Note that the optics may also look to the side in case the target object (e.g. a city) is not exactly underneath the orbit, which is of course the most likely case. The pixel size on ground for such a system depends on the angle the satellite points off the nadir position. In nadir view it is about 50m x 50m and in extreme off-nadir view, for images 1 or 1000 and the case of a target at 500km left or right of the orbit, it grows to about 80m x 80m.
The suggested measurement sequence takes all together up to 200s if one allows time for the system to slew forward again to get ready for the next sequence. In the 200s the satellite covered ~1400km on ground, which is also the minimum spatial distance between two sequences. This means the system cannot measure two cities along the orbit, which are closer than 1400km apart. Hence if one wants to map out e.g. Brussels and Amsterdam, one city has to be measured by one satellite in one orbit and the other one either by another satellite or by the same satellite in another orbit.
With a repetition rate of 200s, one could produce 15 high resolution maps inside the ~50min flight over the sunlit portion of the Earth of a LEO. In practice it will rather be <10 maps due to “waiting times'' in between the sequences for two possible reasons: 1) the next target (city) might not be necessarily positioned in such a way, that one can start the sequence exactly when the previous one has finished and 2) one might need to allow for nadir-position periods in between the sequences to recharge the battery sufficiently. Considering that the satellite is over ocean for ⅔ of the time anyway, one will probably use the time over the ocean for optimized battery recharging (except for possibly the tracking of ship-lines) and over land measure as quickly as possible.
With the suggested system one could also make limb measurements by simply pointing the satellite forward. One image would cover an azimuth range of 7° (1000 pixels at 0.007° each) with a FOR in the elevation angle of 0.007°. In order to have a limb scan one would also slew the satellite, but to a very different rate as for the (near) nadir observations.
The measurement mode described above “solves” the problem of spatial resolution. The described target mode is doable for a modern spacecraft. In order to improve the temporal resolution one could build a fleet of such satellites flying in a constellation with different equator crossing times. Since the satellite instrument does not need to be very big, the obvious choice would be to use cubesats, which could be launched all at once and so significantly reduce the mission costs. Such a project could be compared to the GHGSat mission, but measuring reactive trace gases such as NO2, O3, SO2 instead of GHGs.