## THE REALITY, NOW AND UNDERSTANDING

### MERCURY.TXT

#### 1 INTRODUCTION

The purpose of this simulation is to show how two objects move around each other. This movement is studied under different conditions.

The following two body configurations are studied:
1. Mercury around the Sun
2. Earth (planets) around the Sun
3. Sun around a Sun (Binary star system)
4. Mercury around Mercury (Binary elliptical star system)
5. Sun in our Galaxy
6. Two Galaxy's around each other.
7. PSR 1913 + 16

The following conditions (parameters) are studied:
1. The shape of the Sun (Oblateness)
2. The movement of the Sun through space.
3. The speed of gravity propagation
4. Initial conditions (Primarily for Earth)
5. The different planets are studied by means of "subtests"

#### 2.1 THE MOVEMENT OF THE SUN

In order to study the influence of the movement of the Sun through space 2 parameters are important:
The speed v.
The angle phi.

The speed v is the speed of the Sun relative to the other stars. The angle phi is the angle between the direction of the movement of the Sun and the long axis of the trajectory of Mercury.

#### 3 THE MOVEMENT OF MERCURY AROUND THE SUN

For Mercury the basic movement is an ellipse.

#### 3.1 TEST 1A

The purpose of this test is to demonstrate the movement of Mercury around the Sun for v = 0

Now perform the program: MERCURY.EXE
This test requires:
From the Test Selection Display
Select test 1
From the Parameter Selection Display
Set 6 delta time = 100 seconds
From the Test Selection Display
Select S (Start)
After 3 revolutions to select ESC.

The following are the results of this test:

```   angle   revolutions   counts   time     distance    eccentricity   arcsec
0          1         75583    .2      69678616     .20563         -1.07
2        151167    .5      69678616     .20563         -1.07
3        226751    .7      69678616     .20563         -1.07
4        302335   1.0      69678616     .20563         -1.07
```

#### 3.2 TEST 1B

The purpose of this test is to study the behaviour of Mercury when the shape of the Sun is not round.

Now perform the program: MERCURY.EXE
From the Test Selection Display
Select test 1
From the Parameter Selection Display
Set 6 delta time = 100 seconds
Set 17 Oblateness = .0034
From the Test Selection Display
Select S (Start)
After 2 revolutions to select ESC.

The results show that the forward angle is 48.797 arcsec in one century

Repeat the same test but now with Oblateness = .034

The results show that the forward angle is 497 arcsec in one century

#### 3.3 TEST 1C

The purpose of this test is to study the behaviour of the movement of the Earth when the Sun has a speed of v = 100 km/sec for four different values of phi : 0, 90, 180 and 270 degrees.

Now perform the program: MERCURY.EXE
This test requires four times:
From the Test Selection Display
Select test 1
From the Parameter Selection Display
Set 6 delta time = 100 seconds
Set 9 speed of the Sun (v) = 100 km/sec
Set 10 angle phi = 0, 90, 180 and 270
Set 18 initial condition = 0
From the Test Selection Display
Select S (Start)
After 2 revolutions to select ESC.

The following are the results for delta t of 100 seconds and v = 100 km/sec without modified initial conditions. Speed of gravity is 300000 km/second.

```      angle   revolutions   counts        distance    eccentricity   arcsec
0          1         75643        69678614     .205018      -4715
2        151288        69678610     .205018      -4714

90          1         75557        69646637     .205514          3.83
2        151065        69614675     .205503          3.83

180          1         75522        69678616     .206241       4758
2        151045        69678614     .206240       4758

270          1         75608        69710611     .205745          5.0
2        151269        69742623     .205756          5.0
```

Counts is the number of simulation cycles in one revolution i.e. when Mercury is at aphelion (furthest distance from Sun).
Distance is the distance between Mercury and Sun at end of one revolution. Eccentricity is eccentricity of trajectory of Mercury.
Arcsec is forward angle of major axis of trajectory of Mercury in one century.

#### 3.4 TEST 1D

The purpose of this test is to study the behaviour of the movement of the Earth when :

the Sun has a speed of v = 100 km/sec
for four different values of phi : 0, 90, 180 and 270 degrees.
with modified initial conditions (exactly like 4.3 test 2c)

Now perform the program: MERCURY.EXE
This test requires four times:
From the Test Selection Display
Select test 1
From the Parameter Selection Display
Set 6 delta time = 100 seconds
Set 9 speed of the Sun (v) = 100 km/sec
Set 10 angle phi = 0, 90, 180 and 270
Set 18 initial condition = 1
From the Test Selection Display
Select S (Start)
After 2 revolutions to select ESC.

