# Atmospheric influences on earth to satellite visibility and vice versa (e.g. atmospheric seeing)

Are there qualitative differences between observing satellite from earth surface vs. observing earth from the same satellite. Given the same optics on both places.

Does it matter which way we look through a foggy window?

Does atmospheric seeing affect maximum useful aperture for resolution (without using adaptive optics) differently, looking down to the Earth vs up to the sky?

• I'm guessing you'll stipulate that the space telescopes should look at places on Earth near sea level, and the ground telescopes can not cheat and observe from very tall mountains with ideal atmospheric conditions?
– uhoh
Feb 10, 2017 at 20:01

Yes there is. The foggy window is much closer to the ground than to the orbiting satellite. Atmospheric turbulence takes place between 0 and 20km high, and satellites orbit over 200km high.

To give you an order of magnitude, atmospheric turbulence degrades the image for telescopes with diameters larger than 15cm. For space-based telescopes in low orbit, it starts to have an influence around 2m of diameter.

Edit: see https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19690003603.pdf for mathematical derivations.

• Where does that 2m diameter come from - can you add a link or cite something published that I can read? I'd like to understand they physics better - why that is so. The reason I am confused is that I thought the "6 inch telescope" limit (let's call it that) came from the actual physical size of the index of refraction fluctuations in the atmosphere being of the order of tens of centimeters. I think the point here is that when the aperture passes 2 meters, the resolution due to diffraction reaches that 10-20cm level. The problem was always there, just masked by the larger diffraction effects.
– uhoh
Feb 10, 2017 at 19:58
• @uhoh I have added a link with the detailed calculations. I think your interpretation is good, but it misses one aspect: if you increase the wavelength, the diffraction psf will get smaller but the turbulence scale does not have the same behaviour.The way I see it is that the turbulence creates random dephasing cells at around 20km. If the angular diameter of your mirror seen from the ground is smaller than the angular diameter of one cell seen from the ground, you are OK and there are no turbulence effects. If you mirror is bigger than a turbulence cell, the quality gets degraded. Feb 10, 2017 at 20:36
• Thank you for the link! I'll give it a read. Your explanation make perfect sense already. I wasn't thinking far enough. The telescope is actually imaging spherical waves from each point on the Earth, not plane waves, and so the size of the relevant wavefront area at 20km is yep, 10-20cm. That's what I needed. Thanks!
– uhoh
Feb 10, 2017 at 20:45

Atmospheric effects are mostly confined to altitudes where there is appreciable -er- atmosphere. Say below 100,000 feet (nonlinear, so probably 50,000 feet or less is where most turbulence occurs). Recon satellites orbit at ~150 miles or so (KH-11 figure, but commercial earth observation satellites like to orbit above ~400 miles to avoid residual drag). Imagine a line drawn between a ground telescope and the satellite (represents your sight line).

First case, ground to satellite, anchored on the ground... You're turbulence, so grab the line at the 10 mile up mark and wiggle. The satellite end of the (sight)line will be displaced by some distance.

Second case, satellite to ground, anchored at satellite... Again, you're turbulence, so grab the line at the 10 mile mark and wiggle. The ground end of the (sight)line will also move, but over a much smaller distance than the first case.

So my (possibly incorrect) conclusion is that observing the earth from a satellite is less affected by atmospheric conditions than observing a satellite from the earth.