Discussion
A number of degrees of freedom for an astronaut constrained to move on surface of a planet (moving freely in space is) :
Answer: B
The keyed answer is 5.
Treat the astronaut as a rigid body. Moving freely in space, a rigid body has 6 degrees of freedom: 3 for the position of its centre of mass and 3 for its orientation. Being constrained to move on the surface of the planet imposes one equation of constraint, keeping the point of contact on the surface, so it removes one degree of freedom:
\[ 6 - 1 = 5 \]
The question's wording is garbled; 6 is the count for the body moving freely in space, which is what the constraint reduces. Counts of 4 or 2 would apply to a body confined more tightly, for example 2 for a point particle restricted to a surface.
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