, but I believe (and I'll look into it today) that 10% at 3 Hz or 30 ms pulses are long enough.
Would an ordinary disco strobe be bright enough?
Hmm... well I'm not sure how to parse "ordinary" now that LEDs arrays can scale to arbitrary size.
from Amazon
Photographers have available some pretty high power xenon flash tubes, but I am not sure they and their electronics are capable of 3 flashes per second.
I would say that for an extraordinary disco strobe, YES. For an ordinary disco strobe, probably, but it would be pretty dim.
Remember that magnitude 5 is 100 times dimmer than magnitude 0. That would be a piece of cake.
The motivation behind my earlier question Approximate sizes and relative positions of the ISS' cupola windows? was to ponder exactly this scenario!
An array of LEDs and a driver circuit could send signals to the ground in morse code. They would be visible to the eye, and easily captured by a small telescope and photodiode.
In the event of a loss of radio communication for some reason, the ISS could at least "blink" to earth in morse code, and a suitable blinker on the ground could reply.
