- #1
dianaj
- 15
- 0
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
[tex]F = m_i \cdot a[/tex]
We also know that
[tex]F_g = \frac{k \cdot m_g \cdot M}{r^2}[/tex]
where k is a contant yet to be determined. We then have
[tex]m_i \cdot a = m_g \cdot \frac{k \cdot M}{r^2}[/tex]
We observe that a is constant, and therefore that
[tex]m_i \propto m_g[/tex]
Finally we set k = G (gravitational constant), so that [tex]m_i = m_g[/tex]
Am I right? Is this 'the origin' of the value of G?
/Diana
My guess is that it went down like this:
We know that
[tex]F = m_i \cdot a[/tex]
We also know that
[tex]F_g = \frac{k \cdot m_g \cdot M}{r^2}[/tex]
where k is a contant yet to be determined. We then have
[tex]m_i \cdot a = m_g \cdot \frac{k \cdot M}{r^2}[/tex]
We observe that a is constant, and therefore that
[tex]m_i \propto m_g[/tex]
Finally we set k = G (gravitational constant), so that [tex]m_i = m_g[/tex]
Am I right? Is this 'the origin' of the value of G?
/Diana