When we had a look at the ‘rainbow effect’ of planes in flight we mentioned that the offsets of the different images were a result of both the plane’s movement and the movement of the satellite taking the photos. We thought it would be worth having a look at that in more detail.
We know that most imaging satellites follow a sun-synchronous orbit. It is fairly easy to approximate that orbit relative to a plane in flight by drawing a line from the location of the plane to form a tangent on the right hand side of the North pole with the circle of latitude 82° N. For increased accuracy we will try to follow the tail of the plane.
In the image above, the satellite was travelling north to south in the direction of the red line although not necessarily directly overhead.
The satellite captured 4 photos: one high resolution grey scale image which we see at (1), and then after a short delay, blue, red and green images in quick succession which we see overlapping at (3).
If the plane was completely stationary, we would have expected the rainbow images to appear at (2) due to parallax and the motion of the satellite. If the satellite was stationary and the plane moving, then we would expect to see them at (4).
Using Google Earth’s measuring tools the distance from (1) to (2) is about 40 m. The distance from (2) to (3) is about 70 m.
This is enough information such that if we knew which satellite took the image, and how long it pauses between the monochrome and colour images, we could work out the approximate altitude and velocity of the plane. Alternatively, if we knew the altitude and velocity of the plane, we could, work out which satellites could have taken the image.
One useful fact is that all the possible satellites have very similar velocities which we can approximate at 7.5 km/s.
Wikipedia suggests that a typical plane cruises at 878–926 km/h at an altitude of around 12km and that a much higher altitude is not possible.
So, if we start by guessing the planes altitude at 12 km, its velocity at 900 km/h then we get the satellite altitude at about 550 km. Now we look through this list to try and find a matching satellite from DigitalGlobe – keeping in mind the image was captured in 2012 so satellites launched after that date must be excluded. Our best guess is that the image was probably captured by a satellite in a slightly lower orbit such as World-View-1 at an altitude of 496 Km and to make our calculations match up, the plane was probably at a slightly lower altitude of 11 km above sea level. (The ground at this location is 1.3 km above sea level.)
The time between the the monochrome and colour images is about 0.27 seconds.
If any of our readers knows of a reference with satellite orbit data in tabular form for a wide variety of imaging satellites please let us know in the comments.
We also came across this image:
The images of the plane appear to have been sheared and offset slightly in a horizontal direction, but the image of the ground does not seem to have been affected. We don’t know how this happened. Do our readers have any suggestions? One of the images in our earlier post on the ‘rainbow effect’ also includes an plane which seems to have a double tail which may be a related effect.
To find the above planes in Google Earth download this KML file.
We found the above planes using the Google Earth Community aircraft in flight list.