How would Newton's Laws and the rest of physics be changed on a non-inertial frame?
A non-inertial frame, such as a planet that does not have constant velocity in its orbit, would change the laws of physics in many ways. For example, if you stood on the surface of the planet as it accelerated and dropped something, it would seem as if a force pushed it in some direction as it fell.
But how would the people on the planet view the laws of physics? Also, how would the inhabitants react to a visit to Earth?
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They could still tell the difference.
A non-inertial frame involves acceleration of some sort, i.e. non-uniform velocity. Such a frame can certainly have uniform speed, but the direction of motion of an object in the frame will be constantly changing. For instance, an observer on a merry-go-round is in a non-inertial frame, because they are moving in a circle.
We're in a non-inertial frame, because we're on Earth. There are two important reasons for this:
- Earth revolves around the Sun.
- Earth rotates on its axis.
Both of these mean that fictitious forces arise. The Coriolis force is perhaps the most famous one, and plays a role in ocean currents and other systems of circulating fluids.
Even though we're in a non-inertial frame, though, the effects are generally small. The acceleration of Earth around the Sun is relatively tiny; the same goes for the acceleration from its rotation. Therefore, our frame is approximately inertial, and we don't notice most of the fictitious forces.
However, we still know that we're in a non-inertial frame. We can create other non-inertial frames - such as merry-go-rounds and notice that there are fictitious forces there. Therefore, knowing that the Earth moves around the Sun, we can tell that we're in such a frame.
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