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I know there is a gioscopic explanation but I was under the impression that Earth is traveling in a straight line through space that has been curved by our sun's gravity ,so my question is why doesn't one hemisphere always point away from the sun ? It just seems like a bit of a contradiction that gravity can curve the fabric of space but has no effect on earth's axis...

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  • $\begingroup$ For a practical example of this, take a hand-held concrete-cutting saw. It's easy (but not recommended!) to walk around a table with it running, but you'll find you are forced to keep it pointing in the same direction; it takes a lot of muscle power to change its axial direction. That's conservation of angular momentum. $\endgroup$ – Chappo Nov 3 '18 at 23:25
  • $\begingroup$ It's exactly like a spinning top. $\endgroup$ – Fattie Nov 6 '18 at 9:39
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It is just conservation of angular momentum. In order to change the direction of the spin axis of the Earth (which would change the direction of its angular momentum) you would have to subject it to an external torque. The curvature of space has no significant bearing on the question.

In fact the direction in which the Earth's spin axis points does change, but on much longer timescales. The "precession of the equinoxes" (as it is called) is cyclical with a 26,000 year period.

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The path of the Earth in space is curved (by gravity). The explanation of gravity in Relativity is that the Earth follows a geodesic in spacetime, which is not usually a straight line in space.

A ball that is thrown will follow a geodesic, a ball that is thrown harder will also follow a geodesic. The reason that the two balls don't follow the same path, is that they are following geodesics in curved spacetime, not straight lines in curved space.

This being the case, the direction of the Earth's axis has very little to do with curved spacetime. The direction of the axis in space remains fixed, unless some force acts on the Earth to change it. The sun and moon can provide such torque (and cause precession and nutation), but this can be accurately described by the Newtonian approximation of gravity.

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The main effect of the Sun's gravity on the Earth is to keep it in a (very nearly) steady elliptical orbit. So from one perspective, the Sun pulls the Earth towards it according to the inverse square law (with some rather tiny variations given by general relativity). From another perspective, the Sun's mass distorts space-time so that the natural geodesic path that the Earth follows returns to the same place (relative to the Sun and oriented by distant stars) every year. These are two descriptions of the same physics, and both are equally true (or false).

In Newtonian physics (without GR) (and assuming that both the Earth and the Sun were perfectly spherical and that the other planets did not exist) the Earth's axis of rotation would not change at all. General relativity does predict some very small changes: frame dragging and the geodetic effect. Their effect on the Earth, though is incredibly tiny. The effect of the Moon's gravity on the Earth's equatorial bulge is much greater.

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