Roving on the moon...setting up depots...how many??? Please help?

Question

Here's the thing:

A ROVING ON THE MOON

They year is 2047 and it is now 32 years since a Moon base was established. Rather that sit snugly inside of the base, a group of adventurers plan the first surface circumnavigation of the Moon.

They will travel around the lunar equator using a Lunar Roving Vehicle. This vehicle is powered by electric batteries that give it a range of 2000km (i.e. 1000km outbound and 1000km return). The rover can carry the crew, their food and oxygen, and ONE spare battery.

Obviously the adventurers cannot travel further than 2000km from the base on a double set of batteries and expect to return safely to base. Although there is an unlimited set of batteries on the Moon base, the adventurers appear to be constrained to explorations within a 2000km radius of the base.

Or are they? Propose a method by which they could complete a surface circumnavigation of the lunar equator using the existing Lunar Roving Vehicle (i.e.YOU ARE NOT PERMITTED TO USE SOLAR ELECTRIC POWER)

SOME USEFUL INFORMATION: Radius of the Moon is 1739km, π = 3.14, Moon has no impassable obstacles or terrain which reduces range of rover on each battery. Partly used batteries may be set aside and the remaining charge used later (e.g. on the return journey). Batteries cannot be recharged - once discharged the batters are discarded.

HINTS: Polar explorers on Earth have laid in supply depots at regular points along their route. Members of the second expedition to reach the South Pole perished when they failed to reach a supply depot on their return journey to Scott Base. Unlike Scott and his party, you don't have to make a return to base along the same route - you would be circumnavigation the Moon. It would also be wise to investigate whether to lay supplies in one direction only, or whether to lay out supplies both eastward and westward from the Moon base. Also, is it more efficient to use up a battery completely before discarding it, or to partly used some of the batteries and to finish using them at some later time? Also try to find the optimum separation between supply depots.

DADA...can any body help me???

If you do, many thanks. (plus, does anyone know a mathematical formula for this?)

Answer 1

Carry a battery out 1,000 Km, then go back.

On the 2nd trip, carry another out there.

On the 3rd trip, do a battery exchange at the 1,000 Km mark, and drop off a battery at 2,000 Km, then do another battery exachange on the way back.

Repeating this technique will give an infinite range, but take 2^(R/1000) batteries.

Answer 2

Here is what i think, when the rules set in place put your life at risk, then cheat and break the rules and live or follow the rules and die, i say cheat and live every single time.