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Originally Posted by renormalised
Anyway, there's nothing wrong with what you have said except for this. Even though the Sun's gravitational well is much larger than the Earth's, we are subject to a greater acceleration towards the centre of the Earth than we are to the Sun.
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I agree with you completely on this part: we are subjecft to a greater acceleration towards the centre of the Earth than we are to the Sun (by about 3 orders of magnitude).
I have never said otherwise. This is why I was careful to refer to "gravity well" and not "gravitational acceleration" or "force".
Escape velocities give a good feel for the size of the gravity wells:
Escape velocity of Earth = 11.2 km/s
Escape velocity of Sun = 618 km/s
Quote:
Originally Posted by renormalised
Sure, as part of the Earth system, we are in free fall about the Sun and don't feel the Sun's curvature of spacetime, but that's precisely the point. We are much closer to the Earth than we are to the Sun and from our vantage point, the curvature of spacetime the Earth generates is more intense than the Sun's. Hence we don't go floating off into space towards the Sun.
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This is not the reason we don't fall off the Earth though. As the Earth is in free-fall around the Sun, we don't feel the gravity of the Sun directly. We do feel it's massive curvature of the space-time in our vicintiy through tidal effects.
Take care,
Doug