newtonian mechanics - Why can light (photons) bends in a curve through space without mass?

I've heard that light can form a curve if they travel near high-mass stars or even a black hole with strong gravity. Which is according to this Newtonian formula

$$\large F_{g}=\dfrac{Gm_1m_2}{r^2}.$$

But I've also heard that photons do not have (rest) mass! So it doesn't fit that equation anymore! But why can photons be pulled by gravities without (rest) mass? Could someone explain that?

Answer

The equation you are mentioning is the gravitation force derived by Newton. This force doesn't apply to particles such as photons for two reasons:

1. 
   
   

   Photons are too small, and you can't use Newtonian physics to describe their properties.

   
   


2. 
   

   Photons travel too fast (their velocity is the speed of light) and at such a velocity Newtonian mechanics cannot be applied.

   
   

Newton's gravitation law is really useful to understand the motion of planets around the sun for example, or the motion of a pendulum. But as it comes to light and space one has to look at Einstein's theory of relativity in order to fully understand phenomena.

Einstein's general relativity theory is a way to explain gravitation (and Newton's gravitation law is another). The main idea is that the space-time is curved by the presence of mass. What we do know (and that is always true) is that photons travel in a straight line in a vacuum. A big mass, such as a black hole, may curve space-time so much that a straight line in space-time isn't straight anymore. When we look at photons in space, they seem to bend in a curve through space.

To summarize:

1. Light can form a curve if it travels near a big mass.


2. You are right, photons don't have mass.


3. You are also right, photons doesn't follow Newton's gravitation law.


4. Photons can be pulled by gravity not because of their mass (they have none) but because gravity bends space-time.