## THE REALITY, NOW AND UNDERSTANDING

### FIGURE.TXT

#### 1.0 INTRODUCTION

This document describes the program FIGURE

The program FIGURE draws the following figures:
1. Figure 1 of program SUNRAD
2. Figure 2 of program SUNRAD
3. Figure 3 of program SUNRAD
4. Figure 3 of program PLANETS for TEST 6C
5. Our Galaxy with Sun and Mercury in 3D .. Now
6. Gravitational Microlensing and Dark Matter
7. Light Bending calculation
8. Our Galaxy in 3D
9. Light ray around the Sun

This program is part of SUNRAD, PLANETS and PROVE

#### 2.1 FIGURE 1 OF PROGRAM SUNRAD

This figure is part of virtual mass calculation described in chapter 4 of program SUNRAD.

Now perform the program: FIGURE.EXE
From the Test Selection Display
Select test 1

#### 2.2 FIGURE 2 OF PROGRAM SUNRAD

This figure is part of the center of the Sun calculation (oblateness) described in chapter 2 and 3 of program SUNRAD.

Now perform the program: FIGURE.EXE

From the Test Selection Display
Select test 2

#### 2.3 FIGURE 3 OF PROGRAM SUNRAD

This figure is part of the center of the Sun calculation (oblateness) described in chapter 2 and 3 of program SUNRAD.

Now perform the program: FIGURE.EXE
From the Test Selection Display
Select test 3

#### 2.4 TEST 6C OF PLANETS

Figure 3 of program planets shows the movement of the planet Mercury for different positions of the Sun when the Sun moves through our Galaxy for c = 300000 km/sec

The Sun is shown at four positions: Top, Left , Bottom and Right.

In order to select the Sun use the TAB key

With each position of the Sun, Mercury is also shown at four positions

In order to select Mercury use the four arrows keys.

Centre of Galaxy has a speed of 230 to the right

The Sun moves counter clockwise with a speed of 250 km/sec At top position to left : 250 - 230 = 20 km to the left At bottom position to the right : 250 + 230 = 480 km to the right

Now perform the program: FIGURE.EXE

From the Test Selection Display
Select test 4

Return back to CHAPTER5.TXT

#### 2.5 OUR GALAXY .. NOW

This figure shows the movement of our Galaxy, the Sun and Mercury relative to the plain of the Sun. The dimensions are wrong.

Now perform the program: FIGURE.EXE
From the Test Selection Display
Select test 5

The purpose of this display is to answer three questions:
1. What is the speed of our Galaxy
2. What is the angle between the movement of our Galaxy with the movement of the Sun.
3. What is the angle between the movement of the Sun and the long axis of Mercury

Return back to END.TXT

#### 2.6 GRAVITATIONAL MICROLENSING AND DARK MATTER

This figure shows what an observer sees when an invisible object (dark matter) moves between the observer and a visible star at different distances.

This figure consists of 2 parts:
• On the left side we see how lightrays are emitted from a visible star and moves around an Invisible Object (IO)
• On the right side we see the intensity of the light from the visible star at different distance from the observer.

Five different positions are considered:
• A: Before IO Intensity is constant
• B: Immediate behind IO Intensity shows a gap The distance of this gap is larger then the size of the invisible object because light that moves along the rim of the object (seen from the observer) is also drawn into the object.
• C: Half between the distance were light from both sides meet.
• D: At the distance were light from both sides meet. Intensity at the middle show a peak because light from all sides is collected.
• E: At a distance were light from both sides overlap. There is a small jump at the beginning were both sides start to overlap.

Now perform the program: FIGURE.EXE
From the Test Selection Display
Select test 6

The area in grey at each position has the same surface. This is the amount of light influenced by (the gravity of) dark matter.

Return back to PROVE.TXT

#### 2.7 LIGHT BENDING CALCULATION

The above figure is calculated using the following method.

Radius invisible star is R0. Radius of area that is effected is R1
For x between R0 and R1 we calculate the variable a

a = R1 - x (i.e. a is the distance from R1)

Light in this area (between R0 and R1) is bended, the further away the more from its straight path. The new distance from R1 is b.

b = a + h * c1 * a² (1)

h is the distance behind the invisible star

i.e. the values h=0, 0.5, 1, and 1.5 c1 is a constant such that for h=1 light from both sides just meat. i.e. for a=R0, b= R1
R1 = R0 + 1 * c1 * R0²
c1 = (R1 - R0) / R0²

The density at h = 0 is every where the same i.e. dens1
What we want to calculate is the density at h<>0 i.e. dens2

There are two strategies.

