Fig. 1

We are now pursuing a new lunar rover concept which involves deploying a rover that hovers above the lunar surface once the lander is secure on the lunar surface.
This new lunar rover uses a tether on a spool attached to a counterbalance. As the spool rotates, the cable unwinds in a measured and tightly controlled fashion ensuring a gradually increasing, spiral orbit for the rover around the lander as the rover attempts to travel the required 500m distance. Because centripetal force will vary based on the radius of the path travelled by the rover, the rotation speed of the spool must be constantly adjusted to hold the altitude of the rover steady.
If we assume that the total distance of the rover has a shape of an Archimedean spiral (see fig. 2), we can calculate the distance L as follows:

L =a/2[φ(φ²+1)^0.5+Arsinh (φ)]

with

a= k/(2π) (k=constant distance of the spiral arms)
φ= n2π (n=number of turns)

Fig. 2

Once the required 500m distance threshold has been reached, the rover will cease to hover above the lunar surface and will drop down in order to commence taking samples from the lunar surface. Once that remote sampling process is complete including any requisite analysis, the rover will be reeled back to the lander using the tether.