# Calculating the change in aceleration the earth feels when you push an object

I am learning newton's third law, and i got to this conclusion, i wanted to know if it's correct (within the boundaries of Newtonian mechanics)

Say I'm pushing a cupboard with my body, and I apply a force of 10 newtons. That means that the cupboard is applying a force of 10 newtons to me, but I'm not moving because the earth (through friction) is applying 10 newtons of force to me in the opposite direction. That means I am applying a force of 10 newtons on the earth.

That means that I'm changing the acceleration of the planet by applying a force of 10 newtons to a cupboard, and the change in acceleration is given by

$F = M_{mass-of-earth} * a$

I plug in the known values

$10 = 5,972 ×10^24 kg * a$

I solve for a

$a = 1.67448091 × 10^{-24}$

Is this reasoning correct? I feel that if I confirm this I will have understood what I felt I was missing in all my free body diagram exercises where forces are applied by arbitrary magical invisible entities.