## The bending of Light around the Sun

### Questions:

1. Who can write a program that simulates the behaviour of light around the Sun in the correct way.
2. How does the behaviour change when the speed of the Sun is taken into account
3. How does the behaviour change when the speed of gravity propagation is taken into account
4. Is the behaviour symetric ? i.e. does it matter if the Sun moves in one or in opposite direction?

### Purpose

• The purpose of question 1 to compare how Newton's Law and how the Realtivity Theory explain the bending of light around the Sun.
• The purpose of question 3 is to find an answer on the question if the speed of gravity is equal to c.

### Description

A Lightray which passes close to the Sun is bend.
This phenomena can be partly explained using Newton's Law.
Angle is equal to .85834 arc sec. However this value is not correct.
This phenomena can be explained correctly using Relativity Theory.
Angle is equal to 1.74912 arc sec.

For a lightray which passes close to the planet Jupiter the simulation program, with Newton's law, calculates an angle of 0.00793 arc sec.

### Simulation Program of this experiment

Your author has written a program to simulate the bending of light around the Sun, using Newton's Law.
1. For a copy of the program select: LIGHT.BAS.
2. For a listing of the program select: LIGHT.HTM.
3. To execute the program select: LIGHT.ZIP.
4. For an explanation of the program See: program1.htm

By preference the mathematics in the program LIGHT.BAS should be used as a starting point for the answer on this question.

### Answer question 2 and 4

In order to answer question 2 (and 4) we start from a situation where the Star, the Observer and the upper rim of the Sun are on one horizontal line. The Speed v of the Sun is Zero. This is Configuration 2 of the program LIGHT.BAS. See program1.htm for more detail.
Initially, at t = t0, the lightray already makes a small angle through this horizontal line. The lightray has it closest approach at t = t1. At the end, at t = t2, near the Observer, the lightray again makes a small angle through this horizontal line. The total bending angle (for v = 0) is the sum of those two small angles.

Now suppose the Sun has a speed v>0 and moves upwards such that at t = t1 the Sun is exactly at the same position as for v=0. This means at t = t0, at the initial position, the upper rim of the Sun is below the horizontal line (through the Observer and the Star). It also means that at t = t2, when the lightray reaches the Observer, the rim of the Sun is above the horizontal line.

For the time from t=t0 to t=t1 on average the centre of the Sun will be below the horizontal line, that means light bending will be less.

Now suppose the Sun has a speed v>0 and moves down (in the program the speed is than negative) such that at t = t1 the Sun is exactly at the same position as for v=0. This means at t = t0, at the initial position, the upper rim of the Sun is above the horizontal line (through the Observer and the Star). It also means that at t = t2, when the lightray reaches the Observer, the rim of the Sun is below the horizontal line.

For the time from t=t0 to t=t1 on average the centre of the Sun will be above the horizontal line, that means light bending will be more.

What the above predicts is that when the Sun moves through the line between an Observer and a star that at the leading edge of the Sun light bending will be less compared with light bending at a speed of v=0 and at the trailing edge of the Sun light bending will be more.

In short the behavior is asymetric.

This is in accordance with the simulation.

When speed of gravity is taken into account the same behaviour is observed and even stronger.

In short the behavior is more asymetric.

This is in accordance with the simulation.

### Results

The following table shows the results for configuration 1
 v cg angle in arc sec min distance 0 0 .8582267498025824 695998 1000 0 .8579382004959446 696224 1000 1 .8550767125973466 698554 -1000 0 .8585056182720026 695765 -1000 1 .86136053878171914 693451
The following table shows the results for configuration 2
 v cg angle in arc sec min distance 0 0 .8582160568402388 696006 1000 0 .8579274896865867 696232 1000 1 .8550660388758259 698562 -1000 0 .8584949438860237 695772 -1000 1 .8613498276600219 693459

### Feedback

None

Created: 2 January 1995