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They do! Well, at least some of them. There is for example a project called TAMDAR (Tropospheric Airborne Meteorological Data Reporting) that e.g. Icelandair is a part of. There is a document published by the Icelandic Meteorological Office about it.

I work in the aviation industry, specifically repair, maintenance and engineering. While not an engineer myself, I work alongside them.

Adding anything to an airframe, internally or externally, always has a cost in time, materials and funds. Our company is in the process of modifying ERJ regional aircraft with seatside electrical outlets for passenger access. The project manager and our electrical engineer have each spent over 200 hours designing the controls and wiring for the mod, procuring materials and consulting airframe engineers. Our inspectors have consulted with the FAA to have the mod approved. Our structures and interior technicians have designed and produced new panels inside the cabin, and our electricians have installed the controls and wiring.

This project has cost our customer roughly half a million dollars, and this figure does not take into account the inevitable oversights that arise in any engineering project. These additions to the airframe must be carefully considered against the aircraft total weight and the balance on each axis of control. Now add in training time for aircrews to be aware of the mods and how to handle issues.

Your proposal will necessarily cost at least this amount, and may not be feasible if the equipment is too heavy or bulky. In light of the other comments, I conclude that this will never fly. However, the military might be tasked with this kind of job, as they already have dedicated surveillance aircraft.

Good luck in Patagonia.

Is there any insurmountable technical or legal limitation to equip
commercial airplanes with Earth Observing instruments?

This question would probably be better answered on space.se, by people who know what are the advantages of a satellite over an aircraft and the reasons why missions are not conducted on aircraft.

However several aspects indeed differ between a satellite and a commercial plane, three come to mind:

1. The practical area visible for a given field of view: At 400 km altitude (low end of the low earth orbit) the area covered is much larger than at 10 km.
   
   
   
   You can have an idea by comparing what you can view through a camera on each side of a given object, when this object is at 10 m and at 400 m.
   
   
   
   Depending on the mission this can be decisive.
   
   
   
   


2. The degree and frequency of vibrations: Usually, when out of the atmosphere, a satellite is very stable. A plane shows a lot of (comparatively) large amplitude vibrations due to the engines and the aerodynamic pressure, especially at high frequencies.
   
   
   
   This is not a trivial problem, because at 10 km you usually need a very long focal length (or a very small aperture radar array), and the effect of the vibrations is directly proportional to the focal length.
   
   
   
   Large sensors used for good definition and contrasted shots also increase the effect in proportion of their diameter, because if the diameter is twice, the focal length must be twice to maintain the field of view (that's why digital cameras with small sensors have short lens).
   
   
   
   What can be seen as a simple problem on Earth with a 50 mm lens and a full size sensor, is actually a serious one when surveying at 10 km.
   
   
   
   A stabilization mechanism will be required (e.g. inertial platform, or mirror/lens/aerial dynamic correction). However those mechanisms need expensive maintenance and/or calibration to be effective.
   
   
   
   No airline will allow repetitive maintenance windows for that. Even when paid, this won't be comparable to passenger tickets, cargo fees and on-board sales. Airliners are not, for this aspect, comparable to spy aircraft and dedicated surveying aircraft.
   
   
   
   Aircraft also experience permanent roll, pitch and yaw changes, but as they are relatively slow they are easy to counter with a simple stabilized platform.
   
   
   
   


3. Area coverage: Airways are very small corridors in the sky, at specific locations.
   
   
   
   In contrary satellites in low orbit (which are therefore not geostationary) see the Earth rotating below them and cover easily most of the planet area (specially polar orbit ones).

Regarding the cloud coverage preventing satellite observation, the problem will be nearly the same for an airliner. It flies above the clouds, even if polar routes are lower due to the tropopause being closer to the ground.

Aside from the issues of weight and complexity, there are potential legal and political considerations regarding commercial carriage of certain kinds of observational equipment. Korean Airlines Flight 007 was shot down by a Soviet interceptor in 1983 when it inadvertently flew over Soviet territory leading the Soviets to believe it to be a military reconnaissance aircraft. Equipping commercial aircraft with photographic or laser-based earth observation instruments--even if meant to measure ice, water, clouds, or topography--could be seen as potentially hostile, leading to an elevated risk of civilian casualties.

It wouldn't have to be a shoot-down, either: a forced landing and detention of the passengers would make people much less likely to fly that airline. At a minimum, airlines might have to change routes around politically sensitive areas, leading to increased costs, even if only a few aircraft were so configured.

While major powers such as the US, Russia, and China would be unlikely to undertake excessively hostile action, one cannot always predict what a smaller nation might do.

A major reason would be that Earth Observing systems are large, and would take up a significant portion of the interior space of the airliner, space that the company wishes to sell to passengers. they are also heavy, which would impact the range of the plane and trip and drive up fuel costs.

Additionally, airliners want to get from airport to airport as quickly as possible, whereas in observation missions you want to get as many passes over important areas at specific altitudes as possible.

NASA flies many airborne missions every year specifically for earth observations. Some of these are simply proving future satellite sensors, but many more are purely for gathering data on a specific parameter. They utilize their own aircraft though, because the aircraft typically need to be specially modified for the equipment, specifically with portholes cut in the belly of the frame and they then dont have to compete with the needs of a passenger service when it comes to route.

To measure ice field depths and such you must know the actual position of the sensor with greater accuracy than the precision you need for the final measurement. With a satellite ballistically orbiting the earth, that's easy. With a commercial aircraft flight, that's far more difficult, especially including pitch/yaw/roll effects between the GPS, the INS and the sensor.

Further, while adding a sensor to a satellite and orbiting same is very expensive, doing so for a vast fleet of airliners may well be even more so, especially when that includes paying the airlines for the privilege of doing so, including the ongoing maintenance that satellites don't need (they seldom need washing, etc.).

Space fan here, and I think you are underestimating the size of the task.

Earth has a surface area of 510 million km2.

A plane travelling at 500km/h with a 10km observation track can cover 5000km2/h, or 50000km2 per 10 hour operational day, ignoring transit to/from nearest available airport. It would need approximately 10000 days (28 plane-years) to cover the surface of the earth. I'm not sure what the cost of operating say 7 crewed planes throughout daylight hours for 4 years is, but I'm sure it adds up, even for a small plane. With a crew of 2, we're looking at 56 pilot-years of salaries (assuming they work 10 a day hours 7 days a week and never have time off!) which is running into the millions already, before you even consider fuel or maintenance.

In contrast, SpaceX publish their prices and you can charter a Falcon 9 for $62 million to put 22800kg into low earth orbit. Your satellite only weighs 2280kg? No problem, rideshare deals are available, so your budget would be around 6.2 million plus a markup. Just wait for a near polar rideshare (such as the SSO2 mission scheduled to launch on 2 december 2018) and once in orbit your satellite will travel at around 30000km/h, completing 3 laps of the earth every 4 hours. The earth's circumference is 40000km, so with a 10km track you should be able to cover the whole equator in 4000 laps, which is 5333 hours. Accounting for day/night the job should be done in under 2 years with a single satellite.

As discussed in other answers, planes are an option for small areas of particular interest, but just as satellites suffer from cloud obscuration, so can planes be affected by the weather, either by obscuration or by being grounded due to unsafe conditions.

While putting equipment on existing commercial flights is an interesting idea, if the flights follow the same route on a regular basis, only the areas on common flight paths would be mapped, which may or may not coincide with areas of interest.