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graphical model. The code that translates between these two conventions
is likely to be found either in the interface with the physics engine (for
example, the code that updates the position of the objects after the physics
simulation has run), or the code that sets up the reference frame for the
object during rendering.
The center of mass is fixed for a rigid body such as a sledge hammer; this
assumption has been implicit in the whole discussion; otherwise, it wouldn't
make sense to advise setting the origin at the center of mass. However, for
a general system with moving parts, such as Earth, the center of mass is a
dynamic property, not a constant. The center of mass shifts around within
the object as the parts are reconfigured.
For example, imagine if all of the people in the world decided to visit
the North Pole at the same time. Assuming we would all fit and there
were enough earmuffs to go around, the Earth's center of mass would shift
towards the North Pole. This new center of mass, however, would trace out
the exact same trajectory as the old one would have. In other words, while
the trajectory of the Earth's geometric center would be slightly “southward”
from where it would have been if we all stayed at home, the trajectory traced
out by the center of mass is the same in either case.
Or, let's say that instead of visiting the North Pole, we all decided to go
to the Galapagos Islands, which is very near the equator. Would Earth's
rotation suddenly get all “wobbly” like an out-of-balance ceiling fan? No!
Instead, the center of mass would shift towards the Galapagos Islands, and
the Earth would rotate about this new center of mass. So although the
rotation, when viewed from above, might appear asymmetrical, since the
rotation would not be about the center of the spherical Earth (assuming
the Earth were perfectly spherical), the rotation would be smooth. An
unbalanced ceiling fan is wobbly because it is not free to choose its axis of
rotation, and so it must be balanced in order to align the center of mass with
the fixed axis of rotation. Earth, however, is not connected to anything,
and it is free to rotate about its center of mass, wherever that center of
mass may be.
Of course, all the people on Earth put together have less mass than
our moon, so our discussion has been misleading. The point that traces an
ellipse as we orbit the sun isn't the Earth's center of mass at all! It is the
center of mass of the entire Earth-moon system. This point isn't really close
to Earth's geometric center, although it is beneath the surface, but only
because Earth is so much more massive than the moon. As the moon orbits
the Earth, the center of mass of the system shifts around within Earth. It
is this imaginary point that orbits the sun, not the center of mass of Earth
itself.
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