# How can Newton's laws of motion be true on the Earth?

The Earth, effectively a non-inertial frame of reference, is where Newton concluded his laws of motion. However, Newton's first law only holds in an inertial frame of reference.

In the process of inventing the Newton's laws of motion, since almost all (I suppose) the experiments were done in a non-inertial frame of reference i.e. the Earth, why were people confident enough to believe that Newton's first law is true (to some extent, I am not talking about relativity etc.) in an inertial frame of reference?

I am not trying to say that Newton's laws of motion are lies. I just had a logical question: since the research was done in a non-inertial frame of reference, how can we invent the laws regarding motion in an inertial frame of reference?

I suppose that's because the Earth can be approximated to an inertial frame of reference as the effect of the self-rotation (which causes the Earth to be a non-inertial frame of reference, in my opinion) of the Earth on the objects on the Earth is quite small. And, therefore when people did the experiments, the uncertainty caused by the self-rotation of the Earth is too small to be significant (or, maybe they didn't even find/realise such an uncertainty!). And therefore, by inference (or guessing?), we can invent the laws of motion regarding objects in an inertial frame of reference. In theory, if we do the same experiment in a true inertial frame of reference, we will effectively get the same/similar results. (This is just my explanation, which can be very debatable!)

• Does this answer your question? Is Earth an inertial reference frame? Commented Oct 26, 2023 at 14:25
• This seems likely to be a duplicate, but I think it's not a duplicate of the linked question. The one sentence answer is "by declaring your frame to be inertial a priori, then inventing fictitious forces (gravity, coreolis, etc) that act in a particular direction with a magnitude proportionate to inertia"
– g s
Commented Oct 26, 2023 at 21:07
• Voting to reopen. Definitely not a duplicate of the linked question, since the OP recognises that the Earth's surface is not an inertial reference frame. Commented Nov 1, 2023 at 15:22

The earth is rotating very slowly (once per day). Therefore it is, as a good approximation, an inertial frame. Actually the effects from the rotating earth (i.e. the centrifugal force and Coriolis force) are quite small and mostly neglectable.

• Once per day minus once per year, achtually.
– JEB
Commented Oct 26, 2023 at 14:33
• You also need to consider only 2D motion in a horizontal plane. Commented Oct 26, 2023 at 16:00
• Or once per day minus once per year, minus once per rotation of the sun around the center of the galaxy. Commented Nov 2, 2023 at 14:12

If we determine certain physical laws in a laboratory on the surface of the Earth then we have two logical choices:

1. We can assume that these laws hold exactly in the laboratory reference frame, and so only hold approximately in an inertial frame of reference.
2. We can assume that these laws hold exactly in an inertial reference frame, and so only hold approximately in the laboratory reference frame.

In the absence of sufficiently precise measurements to distinguish experimentally between these two options, we can use Occam's razor. Option 1 gives a special status to the laboratory reference frame, which is arbitrary; therefore Option 2, being simpler, is the better explanation.

If I run an experiment one hundred times with the same results, but because the laboratory is closed at weekends I have only ever run the experiment on weekdays, I will nevertheless conclude that if I were to run the experiment at the weekend I would get the same result because this is a simpler explanation that assuming that a different law arbitrarily applies at weekends.