The following are the results for delta t of 100 seconds and v = 100 km/sec using the modified initial conditions.

```      angle   revolutions   counts        distance    eccentricity   arcsec
0          1         75581        69655388     .205283      -4725
2        151163        69655384     .205283      -4725

90          1         75534        69646659     .205514         11.69
2        151042        69614697     .205503         11.60

180          1         75585        69701842     .205976       4748
2        151171        69701841     .205976       4748

270          1         75631        69710627     .205745         12.68
2        151292        69742639     .205757         12.67
```
The following are the results for delta t of 100 seconds and v = 19.7 km/sec using the modified initial conditions.

```      angle   revolutions   counts        distance    eccentricity   arcsec
0          1         75582        69674040     .205561       -933
2        151166        69674040     .205561       -933

90          1         75573        69672316     .205607         -.674
2        151142        69666016     .205605         -.675

180          1         75583        69683192     .205698        932
2        151167        69683192     .205698        932

270          1         75592        69684918     .205652          -.447
2        151191        69691220     .205654          -.448
```

From the above we can see that the forward movement of the of the major axis of the trajectory of Mercury is the greatest for phi = 180 degrees i.e. when the Sun moves away from Mercury.
The smallest for phi = 0 degrees i.e. when the Sun moves towards Mercury. The forward movement increases linear with the speed.

The results of the simulations also show that for phi = 90 the distance between Mercury and the Sun after each revolution decreases (the most) For phi = 270 degrees the distance increases. This change in distance also increases linear with the speed.

The results are also displayed as a figure.
From the Test Selection Display:
Select test 12 Subtest 1
Select test 12 Subtest 2
From the Figure Selection Display:
Select figure 1 for v = 100 and
Select figure 2 for v = 19.7

#### 3.5 TEST 1E

The purpose of this test is to study the behaviour of the movement of the forward angle of the planet Mercury for one complete revolution i.e. in many centuries. Speed of gravity propagation is 300000 km/sec

The speed of the Sun is 19.7 km/second in relation to the other stars. See CW Allen, Astrophysical Quantities, Athlone Press, 1976.

Now perform the program: MERCURY.EXE
From the Test Selection Display
Select test 1
From the Parameter Selection Display
Set 5 c (Speed of gravity propagation) = 300000
Set 6 delta time = 400 seconds (and 100)
Set 16 Virtual Planet Condition = 3
From the Test Selection Display
Select S (Start)

The results are presented in figures
From the Test Selection Display
Select test 12 Subtest 5 From Figure Selection Display
Select 5.

Figure 5 shows that the forward angle describes an "ellipse" on the right side of the Sun.
The problem with this simulation is that only for a very small period the forward angle is approximate equal to 574 degrees (and may be never).
This time is 0.9 years at two instances.
Time of one complete revolution is 14552.8 years

#### 3.6 TEST 1F

The purpose of this test is to study the behaviour of the movement of the forward angle of the planet Mercury for one complete revolution i.e. in many centuries. Speed of gravity propagation is 6000000 km/sec

The speed of the Sun is 19.7 km/second in relation to the other stars.

Now perform the program: MERCURY.EXE
This test requires:
From the Test Selection Display
Select test 1
From the Parameter Selection Display
Set 5 c (Speed of gravity propagation) = 6000000
Set 6 delta time = 400 seconds (and 100)
Set 16 Virtual Planet Condition = 3
From the Test Selection Display
Select S (Start)

The results are presented in figures
From the Test Selection Display
Select test 12 Subtest 7
From Figure Selection Display
Select 7

Figure 7 shows that the forward angle describes a "circle" which stays to the right of the Sun. The forward angle is displayed at the top right corner. Time of one complete revolution is 123757 years. Time that the forward angle is 574 is 475.5 years

#### 3.7 TEST 1G

The purpose of this test is to study the behaviour of the movement of the forward angle of the planet Mercury for one complete revolution in our Galaxy i.e. in many centuries. Speed of gravity propagation is 12000000 km/sec

The speed of the Sun is 19.7 km/second in relation to the other stars.

