The lunar module's descent engine should have dug a huge crater in the lunar surface.

I have yet to see a conspiracist who has given any kind of quantifiable justification for this belief. We could simply ask, "Why do you expect a crater?" and probably be done with it. A few have made vague references to other vehicles in other situations that produce some kind of visible interaction with the soil underneath them. But none can explain why that ought to be immediately generalized to include the lunar module.

The Lunar Landing Training Vehicle, for example, didn't produce any craters. And it directed even more downward thrust than the lunar module. Harrier jets and large helicopters routinely produce vast amounts of downward thrust without leaving large craters behind.

The rocket engine's thrust was focused on one point for quite some time. Surely there would be a significant visible effect.

Not necessarily. It's difficult to tell from the landing film footage just how high above the surface they were. But until the very last few seconds, the approach profile for the lunar module called for significant forward motion. The exhaust probably wasn't focused on any one spot for very long.

The notion that it was focused at all displays some misunderstanding of how rocket engines behave in a vacuum. Watch very carefully at the next rocket launch. As the rocket climbs higher and higher, the exhaust plume spreads out. Because the surrounding air gets thinner as the rocket climbs, there is less air pressure to impede the dispersal of the exhaust gasses.

The lunar module's descent engine produced 10,000 pounds (4,550 kgf) of thrust. Surely 10,000 pounds of pressure is enough to dig a very large hole.

Basic Newtonian physics solves this problem.

Weight is simply the force of gravity between two masses. If something weighs 1 pound (2.2 kg) on earth, that's the same as saying a force of 1 pound exists between the earth and the object. The force of gravity is computed partly by multiplying the masses of the two objects in question. The moon has less mass than the earth, and so exerts less gravity. So the force between the moon and that same object would only be about three ounces (75 g).

Galileo's principle lets us treat force, weight, and acceleration as identical concepts when dealing with gravity. A falling object accelerates downward because gravity imparts a constant force resulting in a constant acceleration. This acceleration produces an increase in downward velocity.

So if you want to descend at a constant rate you have to precisely negate that gravitational force so that your acceleration along the vertical axis is zero. This means the net force along the vertical axis must also be zero. So if you can apply a force exactly equal to the force of gravity, but in the upward direction instead, you can achieve that constant velocity. (Hovering is the same principle, but with the constant velocity being zero in that case.)

The Apollo 12 lunar module, for example, weighed 33,325 pounds (15,148 kg) fully loaded. But near the end of the descent it was not fully loaded. Most of the descent engine (DPS) propellant had been burned away. Fortunately there are ample references to how much DPS propellant was burned away. We can therefore calculate the weight of the lunar module very accurately. According to telemetry, 705 pounds (320 kg) of DPS propellants remained from an initial load of 18,226 pounds (8,285 kg).[Reports12] This means at touchdown the lunar module had shed at least 17,521 pounds (7,964 kg) by burning its descent fuel. Subtracting this from the launch weight gives a landing weight of 15,804 pounds (7,184 kg).

But we have to remember to convert its weight (exerted gravitational force) to lunar values. Dividing by six produces a landing weight in lunar gravity of 2,634 pounds (1,197 kg).

So in order to negate the downward force of 2,634 pounds (1,197 kg) we merely have to apply an upward force of the same magnitude. Therefore a thrust of 2,634 pounds was required to hover or descent at a constant rate.

Yes, it really is that easy.

This describes the situation seconds before touchdown. The initial descent was of course very fast. And so to slow the rate of descent it would have been necessary to apply a larger thrust that surpasses the force of gravity. This amount of thrust was applied at high altitude where it did not affect the lunar surface.

By comparison, a fully-loaded Harrier jump jet produces 27,000 pounds of thrust at liftoff -- almost an order of magnitude more than a lunar module. Yet no one sees (or expects to see) a crater under a Harrier. This is because popular intuition dictates that a rocket engine of any size is automatically more powerful than a jet engine of any size. In fact, most jet engines are more powerful than the lunar module's rocket engines.

The published strength of the lunar module descent engine is 10,000 pounds, not 3,000 pounds. With weight at a premium on the lunar module, the designers wouldn't have specified an engine larger than necessary. Therefore it's wrong to say that only 3,000 pounds of thrust was applied. [David Percy]

Poor Mr. Percy. With arguments like this it's no wonder he has such poor credibility. The published capacity of the lunar module descent engine (DPS) is indeed just under 10,000 pounds (4,550 kgf), and weight certainly was at a premium. But managing the descent and hovering over the lunar surface wasn't the DPS's only task. It was also used to perform orbital maneuvers prior to the landing. The lander was bloated with fuel and supplies, and orbital maneuvers are very time-critical. Having a large engine ensured they were carried out precisely with short burns, not sloppily with long burns from a weaker engine.

Physics is obviously a mystery to Percy. He's clearly grasping at straws. With 10,000 pounds of thrust applied upward, a constant rate of descent would have required an equal force of lunar gravity applied to the lander in order to produce zero net force and therefore no acceleration. Since gravity is six times stronger on earth, this means the lander would have weighed 60,000 pounds on earth -- nearly twice its published takeoff weight. Percy is only looking at the the published lunar lander data that supports his theory. Then he apparently just hopes the physics will all work itself out.

They don't.

Is there any evidence in the photographic record of the effect of the lunar module's descent engine?

Of course.