# Weak Equivalence Principle (WEP)

1. Aug 2, 2009

### 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

2. Aug 3, 2009

### 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.

3. Aug 4, 2009

### atyy

All free falling objects have the same acceleration.

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