First we can divide a in small increments.

At distance a1 we can calculate b1 using (1)
At distance a2 we can calculate b2 using (1)

The density dens2 between b2 and b1 is then equal to:

dens1 * (PI * a2² - PI * a1²) = dens2 * (PI * b2² - PI * b1²)
dens2 = dens1 * (a2 + a1) * (a2 - a1) / (b2 + b1) * (b2 - b1)

This becomes difficult to draw as a figure when the two parts starts to overlap. This becomes difficult for h > 1

A second strategy is not to divide a in small segments, but b.

From equation (1) we can solve:

```        h * c1 * a² + a - b = 0
-1 + SQR(1 + 4*b*c1*h)
a =  ----------------------                    (2)
2*c1*h
```
if a > R0 then a = R0

At distance b1 we can calculate a1 using (2)
At distance b2 we can calculate a2 using (2)

The density dens2 between b2 and b1 is then equal to:
```      dens1 * (PI * a2²-PI * a1²) = dens2 * (PI * b2²-PI * b1²)
dens2 = dens1 * (a2 + a1) * (a2 - a1) / (b2 + b1) * (b2 - b1)
```

b1 and b2 are the distance to R1 (b1 = R1 - b)
b3 and b4 are the distance to -R1 (b3 = R1 + b)

At distance b3 we can calculate a3 using (2)
At distance b4 we can calculate a4 using (2)

The density dens3 between b4 and b3 is then equal to:

dens3 = dens1 * (a4 + a3) * (a4 - a3) / (b4 + b3) * (b4 - b3)

Total density is then equal to:

dens total = dens2 + dens3

Now perform the program: FIGURE.EXE
From the Test Selection Display
Select test 7

Return back to PROVE.TXT

#### 2.8 OUR GALAXY IN 3D

In order to see our Galaxy in 3D perform the following:

Now perform the program: FIGURE.EXE
From the Test Selection Display
Select test 8

Our galaxy consists of two parts:

A central bulge
A disk

In order to make the calculation "smooth" the mass of the disk is considered to continue into the bulge.

The density of the bulge is a function of 1/R
The density of the disk is constant.

For the disk three parameters are important:

R0, R1 and R2.

For x < R0 the height of the disk is constant i.e. z = z0
For R0 < x < R1 the height of the disk changes linear towards z = alpha * z0
For x > R1 the height of the disk z = 0

Between R0 < x < R1

z = a * x + b (1)
z0 = a * R0 + b (2)
z1 = alpha * z0 = a * R1 + b (3)

Subtracting (2) from (3) yields:

z0 * (1-alpha) = a * (R0 - R1)
a = z0 * (1 - alpha) / (R0 - R1) (4) Entering (4) into (2) gives:
b = z0 - z0 * (1- alpha) * R0 / (R0 - R1)
b = z0 * (alpha * R0 - R1) / (R0 - R1) (5)

Entering (5) and (4) into (1) yields:

z = z0 * {(1-alpha) * x - alpha * R0 - R1} / (R0 - R1)

Return back to PROVE.TXT

#### 2.9 LIGHT RAY AROUND THE SUN

This demonstration shows how a light ray is bended around the Sun using only Newton's Law

Now perform the program: FIGURE.EXE
From the Test Selection Display
Select test 9

For factor select 1 (normal) 2 and 4.

The results of the demonstration shows that the angle is twice to small as accordingly to general accepted concepts.

Return back

#### 3.0 OPERATION

The program uses the following standard feature:

When you select Esc you will terminate the program (Escape)

In order to simulate the different conditions the parameter selection display is used

#### 3.1 PARAMETER SELECTION DISPLAY

From the Parameter Selection Display the following parameters can be changed:

```        0 = Select test display

1 = Set standard parameters.

2 = Screen mode. Valid values are 7,8,9 and 12. Standard value = 9
3 = Wait time in second. Physical wait time between each simulation
cycle. Standard value = 0
```