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:

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:

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:

and

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

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:

All the planets influence each other.

To observe how planets each other perform the program:

and:

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)

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:

and:

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

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

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.

To observe the behaviour of Mercury and all the planets perform

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.

To study the behaviour of Mercury and Venus perform

and

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.

To study the behaviour of Mercury and all the planets except the three outer planets perform:

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)

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.

Perform the program:

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

To simulate the influence of Venus on Mercury perform the program:

The result is a forward angle in one century

Those results are immediate obtained after one revolution.

To simulate the influence of Venus and Earth on Mercury perform the program

The result is a forward angle in one century

To simulate the influence of all the planets on Mercury perform the program

The result is a forward angle in one century

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

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

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

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.

To study the movement of the Planet Mercury for:

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)

To study the movement of the Planet Mercury

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.

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.

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

To study the movement of the Sun in our Galaxy and Mercury around the Sun when the speed of the galaxy is 0 km/sec perform program:

To study the movement of the Sun in our Galaxy and Mercury around the Sun when the speed of the galaxy is 229 km/sec perform program:

To study the movement of the Sun in our Galaxy and Mercury around the Sun for a long period of time perform the demonstration (figure):

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)

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

To study the movement of Mercury around the Sun

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

To study the movement of the Sun in our Galaxy and Mercury around the Sun

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