Now perform the program: MERCURY.EXE
This test requires:
From the Test Selection Display
Select test 1
From the Parameter Selection Display
Set 5 c (Speed of gravity propagation) = 12000000
Set 6 delta time = 400 seconds
Set 16 Virtual Planet Condition = 3
From the Test Selection Display
Select S (Start)

The results are presented in six figures: 9, 11, 12, 13, 14 and 15

The present initial distance from Mercury to the Sun, when Mercury is at aphelion is 69600000 km. In figure 9 the initial distance is 73100000 km. In figure 11 the initial distance is 87000000 km. In figure 12 the initial distance is 89100000 km. In figure 13 the initial distance is 90000000 km. In figure 14 the initial distance is 90500000 km. In figure 15 the initial distance is 94000000 km.

Because the initial distance is larger the influence caused by the planets on the forward movement of Mercury will increase. In figure 15 the most

Now perform the program: MERCURY.EXE
From the Test Selection Display
Select test 12 Subtest 9
From Figure Selection Display
Select Figure 9

Figure 9 shows that the forward angle describes a "circle" which stays to the right side of the Sun. Time of one revolution is 191967 years Time that the forward angle is 574 is 138.76 years

Now perform the program: MERCURY.EXE
From the Test Selection Display
Select test 12 Subtest 11
From Figure Selection Display
Select Figure 11

Figure 11 is almost identical as figure 9. Time that the forward angle is 574 is 68.69 years. Time of one revolution is 244444 years.

Now perform the program: MERCURY.EXE
From the Test Selection Display
Select test 12 Subtest 12
From Figure Selection Display
Select Figure 12

Figure 12 is also like figure 11 and 9. Time that the forward angle is 574 is 69.59 years. Time of one revolution is 291903 years.
This trajectory is highly remarkably because the aphelion stays to the right side of the Sun. No collision with the Sun takes place. See Note (1) below.

Now perform the program: MERCURY.EXE
From the Test Selection Display
Select test 12 Subtest 13
From Figure Selection Display
Select Figure 13

Figure 13 is also like figure 12 but highly pronounced. Time that the forward angle is 574 is 73.06 years. Time of one revolution is 349900.8 years.

Now perform the program: MERCURY.EXE
From the Test Selection Display
Select test 12 Subtest 14
From Figure Selection Display
Select Figure 14

Figure 14 shows that the forward angle describes a complete circle around the Sun. Time of one revolution = 305765.6 years. Time that the forward angle is 574 is 75.33 years

From the Test Selection Display
Select test 12 Subtest 15
From Figure Selection Display
Select Figure 15

Figure 15 shows (when completed) that the forward angle describes a complete circle around the Sun. This figure is almost identical as figure 13. Time that the forward angle is 574 is 109.81 years Time of one revolution = 150365.4 years

It is also possible to see all the pictures in one frame. Repeat the last test i.e. subtest 15 When the picture is completed enter 5 then 7 then 9 then 11 then 12 then 13 and finally 14.

Note (1) The original text was:
The expectation is that Mercury in this configuration will collide with the Sun. Most probably this will happen at 21 July 1994.

#### 4 THE MOVEMENT OF THE EARTH AROUND THE SUN

The movement of the Earth around the Sun is a circle i.e. eccentricity is 0.
The movement of the planets is also studied.

#### 4.1 TEST 2A

The purpose of this test is to demonstrate the movement of the Earth around the Sun for v = 0

Now perform the program: MERCURY.EXE
This test requires:
From the Test Selection Display
Select test 2
From the Parameter Selection Display
Set 6 delta time = 400 seconds
From the Test Selection Display
Select S (Start)
After 3 revolutions to select ESC.

The following are the results of this test:

```                               delta t = 400 sec          delta t = 100 sec
```

```      angle   revolutions   counts        distance      counts      distance
0          1         78695       149600000      314775     149600001
2        157388       149600001      629549     149600002
3        236082       149600002      944323     149600003
```

The results of this test shows:
1. That the time in counts of each revolution is constant.
78695 counts = 78695 * 400 seconds
= 78695 * 400 / (24*60*60) days = 364 days
2. That the distance between the Sun and the Earth is constant.

