What are inertia and non-inertia frames
Which is inertia frame?
How am I supposed to decide which one accelerates, the earth or man?
Here is a pre-relativistic take on the subject.
In Newton's view, the acceleration that appears in his laws of motion has a certain absolute value, which means that it relates to a certain frame of reference known as absolute space (Frame) is called. It is a hypothetical thing (I imagine something like a rigid set of points) that permeates the entire universe in which laws of mechanics (3 laws of motion + the law of gravity) are valid.
The concept of the absolute frame, however, has bothered people, perhaps also because it suggests the image of a frame, while all of its characteristic features - the validity of Newton's laws - are shared (according to Newton's view) with an infinite number of frames of reference that are rectilinear into Regarding move it. Absolute space has never been identified with a body. It remained hypothetical.
Therefore, the term frame of inertia is often preferred - it is any frame in which Newton's 3 laws of motion are valid.
With that term, one possible answer to your question is find one Frame of reference in which these 3 laws are valid, and measure / calculate the accelerations of bodies in relation to this frame!
In this sense, is the astronaut an inertial frame? Let's see. The astronaut knows that there is a force acting on him because of the earth, but he does not move within his own framework. Oops. Similarly, humans on earth know that they should be attracted to the astronaut, but neither see any acceleration of their body. None these two frames thus perfectly meet the requirements placed on the concept of the inertia frame.
However, if we assume that the earth is inert and calculate the astronaut's movement in the future or past, we will get very good answers close to his actual movement. However, if we assume that the astronaut is sluggish, we calculate the motion of the earth in ridiculously inaccurate results. Even if neither is absolutely sluggish, the earth is much closer.
Another example, the motion of the earth and the sun, is well described by Newton's mechanics, assuming the sun is sluggish. If the earth is believed to be inert, it will not work well for the movement of the sun - the value of the calculated Gravitational acceleration of the sun due to the gravitational force of the earth is far too weak to explain the acceleration of the sun in the frame centered on the earth.
So it looks like the heaviest body in the system is a good choice for the frame of reference in which the 4 laws are to be applied. If you want to be as accurate prediction / feedback as possible I would use the 4 laws within the framework of the
is centered in the center of mass of the system
has axes that do not move with respect to distant stars.
It won't be absolutely sluggish, but it should be close enough (assuming other bodies are much further away).
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