## THE REALITY, NOW AND UNDERSTANDING

### 3OBJECTS.TXT

#### 1.0 INTRODUCTION

This document describes the program 3OBJECTS

The purpose of this program is to simulate the movement of three objects m0, m1 and m2 by using Newton' Law under 13 different conditions. The simulations are subdivided in 7 groups.

```  test   group     m0         m1       m2      ellipse    oblateness
1      1    100000       1000       1
2      2     10000       1000      10
3      2     10000       1000      10        m1
4      3      1000       1000      10
5      3      1000       1000      10        m2
6      3      1000       1000      10        m1
7      4      1000       1000      10
8      4      1000       1000      10        m2
9      5      1000         .1      20
10      5      1000         .1      20        m1
11      6       100        .01       0        m1           0
12      6       100        .01       0        m1           1
13      7       100        100       1
```

The movement of the objects of the tests 1,2,4,7,9 and 13 involve straight lines and circles. They are part of CHAPTER 2. The movement of the tests 3,5,6,8,10,11 and 12 involve ellipses and are more complex. They are part of CHAPTER 5

2.0 TEST DESCRIPTIONS

#### 2.1 TEST 1

Test 1 consists of:

```	 One star m0.          Mass of m0 = 100000
One planet m1.        Mass of m1 = 1000
One moon m2.          Mass of m2 = 1
Distance between m0 and m1 is large: 5000
Distance between m1 and m2 is small: 10
```

Moon m2 revolves around the planet m1. Planet m1 has no speed in the y direction i.e. planet m1 will move in a straight line towards the star m0.

Now perform the program: 3OBJECTS.EXE
From the Test Selection Display:
Select test 1
Select S (Start)

This simulation shows two things:
1. The speed of planet m1 increases when it moves towards star m0
2. The revolution time of the moon also increases at the same time

Now consider the planet and the moon as a clock.
1. The speed of the clock as a whole increases.
2. The speed the clock as a time device (i.e. its dials which indicate time) decreases i.e. runs slower.

The results are made visible in figure 1.

From the Test Selection Display

Select test 19 Subtest 1
From the Figure Selection Display
Select figure 1.

#### 2.2 TEST 2

Test 2 consists of:

```	 One big star m0.                           Mass of m0 = 10000
One smaller star m1.                       Mass of m1 = 1000
A planet m2 revolving around the star m1.  Mass of m2 = 1
Distance between m0 and m1 is large:    500.
Distance between m1 and planet is small: 10.
```

```				  |
|
..............................
|                            |
m0                           |
............
|          |
m1         m2
```

This simulation is similar as m0 representing our sun, m1 the earth and m2 our moon.

Now perform the program: 3OBJECTS.EXE
From the Test Selection Display:
Select test 2
Select S (Start)

What the simulation shows is that the revolution time of the moon is constant and approximate 6.28 seconds.

The results are made visible in figure 2 for delta time of 0.001

From the Test Selection Display
Select test 19 Subtest 2
From the Figure Selection Display
Select figure 2.

#### 2.3 TEST 3

Test 3 is identical as test 2.

Trajectory of the smaller star m1 is an ellipse.

This simulation is similar as :

m0 our Sun , m1 the planet Mercury and m2 a moon of Mercury.
m0 our Galaxy , m1 the Sun and m2 the Earth

Now perform the program: 3OBJECTS.EXE
From the Test Selection Display:
Select test 3
Select S (Start)

What the simulation shows is that the revolution time of the moon is not constant:
The revolution time of the moon m2 increases (i.e. the moon moves slower) when the speed of the planet m1 increases.
The revolution time of the moon m2 decreases (i.e. the moon moves faster) when the speed of the planet m1 decreases.
After one full revolution of Mercury the revolution time of the moon is the same.

The results are made visible in figure 3 for delta time of 0.00002

Now perform the program: 3OBJECTS.EXE
From the Test Selection Display
Select test 19 Subtest 3
From the Figure Selection Display
Select figure 3.

#### 2.4 TEST 4

Test 4 consists of:

```	 One double star  m0 and m1.                m0 = 1000, m1 = 1000
A planet m2 revolving around the star m1.  m2 = 10
Distance between m0 and m1 is large i.e. 500.
Distance between m2 and double star is small i.e. 50.
```

```				  |
|
..............................
|                            |
m0                           |
............
|          |
m1         m2
```

This simulation shows the behaviour of our sun through our galaxy. m0 represent our galaxy, m1 is the sun and m2 is the earth.

Now perform the program: 3OBJECTS.EXE
From the Test Selection Display:
Select test 4
Select S (Start)

What the simulation shows is that the revolution time of the earth is constant and approximate 24.82 seconds.

#### 2.5 TEST 5

Test 5 is identical as Test 4.

Trajectory of the star m1 is an ellipse.
Trajectory of the planet m2 is a circle.