The following results for the Earth are observed if different values for gravity propagation are considered:

If the speed of c = 3000 km/sec the folling values for distance are observed:
(delta t = 100 sec)

```        149600111       149600222       149600334
```

If the speed of c = 30000 km/sec the folling values for distance are observed:

```        149600010       149600021       149600032
```

#### 4.1.1 TEST 2A VENUS

Now perform the program: MERCURY.EXE
This Venus test requires:
From the Test Selection Display
Select test 2 Subtest 1

For the planet Venus c = 300000 km/sec (v=35) the values are the following:

```        107999999       108000000       108000001       108000002
```

#### 4.1.2 TEST 2A MARS

Now perform the program: MERCURY.EXE
This Mars test requires:
From the Test Selection Display
Select test 2 Subtest 2

For the planet Mars c = 300000 km/sec (v=24) the values are the following:

```        227999999       228000000       228000000       228000000
```

#### 4.1.3 TEST 2A JUPITER

Now perform the program: MERCURY.EXE
This Jupiter test requires:
From the Test Selection Display
Select test 2 Subtest 3

For the planet Jupiter c = 300000 km/sec the values are the following:

```        778299999       778300809       778301618       778302427
```

For the planet Jupiter c = 30000000 km/sec the values are the following:

```        778300000       778300007       778300016       778300024
```

How faster the speed of gravity propagation, the more stable the revolutions are. (lineair relation)

#### 4.1.4 TEST 2A SATURN

Now perform the program: MERCURY.EXE
This Saturn test requires:
From the Test Selection Display
Select test 2 Subtest 4

For the planet Saturn c = 300000 km/sec (v=9) the values are the following:

```       1429999999      1430000329      1430000659      1400000988
```

#### 4.1.5 TEST 2A URANUS

Now perform the program: MERCURY.EXE
This Uranus test requires:
From the Test Selection Display
Select test 2 Subtest 5

For the planet Uranus c = 300000 km/sec (v=6) the values are the following:

```       2874999999      2875000072      2875000143      2875000214
```

Observing the above results indicates that Jupiter is the most "unstable"

#### 4.1.6 MATHEMATICS

The previous results can be mathematical described accordingly to the following rules.

1. dRe is the increase per year of the Earth = 1.11
2. dRpl is the increase for a planet.
3. Me = mass of Earth
4. Mpl = mass of planet
5. Re is the distance of Earth Sun
6. Ppl is the distance of Planet Sun
The increase per revolution of a planet dRpl = dRe * (Mpl/Me)* SQR (Rpl/Re)
The revolution time for a planet = SQR (Rpl/Re)^3
Increase of a planet dRPl per year = dRe * (Mpl/Me)*(Re/Rpl)
 planet mass distance AU rev time dRpl/rev dRpl/year Mercury 0.06 0.39 0,244 0,041 0,17 Venus 0,82 0.72 0,611 0,772 1,264 Earth 1 1 1 1 1 Mars 0,11 1.52 1,874 0,15 0,08 Jupiter 317.89 5.2 11.857 804,63 67,857 Saturn 95,15 9.54 29,466 326,216 11,07 Uranus 14,54 19.18 83,399 70,682 0,841 Neptune 17.23 30.06 164,81 104,858 0,636

In the book: "Problem book in relativity and gravitation" by Alan P Lightman e.a. ISBN 0-691-08162-X at page 350 in the solution 12.4 the follwing equations are used, with v+ = speed of Earth and M0 is the mass of the Sun.

(1) angle theta = v+/c
(2) t-t0 = c/4GM0 * (r�-r0�)

Next is written: In particular, the earth's orbit has r=1.5 *10^8 km, v+=30km/sec, the radius of the sun is r0=7*10^5 km so Theta = 10^-4 and t-t0 = 1.3*10^10 sec = 400 years.

The problem with equation 2 is that the stability is a function of the mass of the sun while in the simulation it is a function of the mass of the planet.

It is assumed that v0 = speed of Sun and M+ is the mass of Earth.
Accordingly to the text the Earth energy increase is a function of v+*Theta = v+*v+/c.
IMO this should not be the theta defined by the speed of the Earth but the theta defined by the speed of the Sun. As such the Earth energy increase is a function of v+*v0/c, which is a much smaller value.
And because v0 is a function of M+, this explains the dependency of the mass of the planet.
I expect equation 2 has to be rewritten as: t-t0 = c/4G*SQR(M0*M+) * (r�-r0�)

This leaves the major problem: Is the "instability" of jupiter acceptable and accordingly to observations.

#### 4.2 TEST 2B

The purpose of this test is to study the behaviour of the movement of the Earth when the Sun has a speed of v = 100 km/sec for four different values of phi : 0, 90, 180 and 270 degrees.

