little math problem October 2018
10-22-2018, 06:17 PM
Post: #22
 EugeneNine Member Posts: 243 Joined: Feb 2017
RE: little math problem October 2018
(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.
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 Messages In This Thread little math problem October 2018 - pier4r - 10-20-2018, 06:48 PM RE: little math problem October 2018 - Zaphod - 10-20-2018, 06:55 PM RE: little math problem October 2018 - pier4r - 10-20-2018, 07:40 PM RE: little math problem October 2018 - Thomas Okken - 10-20-2018, 08:05 PM RE: little math problem October 2018 - Zaphod - 10-20-2018, 10:03 PM RE: little math problem October 2018 - EugeneNine - 10-22-2018 06:17 PM RE: little math problem October 2018 - Mark Hardman - 10-20-2018, 08:14 PM RE: little math problem October 2018 - pier4r - 10-20-2018, 09:41 PM RE: little math problem October 2018 - sasa - 10-20-2018, 09:35 PM RE: little math problem October 2018 - Gene222 - 10-21-2018, 06:53 PM Two little robots done got themselves lost - brickviking - 10-20-2018, 10:50 PM RE: little math problem October 2018 - Mark Hardman - 10-20-2018, 11:49 PM RE: little math problem October 2018 - Dave Shaffer - 10-21-2018, 06:27 PM RE: little math problem October 2018 - Paul Dale - 10-21-2018, 12:42 AM RE: little math problem October 2018 - Thomas Okken - 10-21-2018, 08:21 PM RE: little math problem October 2018 - sasa - 10-21-2018, 01:45 AM RE: little math problem October 2018 - Ken S - 10-21-2018, 02:58 AM RE: little math problem October 2018 - Dave Shaffer - 10-21-2018, 06:31 PM RE: little math problem October 2018 - ijabbott - 10-21-2018, 10:07 PM RE: little math problem October 2018 - EdS2 - 10-22-2018, 08:17 AM RE: little math problem October 2018 - pier4r - 10-22-2018, 09:31 AM RE: little math problem October 2018 - ijabbott - 10-22-2018, 06:05 PM RE: little math problem October 2018 - Zaphod - 10-22-2018, 06:33 PM RE: little math problem October 2018 - Dave Shaffer - 10-22-2018, 08:14 PM RE: little math problem October 2018 - Albert Chan - 10-22-2018, 06:40 PM RE: little math problem October 2018 - Csaba Tizedes - 10-23-2018, 06:02 PM RE: little math problem October 2018 - Csaba Tizedes - 10-23-2018, 06:08 PM RE: little math problem October 2018 - EugeneNine - 10-23-2018, 06:45 PM RE: little math problem October 2018 - Albert Chan - 10-23-2018, 07:09 PM RE: little math problem October 2018 - Maximilian Hohmann - 10-23-2018, 07:44 PM RE: little math problem October 2018 - pier4r - 10-24-2018, 03:26 PM RE: little math problem October 2018 - Maximilian Hohmann - 10-24-2018, 03:43 PM RE: little math problem October 2018 - Thomas Okken - 10-24-2018, 06:08 PM RE: little math problem October 2018 - pier4r - 10-24-2018, 07:37 PM RE: little math problem October 2018 - sasa - 10-25-2018, 09:30 AM RE: little math problem October 2018 - EdS2 - 10-25-2018, 09:50 AM

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