Now perform the program: 3OBJECTS.EXE
From the Test Selection Display:
Select test 5
Select S (Start)

This simulation is almost identical as test 3. The major difference it that there are 2 planets similar as Mercury. One of the planets has a moon which services as a clock.

The results are made visible in figure 5.

Now perform the program: 3OBJECTS.EXE
From the Test Selection Display
Select test 19 Subtest 5
From the Figure Selection Display
Select figure 5

#### 2.6 TEST 6

Test 6 is identical as test 4.

Trajectory of the star m1 is a circle.
Trajectory of planet is m2 is an ellipse i.e. like the planet Mercury.

Now perform the program: 3OBJECTS.EXE
From the Test Selection Display:
Select test 6
Select S (Start)

This simulation shows the behaviour of our sun through our galaxy. m0 represent our galaxy, m1 is the sun and m2 is the planet Mercury.

The simulation shows that the major axis of the trajectory of the planet m2 moves forward.

The following forward angles are observed after one, two and three revolutions of m0 and m1:

6.22 (22), 13.65 (45) and 20.03 (67)

The number in brackets indicates the number of revolutions of m2 (Mercury)

This means after approximate 120 revolutions of m0 and m1 that the major axis of the planet m2 has also made one complete revolution.

The results are made visible in figure 6.

Now perform the program: 3OBJECTS.EXE
From the Test Selection Display
Select test 19 Subtest 6
From the Figure Selection Display
Select figure 6.

#### 2.7 TEST 7

Test 7 consists of

```	 One double star  m0 and m1.    m0 = 1000, m1 = 1000
A planet m2 revolving around the double star. m2 = 10
Distance between m0 and m1 is small i.e. 160.
Distance between m2 and double star is large i.e. 500.
```

```			  |
|
..............................
|                            |
............                      m2
|          |
m0         m1
```

Now perform the program: 3OBJECTS.EXE
From the Test Selection Display:
Select test 7
Select S (Start)

What the simulation shows is that the revolution time of the planet m2 is constant and approximate 1547 seconds.

#### 2.8 TEST 8

Test 8 is identical as test 7.

Trajectory of planet m2 is elliptical i.e. like the planet Mercury.

From the Test Selection Display:
Select test 8
Select S (Start)

This simulation shows that the major axis of the trajectory of the planet m2 moves forward.

Observed values are : 6.2, 13.1, 19.9, 26.7, 33.0, 38.7 degrees.

The results are made visible in figure 8

Now perform the program: 3OBJECTS.EXE
From the Test Selection Display
Select test 19 Subtest 8
From the Figure Selection Display
Select figure 8

Return back to CHAPTER5.TXT

#### 2.9 TEST 9

Test 9 consists of:

```	one star m0       m0 = 1000
one planet m1     m1 = .1        distance m0 and m1 = 110
one planet m2     m2 = 10        distance m0 and m2 = 200
```

```			|
|
..............................
|                            |
...................               m2
|                 |
m0                m1
```

The purpose of this test is to show how the revolution time of one planet m1 is influenced by an outer planet m2. The trajectory of both planets is a circle.

The tests consists of two parts.

In part 1 m2 is close to m1
In part 2 m2 is far away from m1.

This simulation is similar as m0 being our Sun, m1 the Earth and m2 one of the outer planets.

#### 2.9.1 TEST 9 (PART 1)

Now perform the program: 3OBJECTS.EXE
From the Test Selection Display:
Select test 9
Select S (Start)

What the simulation shows is that the revolution time of the Earth is constant. approximate 226 seconds.

#### 2.9.2 TEST 9 (PART 2)

Now perform the program: 3OBJECTS.EXE
From the Test Selection Display:
Select test 9
From the Parameter Selection Display:
Set 13 distance 2 = 2000
From the Test Selection Display:
Select S (Start)

What the simulation shows is that the revolution time of the Earth is constant. approximate 229 seconds.

Comparing part 1 with part 2 shows that when a planet has a close companion, the revolution time becomes shorter i.e. its speeds increases.

Return back to CHAPTER5.TXT

#### 2.10 TEST 10

Test 10 is identical as test 9. m0 is our Sun

Trajectory of the inner planet m1 is an ellipse
i.e. like the planet Mercury.
Trajectory of planet outer planet m2 is a circle
i.e. like the Earth

Now perform the program: 3OBJECTS.EXE
From the Test Selection Display:
Select test 10
Select S (Start)

The simulation shows that the major axis of the trajectory of the planet m1 moves forward.

The angle is irregular. After each revolution those values are:

10.25, 9.53, 7.58, 6.24, 9.27, 11.30, 11.36, 13.26, 16.06, 14.72

The results are made visible in figure 10

Now perform the program: 3OBJECTS.EXE
From the Test Selection Display
Select test 19 Subtest 10
From the Figure Selection Display
Select figure 10.

