# How to resolve this asymmetry in an example for the weak equivalence principle?

I am trying to unknot an obvious error in my understanding of the following example:

Fact 1: An observer on the moon watches a tiny ball of uranium and a tiny ball of iron fall. Both fall fall at the same speed.

Fact 2: In the gravitational field of venus, both balls will fall faster than in the gravitational field of the moon.

Rephrasing of fact 2: For an observer on the tiny ball of iron the moon falls faster in the gravitational field of the iron ball than the venus.

Problem: This rephrasing somehow clashes with fact 1 and with my (probably) wrong understanding of the weak equivalence principle.

I recall that the weak equivalence principle sometimes is formulated only for small test objects. But then: How small are they supposed to be? And then: If we assume this limitation, then it actually is not true but only a weak field approximation.

Quite obviously I am getting something very much wrong - but I currently fail to see what it is.

Add on: Quite clearly, the physical description should not depend on where we place the observer. So, how would a description of the weak equivalence principle look like which does not place the observer on the "heavier" object?

• See this related question and links therein.
– rob
Mar 26, 2022 at 20:38
• Great link. The conclusion I draw is that the frequently found formulation that objects fall at the same speed lacks the necessary precision and may be regarded only as an approximation. Right? Mar 26, 2022 at 20:56