Consider the following drawing

```                           .  B  .
.                 .
.                        .

C            S              A

.                        .
.                 .
.   D  .
```

The earth moves, starting from A, via B, through C and D back to A. This is one revolution

There are four basic initial arrangements possible:
1. S moves towards A : Phi = 0
2. S moves towards B : Phi = 90
3. S moves towards C : Phi = 180
4. S moves towards D : Phi = 270

What we want to study if it makes any difference if you start your simulation from the points A, B, C, or D. Their should not be any difference because what you are simulating is the same physical system i.e. the Earth around the Sun

Now perform the program: MERCURY.EXE
This test requires four times:
From the Test Selection Display
Select test 2
From the Parameter Selection Display
Set 6 delta time = 400 seconds
Set 9 speed of the Sun (v) = 100 km/sec
Set 10 angle phi = 0, 90, 180 and 270
Set 18 initial condition = 0
From the Test Selection Display
Select S (Start)
After 2 revolutions to select ESC.

The following are the results of this test:

```                                delta t = 400 sec          delta t = 100 sec

angle phi   revolutions  counts      distance       counts      distance
0           1         78774     149599987       315090     149599997
2        157546     149599976       630179     149599995

90           1         78691     149600002       314759     149600001
2        157384     149600003       629533     149600001

180           1         78616     149600013       314461     149600004
2        157231     149600026       628920     149600008

270           1         78699     149599998       314792     149600000
2        157393     149599999       629566     149600001

```

The results of the test shows:
1. That the duration in counts of the first revolution for different values of phi is quite different
2. That the distance between the Sun and the Earth after one revolution is slightly different.

The fact that the distance is not identical is a matter of accuracy. For phi = 0 both the distance for delta time is 400 seconds and delta time is 100 seconds are shown. The last two values are almost identical i.e. they should become identical for delta time is even smaller.

For phi = 90 and phi = 270 the duration in counts is almost identical as for the case when v = 0
For phi = 0 the duration is larger
For phi = 180 the duration is smaller.

The fact that the duration in counts is different is wrong because this is a simulation of the same physical system. The duration should be identical.

#### 4.3 TEST 2C

The purpose of this test is to study the behaviour of the movement of the Earth when:

the Sun has a speed of v = 100 km/sec
for four different values of phi : 0, 90, 180 and 270 degrees.
the initial conditions are modified.

Now perform the program: MERCURY.EXE
This test requires four times:
From the Test Selection Display
Select test 2
From the Parameter Selection Display
Set 6 delta time = 400 seconds
Set 9 speed of the Sun (v) = 100 km/sec
Set 10 angle phi = 0, 90, 180 and 270
Set 18 initial condition = 1
From the Test Selection Display
Select S (Start)
After 2 revolutions to select ESC.

In order to make the simulations identical the initial conditions are modified:
for phi is 0 the distance between Sun and Earth is made smaller. for phi is 180 the distance between Sun and Earth is made larger. The amount in both cases is the same and equal to:

```        v * distance    100 * 149600000
------------  = --------------- = 49866.6 km
c             300000
```

The following are the results of this test:

delta t = 400 sec delta t = 100 sec

```        angle    revolutions   counts      distance        counts    distance
0           1         78695      149550121       314775    149550131
2        157388      149550110       629549    149550129

90           1         78695      149600002       314775    149600008
2        157388      149600005       629549    149600009

180           1         78695      149649879       314775    149649870
2        157388      149649893       629549    149649875
270           1         78695      149600014       314775    149600010
2        157388      149600014       629549    149600011
```

The results of the test shown that with modified initial conditions the time of one revolution becomes identical and independent of phi i.e. initial condition.

```       angle       revolutions       v       delta t       distance
90             1             0         10          149600001
90            20             0         10          149600021
90             1             50        10          149600003
90            20             50        10          149600023
90             1            100        10          149600009
90            20            100        10          149600045

90             1            200        10          149600032
90            11            200        10          149600044
90            21            200        10          149600043
90            31            200        10          149800079
```

For phi = 90 the results show that distance increases approximate with 1 km each revolution and is independent of the base speed v.

