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By newton's first law, an object will continue to be in the state of motion of rest until and unless an external force is acting on it. To prove or verify it experimentally today, is there any way out to diminish the problem of friction?

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Objects in orbit come pretty close.

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If you don't mind venting the cabin or taking a walk outside, even air drag can be very nearly eliminated.

All you have left are very small forces due to being in a non-inertial reference frame, and drag from the very, very thin atmosphere. Neither would be noticed without some very precise equipment.

To reduce these forces further, you can travel farther from Earth (and any other massive object). Although it's pretty expensive, it's been done.

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Have you heard of superfluidity? It happens when you cool liquid helium below about 2 Kelvin. The helium then will flow freely and without any friction. If you induce a current vortex in liquid helium, it will remain flowing until the end of time (however, you cannot draw energy from it, because the liquid is frictionless) or until it warms up again. So, in a way Newton's first principle has been verified in a laboratory.

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