The INMARSAT 3-F1 is in a geostationary orbit above the earth at a nominal 35786km distance. At that nominal height its orbital speed enables it to remain stationary over the Equator and at 64.5°E. However, as the satellite is geosynchronous with a small offset to allow it to remain geostationary, causes its position both in distance above the earth and its nominal position, to change over a period of 1 siderial day (23.934 hours). This positional change is a small ellipse with a 1.6580° inclination that extends 1.59° north and south of the Equator in a very skinny figure of 8 shape.
The fact the eccentricity is predominately N and S has presented the possibility of determining the values of small doppler shifts in a signal being received from an aircraft that is either traveling N or S below it.
The above was extracted from
http://www.n2yo.com/?s=23839 as the satellite had just started moving south in its eccentric ellipse.
The satellites eccentric speed (in relation to its Earth position) as it passes over the Equator every 11.97 hours is approximately 90m/s. This provides no Doppler shift effect to an observer directly below it, but the Doppler shift will become more evident the further N or S the earth observer is located.