Are photons affected by Earth's gravity? Just wondering if  the Earth's gravity affects the photons? We can obviously think about equivalent mass of photons by using de broglie relation and then use it to calculate force of gravitational interaction. But still this thought is very revolting. Help would be appreciated?
 A: Yep. Gravity effects photons. Here's a thought experiment from Einstein:
Suppose you have a block having mass $m$ at the top of a tower. Drop it. 
It picks up speed due to gravity as it falls, gaining kinetic energy. 
Now suppose there's some super efficient means of converting mass to energy at the bottom of the tower and the newly created photons were fired back at the source point. Once they arrived at the source point, we reconverted the photons back to mass and started over again. 
If we assume no loss of energy on the way up, then we have the makings of a perpetual motion machine. 
We have to lose energy on the way up which  means we have a reduction in frequency. Because the product of frequency with wavelength is a constant, the speed of light, the reduction in one implies the increase in the other. So the wavelength of the photon increases as it rises back to the top of the tower. This is a Red Shift.
More generally, gravity distorts space-time. Space itself is curved. Just as the shortest distance between two points on a globe is not a straight line, the shortest distance paths between two points in curved space time, i.e. in a gravitational field, is also not a straight line. The lines do not exist. So the path's of photons must change.  
A: I think you're right to be uncomfortable in calculating a "mass" of a photon.  The true reason that light is deflected around any massive object is because all massive objects distort spacetime.
You've probably heard the phrase "Light travels in straight lines", and we can apply this line to the bending of spacetime too.  Without too much mathematical detail, we can imagine what would happen to a "straight line" on a flat piece of spacetime when the spacetime itself is bent.  The classic demonstration is a trampoline sheet with heavy balls on it.  Anything trying to zip past a heavy ball (including light) is bent - see this popular YouTube video.
(Using more precise terminology, light follows what are called "null geodesics" in spacetime.  In flat spacetime (with no gravity) these are just straight lines.  However in curved spacetime, they are no longer straight lines, and indeed massive objects bend the space around them sufficiently to bend the light's path).
