Newton's Mechanics is valid in any
inertial frame of reference.
This will be upheld and even extended when we study Special Relativity.
Some convenient frames are non-inertial.
The most important case for us is
a coordinate system fixed on the earth.
An earth fixed frame is potentially quite complex but it boils down to a
rotating coordinate system.
The motion of the earth includes:
While all of these involve acceleration, 2-5 are objects in free fall in a gravitational field.
force of external gravity on an object on the earth is canceled by the acceleration of the earth due to that force.
Just like an astronaut inside a satellite in orbit around the earth feels no force of gravity or fictitious force due to the
acceleration of the satellite. They just cancel.
(But they only cancel at the center of the earth, leaving tidal forces elsewhere.)
In fact in general relativity, we understand that acceleration and gravity are the same thing and there are no forces on objects
rotation around an axis perpendicular to the
- orbital motion around the sun
- orbital motion with the moon
- the sun's motion in the galaxy
- the motion of the galaxy in the cluster of galaxies and the rest of the universe.
This is not true for the
rotation of the earth.