Return back to CHAPTER5.TXT

#### 2.11 TEST 11

The purpose of this demonstration is to test if the shape of m0 has any influence on the trajectory of m1.
In this demonstration the oblateness of m0 = 0 i.e. round

Test 11 consists of:

```	one star m0       m0 = 100
one planet m1     m1 = .01       distance m0 and m1 = 60
```

```			|
|
..............................
|                            |
m0                            m1
```
This simulation is similar as m0 being our Sun and m1 the planet Mercury.

Now perform the program: 3OBJECTS.EXE
From the Test Selection Display:
Select test 11
Select S (Start)

The simulation shows no forward movement of the major axis of the planet when oblateness = 0

#### 2.12 TEST 12

The purpose of this demonstration is to test if the shape of m0 has any influence on the trajectory of m1.
In this demonstration the oblateness of m0 = 1 i.e. not round

Now perform the program: 3OBJECTS.EXE
From the Test Selection Display:
Select test 12
Select S (Start)

This simulation shows that the major axis of the trajectory of the planet m1 moves forward.

For oblateness of 1 the angles are respectively : 67.2, 134.4 etc.

Return back to CHAPTER5.TXT

#### 2.13 TEST 13

Test 13 consists of

m0 and m1 are a double star. m0 = m1 = 100
m2 is one planet

The purpose of this test is to see how one planet behaves when it is attracted towards a binary star system.

Now perform the program: 3OBJECTS.EXE
From the Test Selection Display
Select test 13
Select S (Start)

The result of the demonstration show that the planet is finally ejected with high speed.

In order to see a different combination perform the following: Now perform the program: 3OBJECTS.EXE
From the Test Selection Display
Select test 13 Subtest 1
From the Parameter Selection Display
Set parameter 15 angle = 150 degrees
From the Test Selection Display
Select S (Start)

#### 2.13.1 TEST 13A

In order to see all the combinations in a range over 180 degrees perform the following test:

Now perform the program: 3OBJECTS.EXE
From the Test Selection Display
Select test 13 Subtest 2
Select S (Start)

What this demonstrations "proves" that (only?) from a binary system high objects can be ejected at high speeds. This could be two stars from which a third star is ejected or two galaxies from which a third galaxy is ejected. The speed of this third galaxy is not in agreement with Hubble's Law i.e. that the speed has a linear relation with its distance.

#### 3.0 OPERATION

The program uses two standard features:

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

#### 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 = Directory name. Standard name is C:\NOW\FIG

4 = Wait time in second. Physical wait time between each simulation
cycle.          Standard value = 0
5 = Speed of light. Standard value is 10

6 = Delta time in seconds between each calculation cycle.
Standard value is .02
7 = Origin Body.    Standard value = 0

8 = Eccentricity.   Standard value = 0.3

9 = Distance between m0 and m1. Standard value = 1000

10 = Display condition.
-1 means once each revolution of Mercury
x  means after each x calculation cycles

11 = Save condition
0 means no file save
1 means file save of results

12 = End Condition
-1 no end
x means after x revolutions of Mercury

13 = Sub Test. Sub test are used to select a specific command file
0 = no sub test
1 = Test with special condition 2
4 = Test with Mercury and Venus
5 = Test with Mercury, Venus and Earth.
6 = Test with Mercury and all the planets except Pluto.

14 = Oblatness of Sun.  Standard value = 1

15 = Angle alpha for test 13. Standard value = 0

16 = # of calculation cycles saved. Standard value = 0
0 means no calculation value saved.
```

#### 4.0 TECHNICAL INFORMATION

```
m0-------->a0                   a1<-------m1
<--------------------r------------------->
<----------r0------->X<--------r1-------->
```

Two masses m0 and m1.
Distance between m0 and m1 is r.
a0 is acceleration of m0 towards m1.
a1 is acceleration of m1 towards m0.
X is the center of mass

The force between the two masses m0 and m1 is described by Newton's Law (G=1):

```	    m0 * m1
F = ------- = m0 * a0  = m1 * a1
r˛

m1                m0
a0 = --           a1 = --
r˛                r˛
```

r0 is distance m0 to center of mass X r1 is distance m1 to center of mass X

```      r0 + r1 = r
r0 * m0 = r1 * m1
r0 * m0 = (r - r0) * m1
r0 * (m0 + m1) = r * m1
r * m1                   r * m0
r0 = -------             r1 = -------
m0 + m1                  m0 + m1

```
For a circle with radius r0
```
v0˛    v0˛ * (m0 + m1)     m1
a0 = --- =  --------------- =   --
r0         r * m1          r˛

m1˛
v0˛ =  -------------
r * (m0 + m1)

1
v0 = m1 *  sqrt { ------------- }
r * (m0 + m1)

1
v1 = m0 *  sqrt { ------------- }
r * (m0 + m1)

For example : m0 = 1000
m1 = 0
distance = 10

1          1000
v0 = 0            v1 = 1000 * sqrt { --------- } =  ----  = 10
10 * 1000       100

2 * pi * r    2 * pi * 10
T0 = 0            T1 = ----------  = ----------- = 2 * pi = 6.28
v1            10
```

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