# Observed Effects of Gravitational Lensing 2

So what is the minimum amount of mass that is required for the gravitational lensing effect to be visible? For instance, we can not observe the suns light during a solar eclipse because the moon does not have enough mass to curve space sufficiently for the suns light to be visible here on earth. So what is the minimum amount of mass required for the effect to be visible. does a single star have enough mass, or does a small solar system have enough mass, or does it take the mass of a entire galaxy or or galaxy cluster to make the effect visible. Is there a known amount or is there an equation that tells us the minimum amount of mass required for the effects of gravitational lensing to be visible?

• It depends on what you mean by visible. It makes a difference if you mean visible to the human eye verses visible to a telescope on earth verses visible to the Hubble telescope. It also depends on the distance the source is away. Sep 22, 2016 at 20:01
• I believe the MACHO surveys of the 90's and forward found objects of mass similar to that of our gas giant planets, but I don't have references or any notion of what the lower limit might be. This is of course for the micro-lensing of star light from nearby dwarf galaxies and globular clusters by objects inside the Milkyway. Sep 22, 2016 at 20:48

$$\delta\phi=\frac{2r_g}{\rho}=\frac{4GM}{c^2\rho}$$ This gives the deviation from the unperturbed trajectory as a function of the mass of the body $M$ and the minimum distance from the body $\rho$. For example for a beam passing close to the sun we have $\delta\phi=1.75''$ (result found on Landau-Lifshitz) which is not so small for modern accuracies. But whether this is observabe (and by who) depends on the position of the observer and the experimental apparatus that he has.