Due to rotation and low friction, can the Earth be considered a gyroscope? If so, any interesting implications to this? Thanks
A spinning celestial body can indeed be considered to be a gyroscope.
Part of the motion pattern of the Earth is that it is subject to a gyroscopic precession with a period of about 26.000 years. The common name for this gyroscopic precession is 'precession of the equinoxes'. The precession of the equinoxes was noticed many hundreds of years before it was recognised that it is a case of gyroscopic precession.
The word 'gyroscope' doesn't necessarily have a sharp definition, but generaaly 'gyroscope' is taken to mean an axially symmetric spinning body, suspended in such a way that the effective point of suspension coincides with the center of mass.
(The expression 'spinning top' on the other hand is commonly used to refer on a spinning object that is standing on a tip, so that the point of suspension (the point where the weight of the object is supported) does not coincide with the center of mass.)
So in all, yeah, the Earth is a gyroscope.
The center of mass arises from the inertial mass of the object, and the center of gravitational attraction arises from the gravitational mass. As we know, gravitational mass and inertial mass are equal, therefore in a uniform gravitational field the center of gravitional attraction and the center of mass will coincide.
When a celestial body is non-spinning, and large enough so that its own gravity pulls it into a perfectly sphere, then the center of gravitational attraction and the center of mass will coincide perfectly.
In the case of the Earth: due to its spinning motion there is an equatorial bulge. Whenever an object is not perfectly spherical, the center of gravitatinal attraction and the center of mass to not quite coincide.
In the case of the Earth the gyroscopic precession is due to the gravitational influences of the Sun and the Moon.
The gyroscopic motion of the Earth is the reason we have seasons. For half the year the northern hemisphere is closer to the sun than the southern hemisphere, and for the other half of the year the opposite is true. This is because the axial direction of the Earth stays fixed as it rotates around the sun, a direct result of the gyroscopic motion of the Earth (resulting from the Earth's rotation).
The moon’s gravity exerts a torque on the earth, which causes the earth’s axis to precess (as a gyroscope subjected to an off-axis torque does). So the North Star is only approximately above the North Pole currently. In 13000 years, earth’s axis will point somewhere totally different, and in 26000 years or so it will be back where it is now.