Gravitational lensing due to earth

[sodaboy7]

It is known that light from stars bend near surface of sun due to its mass. Similarly light will bend near Earth's surface (may be insignificant due to less mass). My question is that sunlight that strikes Earth's surface travels a straight path from sun or a curves near Earth's surface ?

 

[soothsayer]

It depends on the trajectory of the light. If it is traveling perpendicular to the Earth's surface, the light will only be slightly blue-shifted. Otherwise, it will be slightly bent by the Earth's surface. Basically. All light will tend toward the center of mass of the Earth. You are correct though, the amount of curvature or blue-shifting is pretty insignificant.

 

[sodaboy7]

I am new to general relativity.

Basically. All light will tend toward the center of mass of the Earth. You are correct though, the amount of curvature or blue-shifting is pretty insignificant.

1)Can we mathematically calculate the amount of curvature or deviation ?
2) Can we calculate the angle at which sun light strikes the surface of Earth (at a particular place) considering this bending (even if its is small)
3) Are you really sure, light tends towards center of mass ?

 

[Nabeshin]

Yes, and it is easily calculable, see the wikipedia article and formula:
http://en.wikipedia.org/wiki/Gravitational_lens#Explanation_in_terms_of_space.E2.80.93time_curvature

 

[soothsayer]

soda:
1) Yep, we definitely can! In the same way you would calculate it for a black hole or star.

2) Yes, we can probably figure it as a function of the angle between the incoming light and the tangent plane to the surface of the Earth.

3) Yep. If you do Gauss' law on a planet like Earth, you'll see that any object that is located outside of the Earth's surface will only "see" the gravitational field as that of a singular point with the same mass as the Earth located exactly at the center of mass. Newton invented calculus for this exact reason: to prove this idea for his theory of gravity. It doesn't matter what angle the light makes or where it passes in relation to the Earth.