# How much Gravity is needed to bend light?

ARC123
By gravity I mean the mass of a object capable of bending light. I don't want a explanation too say about how or why it will bend, just want the mass in numbers or equation please.

OldYat47
Any mass at all will bend light. Gm/(r*c^2) where G is the gravitational constant, m is the mass you're considering, r is the radius from the center of mass to the light path, c is the speed of light. The result is in radians. I saw a rough calculation that says the mass of the Earth can bend a beam about 10^-9 radians.

Gold Member
By gravity I mean the mass of a object capable of bending light. I don't want a explanation too say about how or why it will bend, just want the mass in numbers or equation please.
From what I've read, things with zero mass can bend light.

Feb 3, 2007
Yes. To amplify this point a bit, in GR, one can say that energy, momentum, and pressure (and not just mass) causes gravity. Specifically, the density of energy and momentum and also pressure are components of an entity called the "stress-energy tensor" that appears on the right hand side of Einstein's equation. This "stress energy tensor" can be regarded as the "source" of gravity in General relativity.

Since light has energy and momentum, it causes gravity. The idea that only "mass" causes gravity is a carryover from Newtonian theory, things are different in GR.

It's beyond my comprehension how it works. But since @pervect is staff emeritus, I'm inclined to go with their answer.