Weak Equivalence Principle (WEP)

[dianaj]

As most of you probably know, the WEP states that the intertial mass and gravitational mass of any object are equal. This principle has base in Galileo's observations, that all free-falling objects have a constant acceleration. What I would like to get clear is the order of arguments that leads to this conclusion.

My guess is that it went down like this:

We know that
$$F = m_i \cdot a$$
We also know that
$$F_g = \frac{k \cdot m_g \cdot M}{r^2}$$
where k is a contant yet to be determined. We then have
$$m_i \cdot a = m_g \cdot \frac{k \cdot M}{r^2}$$
We observe that a is constant, and therefore that
$$m_i \propto m_g$$
Finally we set k = G (gravitational constant), so that $$m_i = m_g$$

Am I right? Is this 'the origin' of the value of G?

/Diana

 

[granpa]

the field produced by a massive body depends (by definition) only on its gravitational mass.
the acceleration of a massive body within any given gravitation field depends only on its inertial mass and the strength of that field.

 

[atyy]

All free falling objects have the same acceleration.

In Newtonian gravity, this is modeled by inertial mass being proportional to gravitational mass by a universal constant. In appropriate units, inertial mass equals gravitational mass.