#### 5.1 TEST 3

The following are the results for delta t of 400 seconds and v = 0 km/sec using the unmodified initial conditions.

```      angle   revolutions   counts        distance
0          1        102284        224562083
2        204676        224724226
3        307179        224886427
```

The following are the results for delta t of 400 seconds and v = 100 km/sec using the unmodified initial conditions.

```      angle   revolutions   counts        distance
0          1        102284        224562083
2        204676        224724226

90          1        102278        224562085
2        204671        224724228

180          1        102284        224562083
2        204676        224724226

270          1        102289        224562081
2        204681        224724224
```

The following are the results for delta t of 400 seconds and v = 100 km/sec using the modified initial conditions.

```      angle   revolutions   counts        distance
0          1        102282        224487296
2        204671        224649453

90          1        102284        224562084
2        204676        224724228

180          1        102386        224636869
2        204881        224798999

270          1        102284        224562107
2        204676        224724249
```

#### 6.1 TEST 4

The following are the results for delta t of 400 seconds and v = 0 km/sec using the unmodified initial conditions.

```      angle   revolutions   counts        distance    eccentricity   arcsec
0          1         55682       180591296     .206253        -12.9
2        111442       180765083     .206300        -12.89
3        167280       180938962     .206346        -12.87
4        223195       181112932     .206392        -12.85
```

The following are the results for delta t of 400 seconds and v = 100 km/sec using the unmodified initial conditions.

```      angle   revolutions   counts        distance    eccentricity   arcsec
0          1         55682       180591296     .206253         -7.69
2        111442       180765083     .206300         -7.68
90          1         55682       180591296     .206253        -18.123
2        111442       180765083     .206300        -18.102
180          1         55682       180591296     .206253         -7.697
2        111442       180765083     .206300         -7.68
270          1         55682       180591296     .206253        -18.122
2        111442       180765083     .206300        -18.102
```

This demonstration shows that the distance linear increases after each revolution and is independent of the direction of the movement.

#### 7.1 TEST 5

The purpose of this test is to show the behaviour of the Sun in our Galaxy assuming that all the mass of is concentrated in one point. Mass of galaxy Mg is 1.1 10E11 times the mass of our Sun = 2.2 10E41 kg

Now perform the program: MERCURY.EXE
This test requires:
From the Test Selection Display
Select test 5
From the Parameter Selection Display
No changes are required.
From the Test Selection Display
Select S (Start)
After 1 revolution to select ESC.

The result of the test is that the revolution time is 189 million years. v of Sun is 249 km/sec

#### 8.1 TEST 6

The purpose of this test is to show the behaviour of how two galaxy's which equal mass move around each other. Distance between the two galaxies is like the distance between our galaxy and the Andromeda (M31) galaxy of 2.25 million light years.

The mass used of each galaxy is twice the mass of the previous test or 2 times Mg = 4.4 10^41 kg.

Now perform the program: MERCURY.EXE
This test requires:
From the Test Selection Display
Select test 6
From the Parameter Selection Display
No changes are required.
From the Test Selection Display
Select S (Start)
After 1 revolution to select ESC.

The result of the test is that the revolution time is 80769 million years. v of Galaxy is 26 km/sec.

For a mass of 10 times Mg the revolution time is 36158 million years v of Galaxy is 58 km/sec.

For a mass of 2 times Mg and a distance of 1 million light years the revolution time is 23941 million years and v of Galaxy is 39 km/sec.

#### 9 PSR 1913 + 16

The purpose of this test is to study the binary pulsar PSR 1913 + 16

The mass of the silent companion m0 is 1.442 * M0
The mass of the pulsar (visible) companion is 1.386 * M0
M0 is the mass of the Sun.

For all the simulations it is important first to select test 7 and then to make the modifications in the parameter selection display For all the simulations delta time = 0.02

#### 9.1 TEST 7

The purpose of this test is to show the behaviour of the pulsar with no extra parameters set.

Now perform the program: MERCURY.EXE
From the Test Selection Display
Select test 7
From the Parameter Selection Display
Set 5 c speed of light = 0 (infinite)
From the Test Selection Display
Select S (Start)

The result of the demonstration shows that the longest distance is 3040000 km and the shortest distance is 760000 km (or 1/4) The eccentricity is 0.6

```    angle   revolutions    time          distance              arcsec
0          1        26791.24       3040000                1.75
2        53582.46       3040000                 .122
3        80373.7        3040000                -1.20
```

Values in arcsec are in arcsec per century.

#### 9.2 TEST 7: ANGLE PHI

The purpose of this test is to observe the behaviour of the pulsar for different values of phi i.e. direction of movement of center of gravity of both stars. Speed is constant.

