Correction Appended

NASA's latest Moon mission will end on Monday -- not with a whimper, but a splat.

Two splats, actually.

Ebb and Flow, two space probes the size of washing machines that have been orbiting the Moon and measuring its gravity field, will perform an orchestrated death plunge on Monday, crashing into the body's dark side.

The exercise will not be for the advance of science, but rather something of a garbage-disposal operation, to make sure that the probes -- which are running out of fuel -- do not come to rest in a historically significant place, like on Neil Armstrong's footprints.

The Moon has been affronted this way many times before, especially during the space race of the 1960s, but NASA is now trying to dispose of its litter more carefully.

This time, the first impact will come 40 seconds past 5:38 p.m. Eastern Standard Time on Dec. 17 when Ebb slams into a mountain near the Moon's north pole at 3,760 miles per hour. The second, from Ebb's twin, Flow, will come 20 seconds later.

Unfortunately, since the action will happen on the dark side of the Moon, there will be nothing for earthlings to see.

"We're not expecting a flash that is visible from Earth," Maria T. Zuber, the mission's primary investigator, said Thursday during a telephone news conference.

That is all by design as NASA wraps up its Gravity Recovery and Interior Laboratory mission, or Grail, for short.

To map the gravity, the two spacecraft are in an orbit passing over the Moon's north and south poles. They pass over all parts of the lunar surface as the Moon rotates below.

If the probes' fuel ran out and their orbits decayed, they could crash anywhere on the Moon, including a slim chance -- eight in one million -- that one of them could obliterate those famous footprints or another historic site.

With the spacecraft guided into a mountain, the chances are zero.

Even in their demise, however, Ebb and Flow may be able to aid the cause of science. Another of NASA's spacecraft, the Lunar Reconnaissance Orbiter, will pass over the crash sites, and scientists hope that they will be able to tell something about the mountain -- which is a remnant of a crater rim -- from the gouges created by Ebb and Flow.

Asked what the crash might look like to someone standing there, David Lehman, the project manager for Grail, said, "It'll be like a washing machine landing on top of you, and it'll be a very bad day for you."

Launched in September 2011, the two spacecraft slipped into lunar orbit at the beginning of this year.

For the primary mission, the two spacecraft orbited at an altitude of 34 miles. Wobbles in the distance between them told of variations in the Moon's gravitational field. For example, the gravity would be stronger when the spacecraft passed over a mountain field or a clump of dense minerals.

Because of Ebb and Flow, scientists now have more precise measurements of the Moon's gravity than of the Earth or any other planet.

After the primary mission was completed, the two spacecraft were nudged to a lower altitude of 14 miles -- for more precise measurements -- and then, on Dec. 6, even lower to 6.6 miles. But maintaining that low altitude depleted the maneuvering fuel.

Data from the Grail mission already has shown that the Moon's crust is thinner than had been thought, and that it was pulverized by impacts during the early history of the solar system.

The Moon's density, deduced from the gravity, places constraints on what it could be made of.

For example, Dr. Zuber said, the Moon appears to contain the same abundance of aluminum as the Earth, supporting the theory that the Moon was formed out of a cataclysmic collision of a Mars-size body and the Earth.

The data so far does not support a hypothesis that the Earth once had two Moons that later collided and combined into one.

The gravity data could also help future travelers, human and robotic, navigate to a precise location on the Moon's surface.

"This actually decreases the costs of future exploration of the Moon," Dr. Zuber said.

Correction: December 14, 2012, Friday

This article has been revised to reflect the following correction: An earlier version of this article misstated part of the name of a NASA mission. It is the Gravity Recovery and Interior Laboratory, not the Grail Recovery and Interior Laboratory.

First Published: December 14, 2012, 11:00 p.m.