## THE REALITY, NOW AND UNDERSTANDING

### CHAPTER5.TXT: THE MOVEMENT OF MERCURY

#### 1. INTRODUCTION

In this chapter we discuss the movement of the planet Mercury around the Sun

In order to simulate this movement 4 programs are used:
3OBJECTS, MERCURY, PLANETS and PLANET3D
• 3OBJECTS simulates the movement of 3 arbitrary objects (planets) under different configurations.
• MERCURY simulates the movement of 1 planet around the Sun i.e. Mercury or the Earth.
• PLANETS simulates the movement of the most important planets around the Sun in two dimensions.
• PLANET3D simulates the movement of the most important planets around the Sun in three dimensions.

#### 2 DESCRIPTION

Around the Sun there are 9 planets. Almost all the planets move in a circle around the Sun, with the Sun in the centre. The only exceptions are Mercury and Pluto. The trajectory of both planets is an ellipse. The planet Mercury will be studied in detail in this chapter.

An ellipse is described by three parameters:

The major axis
The minor axis
2 loci The Sun is in one of the loci.

The following pictures explains this:

```                               ..Y..
.....             .....
.                                .
.                                      .
.                                        .
P        S          C          X         A
.                                        .
.                                      .
.                                .
.....             .....
..Z..

```

S = sun at loci 1
X = loci 2
A = Aphelion (furthest position from the Sun)
P = Perihelion (shortest position near the Sun)
Major axis = line through P, S, C, X and A
Minor axis = line through Y, C and Z
dots = curve of Mercury

By definition all the planets move counter clockwise. Mercury starts (arbitrary start position) in A, then moves towards Y, then towards P (shortest distance to Sun), then towards Z and back towards A (furthest distance to Sun). That is one revolution. Then the next revolution starts etc. The speed of Mercury at P is the highest and at A the lowest. Mercury makes roughly 4 revolutions in one year.

In order to observe the movement of Mercury perform the Program:

MERCURY.TXT 3.1 TEST 1A

What makes the study of Mercury so interesting is that the direction of the major axis is not fixed in space but also moves counter clockwise. The total angle of this forward angle is 574 arc seconds in one century.

To explain this there are five possibilities:
The Sun is a double star.
The Sun is not round
Disturbance by the other planets
The movement of the Sun through space
Gravity does not act instantaneous but takes time to propagate i.e.
Gravity propagation (gravitation) has a speed.

#### 3 THE SUN AS A DOUBLE STAR

The easiest way to simulate the forward movement of a planet is when the Sun was not one star but two stars i.e. a double star.

Perform program:

3OBJECTS.TXT 2.8 TEST 8

Test 8 shows that the forward movement is highly irregular.

#### 4 THE SUN IS NOT ROUND

The shape of most of the planets is not round.

```                              N
.      .      .
.           .           .
.             .             .
.
W...............C...M...........E                   Observer
.
.             .             .
.           .           .
.      .      .
S

Figure 1
```

Figure 1 shows the Sun.

The line NS is diameter 0 or D0
The line WE is diameter 1 or D1 (equator)
C is the center of the Sun
M is the center of mass (gravity) of the Sun

The shape of an object is expressed as oblateness. Oblateness = D0 / (D1 - D0) or D1 = D0 * ( 1 + Oblateness)

When Oblateness is 0 the shape is round. When Oblateness is non zero the shape is an ellipse.

When the shape of the Sun is round the Center of Mass (Gravity) of the Sun coincides with the center of the Sun. When the Sun is round in Figure 1 the points C and M coincide.

To demonstrate this perform the program:

> SUNRAD.TXT 3.1 TEST 2A (OBLATENESS = 0)

When the shape of the Sun is not round then the centre of mass for the Sun is not in the middle but varies. The further away the more the centre of mass is in the centre.

To demonstrate this perform:

and:

> SUNRAD.TXT 3.1 TEST 2B (OBLATENESS = 0.0034)

For Mercury the offset (p) of the centre of mass of the Sun is equal to:

```
10000000 * 14.12 * oblateness
p = ----------------------------
r * 0.0034
```

r is the distance from the center of the Sun.

