Let's do some quick math.

Geosynch is 36,000 Km out.

The Moon's albedo is 0.12.

Let's assume we can get a mirror of albedo 0.96 -- this is a little better than polished silver. It's also conveniently 8 times as reflective as the moon.

The Moon's angular diameter is about 0.5 degrees. To match that angular diameter at 36,000 Km, we need a 5.4 Km wide object.

That doesn't sound like it's within the current state of the art. Maybe in another 10 years?

23 million square meters at 2 g/m^2 (aluminized mylar) is 46,000 Kg -- about two Falcon Heavy trips. That doesn't count any framework or booster or other infrastructure.

Ooh. Radiation pressure. 23 million square meters * 8 microN/m^2 = 184 Newtons of thrust away from the Sun. Roughly 1/250 G of acceleration. That doesn't sound like much, but you need to counter it for stationkeeping. It's going to be a big chunk of the mass budget.

> The Moon's angular diameter is about 0.5 degrees. To match that angular diameter at 36,000 Km, we need a 5.4 Km wide object.

The article doesn’t say it’s going to be as big as the moon - it only says it’ll be 8x brighter. You’re also forgetting about the relative shapes of the objects: the moon, being round, reflects what light it does in all directions, while a designed mirror can be made to reflect it all in one specific direction.

All that said, I don’t think this will work, but not be of your math.

8x as much light as the moon is the same angular diameter and 8x more reflectance, or the same reflectance and 8x as much angular diameter. I suppose they could mean "8x as much reflectance but an unknown smaller insolation equivalent", but then they might as well say "we're putting a big spot light on a high-altitude balloon".

The relative sphericity of the moon is nearly immaterial here: when the moon is in full phase, do you see notable dimness around the edges where less sunlight is reflected away from you? Increasing the albedo to a near-perfect mirror cancels it all out.

Not sure, but it seems to me that for a mirror, more than albedo matter, because mirrors have a specular reflection rather than a diffuse reflection.

Now, reflection won't be perfectly coliminated, but if you assume it is, then the mirror essentially becomes a piece of sun. Since the sun is about 400 000 times as bright as the moon, you'd need to scale the diameter of the sun by sqrt(400 000 / 8) =~ 223. Applying that scaling to your 5.4Km yields about 24m of diameter, which seems waaaay to small to me, so I am probably wrong.

That feels really

Not the sun, the sun's irradiance at the distance of the Earth-Moon system.

> That doesn't sound like it's within the current state of the art

> about two Falcon Heavy trips

This does sound like it's within the state of the art! The mirror doesn't have to be one solid piece, it can be assembled from many smaller-ish satellites.

Of course you have overhead, so ... 5 Falcon Heavy trips? This is still very fine, if you're willing to put in the money.

GPS satellites are not in geosynchronous orbits. In fact, they would be close to useless if they were (all in one line orbiting over equator).

https://space.stackexchange.com/questions/10837/why-are-the-...

Why would a geosynchronous satellite have to be in one line over the equator? Why not a higher inclination?

Most people use geosynchronous as a synonym for geostationary.

https://en.wikipedia.org/wiki/Geosynchronous_orbit Popularly or loosely, the term geosynchronous may be used to mean geostationary.[2] Specifically, geosynchronous Earth orbit (GEO) may be a synonym for geosynchronous equatorial orbit,[3] or geostationary Earth orbit.[4] Communications satellites are often given geostationary or close to geostationary orbits so that the satellite antennas that communicate with them do not have to move, but can be pointed permanently at the fixed location in the sky where the satellite appears.

Certainly the comment I responded to (which has been edited to be non-sensical since) meant geostationary. In any case, GPS are not geosynchronous in the general sense of the term, but rather semi-synchronous (period of half a sidereal day). These orbits were historically chosen for convenience, but the syncronicity is not at all a requirement for global positioning satellites: e.g Galileo, GLONASS.

They can have inclination other than 0. If inclination is 0 thats a "geostationary" orbit, a special case of geosynchronous. In fact these are not stable and degrade into mere geosynchronous orbits without station keeping. In general though geostationary orbits are more useful since they are fixed competely in the sky. Ground antenna dont have to track the satellite as it moves north/south in the sky.

In this case a pair of satellites in a Tundra orbit [1] inclined to spend most of its time over this particular city seems like the right orbit for the job (as silly as it is to light a city by satellite), which is why I was curious to get an explanation behind the sweeping statement that geosynchronous (not geostationary in particular) orbits had to be in a line along the equator.

1. https://en.wikipedia.org/wiki/Tundra_orbit

Oh thats interesting. I hadn't heard of Tundra orbits. Wiki says 2 can provide continous coverage over an area. Wouldnt 1 be enough to act as a moon then? You only need it for half of the day and their period is 1 day right?

The problem with using just one is that geosynchronous orbital periods are one sidereal [1] day, not one solar day. So depending on the time of the year, the satellite would be in position in the wrong half of the day. On the other hand a satellite in Tundra orbit spends not half but more than half of its time in the designated area. Maybe a good compromise orbit could be found.

1. https://en.wikipedia.org/wiki/Sidereal_time

If the orbit is inclined the satellite will no longer stay above a single point it will move north and south throughout the day. All orbits pass over the equator twice during each period.

That's true, but it doesn't answer my question.

Geosynchronous satellites can and do modify their inclinations and eccentricities to increase their coverage beyond one spot over the equator.

All GPS satellites are in a geosynchronous orbit.

Citation needed?

You may find this helpful:

http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit5/gps....

The nominal GPS configuration consists of a network of 24 satellites in high orbits around the Earth, but up to 30 or so satellites may be on station at any given time. Each satellite in the GPS constellation orbits at an altitude of about 20,000 km from the ground, and has an orbital speed of about 14,000 km/hour (the orbital period is roughly 12 hours - contrary to popular belief, GPS satellites are not in geosynchronous or geostationary orbits). The satellite orbits are distributed so that at least 4 satellites are always visible from any point on the Earth at any given instant (with up to 12 visible at one time).

No, they are not.