Not required.

Technically, the cloud city would consist of a long tether anchored to the ground at equator that would extend up into space. The tether would be connected to a huge counterweight located in a geosynchronous orbit (GSO) of approximately 35,786 km (22,236 mi) above the surface, because its orbital period of approx. 23h 56m 4s matches the Earth's sidereal rotation period. Tension between the Earth and the counterweight, whose orbit keeps the city over the same location above the surface, would keep the tether taut.