Which formula for gravitational field is correct $\vec{I} = \lim_{m\to0}\frac{\vec{F}}{m}$ or $\vec{I} =\frac{\vec{F}}{m}$ . My teacher told me that the former is correct because for an infinitesimally small mass we can neglect its effect of gravitational field. What does my teacher mean? On the other hand, my textbook has the latter formula. Please explain rigorously which formula is actually correct and why?
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Good question. See, the point is, when you are trying to determine the gravitational field due to $m_1$, the particle on which you are measuring the force should not be heavy enough to displace $m_1$ from its original position. This is because the field of a mass at a point depends on where that mass is. A good way to do this is to make the mass $m_2$ on which you are measuring the force approach $0$. I hope this clears your doubt.
Another way of course is to keep the mass $m_1$ fixed by some other machinery, like holding it tightly in your hands. But the first one is mathematically elegant.
Physiker
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