The easiest way to study the influence of the shape a star on the movement of a planet is the program 3OBJECTS test 11 and 12

In test 11 the oblateness = 0 In test 12 the oblateness = 1

Perform programs:

3OBJECTS.TXT 2.11 TEST 11

and

3OBJECTS.TXT 2.12 TEST 12

To observe the influence of the shape of the Sun on the movement of Mercury perform the program:

MERCURY.TXT 3.2 TEST 1B

The test shows that the shape of the Sun influences the movement of the planet Mercury.
The question of course is: what is the inner shape of the Sun? Most probably almost round. Meaning the shape has no influence.

During the period of the famous comet crash on Jupiter from 16 July - 22 July I was able to detect one sunspot moving along its equator from the Center of the Sun to the border over a period of 7 days, giving a rotation period of 28 days. What I was also able to see was that the Equator of the Sun and the Equator of Jupiter are in the same plane (almost).

On the other hand we have to be very careful if we want to simulate other (binary) stars or black holes.
Two parameters are very important:

their mass and their shape.

#### 5 DISTURBANCE BY THE OTHER PLANETS

All the planets influence each other.

To observe how planets each other perform the program:

3OBJECTS.TXT 2.9 TEST 9

and:

3OBJECTS.TXT 2.10 TEST 10

What test 10 shows is that the major axis moves forward.

All the planets influence the movement of the planet Mercury but not all in the same way. The more the closer and the heavier (more mass). As a result the major axis of the planet Mercury moves forward in time.

There is one major problem with the forward movement of the planet is that this movement is highly irregular. It takes more then one century before the average forward movement can be measured accurately i.e. the error is less then 1 arc second in a century.

The reason is because the forward movement of the planet Mercury for each planet is controlled by two parameters: short cycle and the long cycle. The short cycle is a function of the time of one revolution of the planet considered. In that period Mercury will have made a certain number of revolutions. For example 2.8 revolutions.

In order to explain long cycle start from initial position that Mercury is at Aphelion and the "other" planet is as close as possible to Mercury i.e. Sun, Mercury and "other" planet are in one line. The long cycle depends when Mercury is at Aphelion and the other planet is as close as possible back to this initial position.

In the following example you can see (assuming that in 1 revolution of the planet, Mercury does 2.8 revolutions) that after 14 revolutions of Mercury the Sun, Mercury and the planet considered are back to their initial position. The long cycle is then 14 revolutions.

```		     # of revolutions
Mercury         other planet
2.8               1
5.6               2
8.4               3
11.2               4
14                 5
```

In order to measure the forward angle of Mercury accurately you must measure the position of Mercury for a certain number of long cycles and that for the planet with has the longest long cycle number (taking into account the overall influence of that planet).

The following planet configurations will be studied:
1. Mercury and Venus
2. Mercury and Earth
3. Mercury Venus and Earth
4. Mercury and all the planets (except Uranus Neptune and Pluto)
To observe the behaviour of Mercury and Venus perform the Programs:
PLANETS.TXT 3.1 TEST 2A
PLANETS.TXT 3.2 TEST 2B
and observe the figures (results of the program):
PLANETS.TXT 3.3 TEST 2C
and:
PLANETS.TXT 3.4 TEST 2D

The results show an average forward movement caused by the planet Venus of 289 arc seconds in one century

To observe the behaviour of Mercury and Earth perform of the Program:

PLANETS.TXT 4.1 TEST 3A

and:

PLANETS.TXT 4.2 TEST 3B

The results show an average forward movement of 92.9 arc seconds in one century

PLANETS.TXT 5.1 TEST 4

The results show an average forward movement of 383 arc seconds in one century i.e. the sum of each individual planet.

To simulate all the planets is not necessary. The influence of the three outer planets is very small. To observe the influence of the three outer planets perform

The test shows that the forward angle of Uranus, Neptune and Pluto are very small and can be neglected.

PLANETS.TXT 6.1 TEST 5

The results show an average forward movement of 549 arc seconds in one century

Program PLANETS assumes that all planets move in one plane. In reality this is not true. The plane of planet Mercury is tilted and makes an angle of 7 degrees with the other planets.