Now perform the program: MERCURY.EXE
This test requires four times:
From the Test Selection Display
Select test 7
From the Parameter Selection Display
Set 5 c = 300000000
Set 6 delta time = 0.02 seconds
Set 9 speed of the "Sun"(v) = 1000 km/sec
Set 10 angle phi = 0, 90, 180 and 270
Set 18 initial condition = 1
From the Test Selection Display
Select S (Start)
After 2 revolutions to select ESC.

```    angle   revolutions    time          distance              arcsec
0                       3039989
0          1        26791.36       3040038               -939
2        53583.34       3040087               -941
3        80375.90       3040136               -942

angle   revolutions    time          distance              arcsec
0                       3040000
90          1        26791.5        3040047                 -5.576
2        53583.6        3040095                  2.105
3        80376.3        3040142                  6.06

angle   revolutions    time          distance              arcsec
0                       3040010
180          1        26791.7        3040058                931.8
2        53584.         3040107                926.9
3        80376.88       3040156                948.91

angle   revolutions    time          distance              arcsec
0                       3040000
270          1        26791.58       3040049                -17.15
2        53583.72       3040099                 -9.40
```

#### 9.3 TEST 7: SPEED V

The purpose of this test is to observe the behaviour of the pulsar for different values of v i.e. speed of center of gravity of both stars. Direction (angle phi) is constant.

Now perform the program: MERCURY.EXE
This test requires four times:
From the Test Selection Display
Select test 7
From the Parameter Selection Display
Set 5 c = 3000.00000
Set 6 delta time = 0.02 seconds
Set 9 speed of the Sun (v) = 100 km/sec
Set 10 angle phi = 180
Set 18 initial condition = 1
From the Test Selection Display
Select S (Start)
After 2 revolutions to select ESC.

```    v        revolutions    time         distance              arcsec
0                       3040001
100           1        26791.54       3040049                 86.38
2        53583.7        3040098                 88.92

v        revolutions    time         distance              arcsec
0                       3040001
10           1        26791.54       3040048                 10.01
2        53583.66       3040097                  6.57
3        80376.40       3040146                  6.10

v,phi   revolutions    time          distance              arcsec
0                       3040000
0            1        26791.54       3040048                   .756
2        53583.66       3040097                 -2.09
3        80376.4        3040146                 -3.25
```

#### 9.4 TEST 7: SPEED OF GRAVITY PROPAGATION

The purpose of this test is to observe the behaviour of the pulsar for different values of c i.e. speed of gravity propagation.

Now perform the program: MERCURY.EXE
This test requires four times:
From the Test Selection Display
Select test 7
From the Parameter Selection Display
Set 5 c = 3000.00000, 300.00000, 30.00000, 3.000000
Set 6 delta time = 0.02 seconds
Set 9 speed of the Sun (v) = 1000 km/sec
Set 10 angle phi = 180
Set 18 initial condition = 1
From the Test Selection Display
Select S (Start)
After 2 revolutions to select ESC.

```    c       revolutions    time          distance    degrees    arcsec
0                       3040010
3000.00000       1        26791.7        3040058                931.8
2        53584.         3040107                926.9
3        80376.88       3040156                948.91

c       revolutions    time          distance               arcsec
0                       3040101
300.00000       1        26795.88       3040588                9339

c       revolutions    time          distance    degrees    arcsec
0                       3041013
30.00000       1        26837.74       3045890     .26692     96092.55
2        53585.64       3050772     .26673     96024.768

c       revolutions    time          distance    degrees    arcsec
0                       3050133
3.00000       1        26791.7        3099115      3.48      1224172
2        53584.         3148693      3.48      1217798
```

Values in arcsec are in arcsec per century. Values in degrees are in degrees per year.

#### 9.5 TEST 7: MASS

The purpose of this test is to show the behaviour of the pulsar when the mass of the pulsar m1 is modified.

