little math problem October 2018

[EugeneNine]

(10-20-2018 08:05 PM)Thomas Okken Wrote:  I'm sure this isn't optimal, but just to get started:

The greatest distance at which the rovers can see each other is D. The radius of the planet is R. The rovers can travel at a maximum speed V.

Assumptions: the planet is a perfect sphere, no water, no hills. Visibility is the same everywhere.

One rover stays put, the other starts searching. It searches in an expanding spiral, where each circuit is 2 * D from the last. I'm ignoring the details of the shape of that spiral near its ends.

The rover covers an area of 2 * D * V per unit of time. The area of the planet is 4 * pi * R^2, so it takes a time (4 * pi * R^2) / (2 * D * V) to search the entire planet, and the expected search time is half that.

what if both rovers started in a spiral? I'd think they would meet sooner depending on the speed and increasing radius of the spiral.

Though how would the rovers know they are making a spiral and not just going in a circle or random directions.

Seems like for any given planet we want to explore via rovers we should figure out the min number of gps satellites to deploy.