Relative and absolute tolerance definitions in Matlab solver

Question

I am trying to understand the following Matlab definitions for RelTol and AbsTol parameters:

RelTol — This tolerance is a measure of the error relative to the size of each
solution component. Roughly, it controls the number of correct digits in all 
solution components, except those smaller than thresholds AbsTol(i).The default,
1e-3, corresponds to 0.1% accuracy.

AbsTol — AbsTol(i) is a threshold below which the value of the ith solution 
component is unimportant. The absolute error tolerances determine the accuracy 
when the solution approaches zero.

I do not understand why AbsTol determines the accuracy when the solution approaches zero (indeed, if the solution of my problem is a circular orbit of 7000 km radius this does not meet it) and why RelTol controls the number of correct digits in all solution components, except those smaller than thresholds AbsTol(i). What are the actual expressions for determining each tolerance? I would like to get simpler and understandable definitions.