Apollo 17 (December 7–19, 1972) was the final mission of NASA’s Apollo program, the sixth and most recent time humans have set foot on the Moon or traveled beyond low Earth orbit. Commander Gene Cernan and Lunar Module Pilot Harrison Schmitt (to the right) walked on the Moon, while Command Module Pilot Ronald Evans orbited above. Schmitt was the only professional geologist to explore the Moon.
In the video you see Schmitt attempt to dislodge a rock with a push from his foot. The difficulty is obvious in the way his body reacts to the equal and opposite force from the rock. The rock appears to be roughly twice the diameter of Schmitt’s helmet (≈30 cm), and roughly spherical, so it has a volume of:
V = 4πR3 = 4π(30 cm)3 = 340,000 cm3 = 0.34 m3
Rocks found on the lunar surface have densities between 2500 to 3300 kg/m3 depending on the rock type. Most lunar rock samples are on the high end of this range, so we’ll assume an even 3000 kg/m3 for its density. That gives the rock a mass of:
m = ρ×V = (3000 kg/m3) × (0.34 m3) = 1020 kg
On Earth, that rock would weigh:
F = mg = (1020 kg) × (9.8 N/kg) = 10,000 N (2250 lb)
On the Moon it weighs:
F = mg = (1020 kg) × (1.62 N/kg) = 1650 N (370 lb)
There’s no way you could lift that rock on Earth, but on the Moon a pro weightlifter could handle it easily.
But Schmitt isn’t lifting the rock — he’s pushing it with his foot, so different physics comes into play. The average force the leg can apply as it extends is 177–350 N. We’ll assume 200 N (45 lb) allowing for the fact that Schmitt is wearing a relatively inflexible space suit, and is also trying to maintain his balance. According to Newton’s 3rd Law of Motion, whatever force he exerts on the rock will create an equal and opposite reaction force on his boot:
If Schmitt applies 200 N of force to the rock, he’ll feel 200 N of force pushing back against his boot. That’s why you see him recoiling backward. The same thing happens when Cernan pushes the rock. Even though the rock’s weight is only 1/6th of what it would be on Earth, it still retains the inertia (resistance to changes in motion) bestowed by its 1020 kg of mass. This is also true in weightless conditions, like if they were pushing the rock in a space station or on a trans-lunar trajectory.
Weight depends on where you are and how you’re moving. Mass (and inertia) are constant. The situation is confused by careless use of the terms mass and weight, which have distinct and different meanings. Mass is a scalar measured in units of kilograms, and its inertia reacts the same to forces applied from any direction in accordance with F=ma.
Weight is a force caused by gravity, and is a vector measured in newtons (or pounds). Unlike scalars, vectors have a unique direction. For weight, that direction is “down.”
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