PLANET3D.TXT 3.1 TEST 2A

and

PLANET3D.TXT 3.2 TEST 2B

The results show an average forward movement of 284.8 arc seconds in one century. This is less then the corresponding value of 289 of PLANETS.

For Mercury and Earth with PLANET3D the value is 97 and with PLANETS 92.7

For Mercury Venus and Earth the two values are 383.2 and 383 i.e. almost identical.

PLANET3D.TXT 6.1 TEST 5

The results show an average forward movement of 562.4 arc seconds in one century. This is more then the corresponding value of 549 of PLANETS. and much more then the 531 arc seconds of Literature 7 page 198.

This leaves 12 arc seconds unexplained from the total of 574 arc seconds. (Accordingly to Literature 2 page 348 this should be 43.11 +-.45 arc sec)

#### 6 VIRTUAL PLANET

In paragraph 2.4 is described that all the outer planets influence Mercury in such a way that the angle of the major axis moves forward. The problem is that this angle is highly irregular and even after one century of observations is very difficult to calculate. To solve this problem it is possible to replace all the planets by one virtual planet. This so called virtual planet moves in synchrony with Mercury such that the Sun, Mercury and this virtual planet always move in one line.

The trajectory that this virtual planet follows is the same as Venus. The mass of this virtual planet is a function of the distance between Mercury and the Sun. This function is calculated in the program SUNRAD.

With the virtual planets concept it now becomes very easy to simulate different planet configurations.

PLANETS.TXT 2.1 VIRTUAL TEST 1A

The result is a forward angle in one century

for delta time of 100 second of 289.223 arc sec
for delta time of 50 second of 290.041 arc sec

Those results are immediate obtained after one revolution.

PLANETS.TXT 2.2 VIRTUAL TEST 1B

The result is a forward angle in one century

for delta time of 100 second of 383.200 arc sec
for delta time of 50 second of 384.014 arc sec

PLANETS.TXT 2.3 VIRTUAL TEST 1C

The result is a forward angle in one century

for delta time of 100 second of 549.540 arc sec
for delta time of 50 second of 550.333 arc sec

The results are identical as described in paragraph 5 (i.e. simulation of the real planets after one century). That means the concept of virtual planets is a very good way to study the behaviour of planets. And a must! in order to speed up the calculations

#### 7 THE MOVEMENT OF THE SUN THROUGH SPACE

As explained in Chapter 4 the Sun moves around in our Galaxy

The movement of the Sun through space is described by three parameters:

speed v of the Sun
angle phi between the movement of the Sun and the major axis of Mercury
Speed of Gravity Propagation

The following drawing explains this.

```                                             .C
.
.
.....
.....      .      .....
.            .                   .
.            .                         .
.          .      Phi                    .
P        S                     X         A
.     .                                  .
.                                      .
.    .                                .
.            .....             .....
.                         .....
B

S   = Sun at loci 1
X   = loci 2
B C = the line of the movement of the Sun from B towards A
S X = the major axis of the movement of Mercury.
Phi = angle between the direction of the movement of the Sun and
the major axis
Phi = 0 means Sun moves towards X
Phi = 180 means Sun moves away from X
```

In CHAPTER 3 is explained the speed of Gravity i.e. that Gravity does not act instantaneous but takes time to propagate.

different values of Phi (0, 90, 180 and 270)
and with no virtual planet

perform the program: MERCURY.TXT 3.3 TEST 1C

The results show:
1. that for phi = 90 and 270 there is no forward movement
2. that for phi = 180 the forward movement is at maximum and positive.
3. that for phi = 0 (360) the forward movement is at minimum and negative.
4. the forward movement is linear with speed.
5. that for phi = 0, 180 and 360 the distance between Sun and Mercury is constant
6. that for phi = 90 the distance decreases (the most)
7. that for phi = 270 the distance increases (the most)
for different values of Phi(0, 90, 180 and 270)
with one virtual planet

perform the program: PLANETS.TXT 2.4 VIRTUAL TEST 1D

and: PLANETS.TXT 2.5 VIRTUAL TEST 1E

The importance of those two tests when you place Mercury at four different positions around the Sun is the following:

First the forward angle is not constant. The average forward angle increases with 550 arc seconds in one century. At phi is 90 there is a maximum and at phi is 270 the forward angle is negative

Secondly the distance is not constant after one revolution of Mercury. Again for phi is 90 and 270 the change is the most. At phi is 90 the change is negative and at phi is 270 the change is positive.

