Why does Curiosity use an RTG rather than solar (as Spirit and Opportunity do) for power?

Question

Why did Curiosity choose to go with nuclear power? While solar panels have issues with Martian dust, this was a known factor before the 2004 Spirit and Opportunity mission. Why then did the 2004 rovers choose to use solar panels for power?

Answer 1

Two alternatives (RTG or solar) were investigated in the Mars Science Laboratory Environmental Impact Statement. In summary, solar arrays would limit the MSL to operate between 5°N and 20°N, and for one Martian Year only if at exactly 15°N, whereas RTGs would permit it to operate for at least one Martian year anywhere from 60°S to 60°N.

From page 2-1 (PDF page 35):

Proposed Action (Alternative 1, NASA’s Preferred Alternative) (...) The proposed MSL rover would utilize a radioisotope power system as its primary source of electrical power to operate and conduct science on the surface of Mars. (...)

Alternative 2 (...) The alternative MSL rover would utilize solar energy as its primary source of electrical power to operate and conduct science on the surface of Mars. (...)

Of particular interest is Table 2-5 on page 2-36 (PDF page 70):

^{MSL alternative capabilities as investigated by NASA.}

Accompanying text below the table:

Alternative 1. The MMRTG-powered rover would be capable of achieving all of the target operational capabilities summarized in Table 2-1, including landing at a scientifically interesting location between 60° South and 60° North latitude, and operating and conducting science for at least one Mars year.

Alternative 2. At most latitudes on Mars the amount of time that a solar-powered rover could perform science operations would be limited by the ability of the solar array to generate sufficient power for the rover to survive the extreme thermal environment. At latitudes on Mars between 60° South and 5° North and between 20° North and 60° North a solar-powered rover either would not have sufficient power to operate at all, or would not be able to survive long enough to accomplish even the minimum science. A solar-powered rover could operate for at least one-half Mars year and achieve the minimum science capability only at latitudes ranging from slightly above 5° North to slightly below 20° North, and could operate for a full Mars year and accomplish the full science objectives only at 15° North latitude.

For more details, including a detailed description of both (and other) alternatives as well as a consideration of non-scientific factors, see the Mars Science Laboratory Environmental Impact Statement, Volume 1 and Volume 2. The non-scientific factors include environmental concerns, which speak for solar — considerably less risk in case of a catastrophic launch failure (see also this question on RTG alternatives).

Answer 2

While I've not yet found explicit back up to my recollection of this, the explanation I remember is that solar panels would not provide adequate power to operate the rover and the instruments on it and still fit within the mission profile. Curiosity/Mars Science Laboratory is much larger and more massive and has more instruments than the previous Mars rovers. Thus the power requirements are much higher. Current solar technology is not adequate to power the rover. Solar panels to provide adequate power likely would have increased the size and weight of the spacecraft so much that the mission would have become infeasible.

The following statement from the MSL mission profile does not quite explicitly support the above, but it somewhat addresses the matter:

The rover will carry a radioisotope power system that generates electricity from the heat of plutonium's radioactive decay. This power source gives the mission an operating lifespan on Mars' surface of a full martian year (687 Earth days) or more, while also providing significantly greater mobility and operational flexibility, enhanced science payload capability, and exploration of a much larger range of latitudes and altitudes than was possible on previous missions to Mars.