standing on earth we people explain the motionof planets around the sun by applying newtons laws of motion (3rd law), but how can we do so as the earth accelerates because newtons lawsisapplicable only in non accelerated frames?

Dear student,

Non-inertial frames can be avoided. Of course, measurements with respect to non-inertial reference frames can be transformed to an inertial frame, incorporating directly the acceleration of the non-inertial frame as that acceleration is seen from the inertial frame . This approach avoids use of fictitious forces (it is based on an inertial frame, where fictitious forces are absent, by definition) but it may be less convenient from an intuitive, observational, and even a calculational viewpoint. As pointed out by Ryder for the case of rotating frames as used in meteorology.

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