Is there a name for the orbit of a natural satellite of a planet who's period is the same as the rotational period of the planet, but the orbital motion has the opposite sense than the planet's rotation?
If there isn't an existing term or name, how would it at least be described, technically?
How much does the tidal effect affect satellites in a retrograde orbit?
No. Such an orbit would be co-incidental and dynamically uninteresting.
For a planet of given mass and rotation period, there is a class of orbits, whose period is equal to the rotation period of the planet. If the orbit is prograde this gives an interesting effect: the satellite would remain in the same position in the sky (or if it had an elliptical orbit, it would return to the same position each day)
If the orbit is retrograde, the orbit would not have any particularly interesting features. While it is possible for tidal locking to produce a synchronous orbit, there is no mechanism to stabilise a retrograde orbit like this, and tidal effects will slowly disrupt it.
There is probably no specific term, as I don't think such orbits occur naturally anywhere, nor there is any sense to launch an artificial satellite into such an orbit.
But in general terms if an orbital period of a satellite is equal to the period of rotation of a body it orbits, such orbits are called synchronous (e.g. geosynchronous if the satellite orbits the Earth). And if the orbit is in the opposite sense w/respect to the rotation of a body, the orbit is called retrograde.
So I would say that "synchronous retrograde orbit" would pretty unambiguosly point to a type of orbit you're describing.