This raises the question how does Mercury behave in many centuries.

#### 8 INITIAL CONDITIONS

In CHAPTER 4 in order to study the behaviour of the Sun the initial conditions are modified.

To study the movement of the Planet Mercury

for different values of Phi(0, 90, 180 and 270)
for v = 100 km/sec
perform the program

MERCURY.TXT 3.4 TEST 1D

The result of the test are not convincing that in order to do a simulation of Mercury that initial conditions have to be modified. For an accurate simulation more tests have to be performed.

#### 9 OUR GALAXY

In order to simulate the movement of the planet Mercury proper it is necessary to do a simulation of one complete revolution of the major axis of Mercury and to take the whole Galaxy into account.

To study this you can use the program

3OBJECTS.TXT 2.2 TEST 2
and
3OBJECTS.TXT 2.3 TEST 3

In test 2 the movement of the planet is a circle. In test 3 the movement of the planet is an ellipse.

PLANETS.TXT 7.1 TEST 6A

PLANETS.TXT 7.2 TEST 6B

MERCURY.TXT 3.5 TEST 1E

The shape of the movement of the aphelion is an ellipse to the right side of the Sun. There is one major problem with this simulation: the time that the forward movement is equal to 574 arc seconds is too small. (i.e. one year)

#### 10 SPEED OF GRAVITY

In the previous tests it is assumed that the speed of Gravity propagation is equal to the speed of light.

when the speed of the Sun is 19.7 km/sec
when the speed of gravity is 120000000 km/sec perform program:
PLANETS.TXT 2.6 VIRTUAL TEST 1F
and
PLANETS.TXT 2.7 VIRTUAL TEST 1G

The important part of those tests is that for all values of phi (from 0 to 360) the forward angle positive is.

when the speed of the galaxy is 229 km/sec
when the speed of gravity is 12000000 km/sec

perform program: PLANETS.TXT 7.3 TEST 6C

and: PLANETS.TXT 7.4 TEST 6D

The information of TEST 6C is also presented in the form of a figure.
Perform:
FIGURE.TXT 2.4 TEST 6C OF PLANETS

for a long period of time
when speed of gravity = 6000000 km/sec perform:

MERCURY.TXT 3.6 TEST 1F

The display shows that the aphelion of Mercury is always to the right side of the Sun

for a long period of time
when speed of gravity = 12000000 km/sec
and for different initial distances
study the following 6 figures:

MERCURY.TXT 3.7 TEST 1G

The display shows that for the aphelion of Mercury there are two possibilities:

a. Will stay to the right side of the Sun and Note (1)
b. Will move around the Sun. Both are possible when the Sun makes a complete revolution true our Galaxy. That means during one part it can be (a) and during the other (b)

The results of those simulations is very remarkably because it means:

that a collision of Mercury with the Sun is highly unlikely.
that the value of the speed of gravity is less critical Most probably between 3000000 and 30000000 km/sec. i.e. between 10 and 100 times the speed of light.

Note (1): Original was written here:

Quote
The display shows that the aphelion of Mercury:
a. Will stay to the right side of the Sun.
b. Mercury will collide with the Sun.
c. Will move around the Sun.

The question is which one of those three possible configurations is true.

(It cannot be b)

Unquote

In the 6 figures of the above test, 5 planets were replaced by one virtual planet.

There are two additional ways to study the movement of Mercury:
1. To replace Venus by a planet with a mass 1.9 times as large.
2. To include the 5 planets.
PLANETS.TXT 6.2 MERCURY IN MANY CENTURIES WITH VENUS * 1.9

What this test shows that this method is not very accurate.

PLANETS.TXT 6.3 MERCURY IN MANY CENTURIES WITH 5 PLANETS

The test shows that the virtual planet concept is very accurate and because of speed of the simulation improvements a must.

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