Why is it so hard to find a Boeing 777?

By now everyone is familiar with the missing Malaysia airplane. But I've repeatedly heard people incredulous that it is so hard to find the missing plane or the debris given the number and quality of the satellites we have in orbit. So I thought I would try to address that here.

Original

5mx5m resolution

First let's consider what it is we are trying to find. A Boeing 777 is roughly 70m long with a 60m wingspan which sounds pretty big and hard to miss but the width of the fuselage is only 6m (ref). So while the planes are very long each bit is quite skinny so to pick the plane out of the background you need a resolution of < 5mx5m/pixel, even that will give such a fuzzy image it would be difficult to recognize as a plane. Above on the left I have a basic silhouette of a plane and on the right I have reduced the resolution to what it Boeing 777 would look like at 5mx5m resolution. And that was when it was intact, debris after the inevitable crash is likely to be much smaller and harder to identify than the whole aircraft (eg. a single seat from an airplane is typically less than 50cm wide).

Fortunately most of the satellite imagery systems can get resolution of 1-3m with the best getting resolution ~0.5m, spy satellites could get even better. However, there is a trade off between resolution and area covered because each camera can only detect a maximum number of pixels at a time so the higher the resolution you use the less area contained in each image. The most recent high resolution commercial satellite imagery system covers ~15kmx15km in each image. Given the search area is thousands of square kilometers we're talking hundreds of individual photographs.

Furthermore imaging satellites are not stationary so only a small portion will be in an appropriate position to photograph the search area at any one time and it could take days for the best resolution satellites to be moved into the relevant position (the Indian Ocean is not of much interest for high resolution images so it is unlikely there are many appropriate satellites in orbits that would cover much of the area). Add to that the potential for the plane/debris to move in between imaging opportunities and it becomes quite a difficult task indeed.

Heat haze at an airport

Lastly, various atmospheric factors can obscure/distort satellite images. For instance satellites cannot see through clouds, and air of different temperatures bends light to different extents which distorts images and causes mirages/heat haze.

So even though we have ~1,000 active satellites in orbit only a small portion of those will be equipped with a sufficiently powerful light camera to be useful for searching for the missing Malaysian plane and only a portion of those will be in an orbit which passes over the search area.  Making it remarkable that any images of debris have been captured not the other way round.