Discussion
The number of degrees of freedom for an astronaut constrained to move on surface of a spherical spaceship freely moving in space, is :
Answer: A
The astronaut has 5 degrees of freedom.
The spaceship moves freely, so the position of its centre needs three coordinates. The astronaut is constrained to the spherical surface, a constraint of fixed distance from the centre, so his position on it needs only two more, such as the angles \(\theta\) and \(\phi\). In all, 3 + 2 = 5 independent coordinates fix the astronaut's position.
Six would count the astronaut as a free particle with the ship's three, ignoring the constraint, or would add the ship's rotation, which does not change where on the sphere he can be. Three ignores the motion of the ship, and four miscounts the surface coordinates.
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