Coaxial conundrum

Q: True or false and why? The top and bottom rotor blades of a coaxial helicopter are separated vertically by a good distance for one simple reason: Designers can’t risk the blades contacting each other when they flex.

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FROM THE OCTOBER ISSUE: Does mass matter to measure mass?

We asked you whether the spacecraft of the Gravity Recovery and Interior Laboratory mission had to have the same mass to do their job of measuring variations in lunar gravity. There was no winner this month, so we asked scientist Michael Watkins, who co-conceived the concept behind GRAIL and similar gravity-mapping missions, to explain:

“From the perspective of gravity alone, the satellites actually didn’t have to match in mass. Here’s why: When the mass of a satellite is very small compared to the mass of the central body like the moon, then the effect of gravity on them is essentially the same regardless of their mass. This idea was proposed by Galileo, but beautifully shown by Apollo 15 Commander David Scott when he dropped a hammer and feather on the moon and they landed at the same time. Therefore, when the lead GRAIL spacecraft passed over an unusually massive interior feature, it was affected the same way as the trailing spacecraft even if the masses were different. Aside from gravity, though, the satellite’s motions were also affected by non-gravitational forces like solar radiation pressure, which are sensitive to the area to mass ratio, and of course, it is generally less expensive to build two nearly identical spacecraft than two very different ones. So, in the end, the spacecraft were close in mass, but not really due to gravitational effects.”

Coaxial conundrum