Now perform the program: MERCURY.EXE
From the Test Selection Display
Select test 7
From the Parameter Selection Display
Set 5 c speed of light = 0 (infinite)
Set 20 delta mass as indicated
From the Test Selection Display
Select S (Start)

After S = set factor m0 as indicated.

set factor m0 as indicated.

m0 = 1 means: mass of m0 is increased each second with delta mass (times 1)
m0 = 0 means: mass of m0 does not change
m0 = -1 means: mass of m0 is decreased each second with delta mass (times -1)
The same for m1

Following are the results when m1 is modified:

```mass    m0    m1  revolutions    time          distance           arcsec
1D+22    0     1       0                       3040000
1        26789.96       3039856            35.39
2        53577.38       3039712            33.64
3        80362.28       3039568            33.42

mass    m0    m1  revolutions    time          distance           arcsec
1D+23    0     1       0                       3040000
1                       3038561            3469.18

mass    m0    m1  revolutions    time          distance           arcsec
-1D+23   0     1       1        26803.94       3041441            3475.99
2        53633.32       3042885            3475.29
```

Following are the results when m0 is modified:

```mass    m0    m1  revolutions    time          distance           arcsec
1D+22    1     0       0                       3040000
1        26789.96       3039856            35.75

mass    m0    m1  revolutions    time          distance           arcsec
-1D+22   1     0       0                       3040000
1        26792.5        3040144            35.84
```

Following are the results when both m0 and m1 are modified:

```mass    m0    m1  revolutions    time          distance           arcsec
1D+22    1     1       0                       3040000
1        26788.7        3039712           139.67
2        53572.32       3039424           138.07
```

Following are the results when both m0 and m1 are modified. Total change in mass is zero.

```mass    m0    m1  revolutions    time          distance           arcsec
1D+22    1    -1       4                       3039999

mass    m0    m1  revolutions    time          distance           arcsec
1D+22   -1     1       7                       3039999
```

#### 9.6 TEST 7: OBLATENESS

The purpose of this test is to show the behaviour of the pulsar for different values of oblateness

Now perform the program: MERCURY.EXE
From the Test Selection Display
Select test 7
From the Parameter Selection Display
Set 5 c speed of light = 0 (infinite)
Set 17 oblateness as indicated
From the Test Selection Display
Select S (Start)

```
oblateness   revolutions    time    distance   degrees        arcsec
0.001           1                 3040000      12.14       4373226

revolutions    time    distance   degrees        arcsec
0.01            1                 3040000     121.68      43805519

revolutions    time    distance   degrees        arcsec
0.1             1                 3040000    1237.616    445541889
```

Values in arcsec are in arcsec per century. Values in degrees are in degrees per year.

#### 9.7 TEST 7: VIRTUAL PLANET

The purpose of this test is to show the behaviour of the pulsar when a virtual planet is included.

Now perform the program: MERCURY.EXE
From the Test Selection Display
Select test 7
From the Parameter Selection Display
Set 5 c speed of light = 0
Set 16 virtual planet condition = 3
From the Test Selection Display
Select S (Start)
After Start enter the mass multiplication factor as indicated

``` mass mull  revolutions    time          distance              arcsec
1          1        26791.24       3040000                 3.63
2        53582.46       3040000                 1.23
3        80373.7        3040000                 0.96

mass mull  revolutions    time          distance              arcsec
10          1        26791.24       3040000                17.787
2        53582.46       3040000                16.526
mass mull  revolutions    time          distance              arcsec
100          1        26791.24       3040000               164.86
2        53582.46       3040000               164.09
```

#### 10 OPERATION

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

#### 10.1 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 300000

6 = Delta time in seconds between each calculation cycle.
Standard value is 100

7 = Initial distance between two objects in km.

8 = Eccentricity of Mercury. Standard value = 0.206
9 = Speed of Sun. Standard value = 0

10 = Angle Phi of Sun in degrees. Standard value = 0

11 = Initial angle of planet in degrees. Standard value = 0

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

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

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

15 = Sub Test. Sub test are used to select a specific command file
0 = no sub test
1 = phi goes from 0 to 360. c = 300000 . VPC = 0
2 = phi goes from 0 to 360. c = 30000  . VPC = 0
5 = Full revolution test with c = 6000000  , delta t = 400
6 = Full revolution test with c = 12000000 , delta t = 100
7 = Full revolution test with c = 300000   , delta t = 400
8 = Full revolution test with c = 300000   , delta t = 100

16 = Virtual Planets Condition (VPC)
0 = no special condition with Mercury simulation
1 = Mercury simulation with virtual planet for Venus
2 = Mercury simulation with virtual planet for Venus and Earth
3 = Mercury simulation with virtual planet for all planets

17 = Oblateness of Sun.  Standard value = 0

18 = Initial condition. Standard value = 1
0 = no initial condition calculation
1 = initial condition calculation type 1

19 = # of calculation cycles saved. Standard value = 0
0 = No calculation values saved.

20 = increase in delta mass per second

```