Gravitational lensing due to earth

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Discussion Overview

The discussion revolves around the concept of gravitational lensing as it pertains to Earth, specifically whether sunlight bends as it approaches the Earth's surface and the implications of this bending. Participants explore the theoretical aspects of light's trajectory in relation to Earth's mass, touching on general relativity and gravitational effects.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant notes that while light from stars bends near the sun due to its mass, a similar effect occurs near Earth's surface, albeit to a lesser extent due to Earth's smaller mass.
  • Another participant suggests that the trajectory of light affects its bending, stating that light traveling perpendicular to the Earth's surface experiences minimal blue-shifting, while light at other angles bends slightly towards the center of mass of the Earth.
  • A new participant inquires about the mathematical calculation of the curvature or deviation of light due to Earth's mass, as well as the angle at which sunlight strikes the Earth's surface considering this bending.
  • A later reply affirms that the curvature can be calculated similarly to that for a black hole or star, and that the angle of incidence can be determined based on the incoming light's angle relative to the tangent plane of the Earth.
  • Another participant asserts that light tends toward the center of mass of the Earth, referencing Gauss' law and the concept that external objects perceive the gravitational field as that of a point mass at the center of the Earth.

Areas of Agreement / Disagreement

Participants express varying degrees of certainty regarding the bending of light near Earth and the implications of gravitational lensing. While some agree on the potential for mathematical calculations, others question the extent of the bending and the conditions under which it occurs. The discussion remains unresolved regarding the specifics of these calculations and the overall impact of Earth's mass on light trajectories.

Contextual Notes

Limitations include the assumptions made about the conditions under which light bends and the dependence on the definitions of gravitational effects. The discussion does not resolve the mathematical steps involved in calculating the bending of light near Earth.

sodaboy7
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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 ?
 
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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.
 
I am new to general relativity.
soothsayer said:
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 ?
 
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.
 

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