Is there any true inertial reference frame in the universe?
Newton's first law states that an object at rest remains at rest, and an object performing uniform motion performs uniform motion, until and unless acted upon by an external force, if viewed from an inertial frame. It is the definition of an inertial frame of reference. And Newton's second law states that the net external force acting on a particle equals its mass times its acceleration. Thus we need to have an inertial frame in order for Newton's 1st and 2nd laws to be applicable.
Scientists claim that Earth is an inertial frame, either the ECEF frame or the ECI frame. Why is that? Earth's different parts have different accelerations when it performs rotational motion about its axis. Now you may say that Earth's axis is inertial, but the Earth is also revolving around the Sun. Thus Earth's frame should be non-inertial.
Even supposing that earth's frame is inertial, then it means that rest of the universe is non-inertial, because only a frame that moves with constant velocity with respect to an inertial frame is also an inertial frame and according to various scientific experiments there is no other matter in this universe which satisfies that criterion. Now you may say that earth is an approximate inertial frame, but still, my question is: is there any perfect inertial frame in the universe where Newton's laws are exactly applicable?
Best Answer
When you ask for a "perfect" or "true" inertial reference frame you are asking for something that cannot be answered in physics. Perfection is only possible in mathematics, not physics.
So in physics, what can be asked is whether or not a given reference frame is an inertial frame to a certain level of accuracy. The surface of the earth is not an inertial frame because of the gravitational field of the earth - not because the earth is moving around the sun and the sun is moving around the galaxy. But if you consider motion only in a horizontal plane on the surface of the earth and if you are only doing the typical high school physics tabletop experiments, the earth is an inertial reference frame as far as the accuracy of the measurements performed is concerned. If you do more accurate measurements, then it would not be an acceptable inertial reference frame.
Consider a satellite in orbit around the earth and examine a relatively small volume near the center of mass of the satellite. That small volume over a suitably small period of time will be an inertial reference frame to a very high level of accuracy. For example, two small masses that are 1 inch apart (radially) in orbit around the earth that start out "exactly" at rest relative to each other will over a time period of 10 seconds come to have a relative speed of 0.006 inches/second due to the differences in orbital velocity for two orbits that differ by 1 inch. So it depends on the level of accuracy needed for an experiment that you want to perform in an inertial reference frame.
To get a reference frame that is more accurately inertial it would necessary to be orbiting much further from all gravitating objects. Thus, it is all about the level of accuracy you require of the inertial reference frame.