The simulation is done assuming that all the planets move in one plane. The program PLANET3D takes into account that the plane of Mercury is tilted.
The results of the tests 2, 3 and 4 (discussed in the paragraphs 3, 4 and 5) show that the planet Mercury is influenced by all the planets. The problem is that this influence is highly "irregular" and takes many years to settle down.
The concept behind the virtual planet is to replace all the planets by one planet in such a way that the influence of this virtual planet is the same as all the planets.
The virtual planet is a planet which moves at the same distance as Venus The position of the virtual planet is such that the Sun, Mercury and this virtual planet are always in one line. That means Mercury is always in-between the Sun and the Virtual Planet. The mass of this planet is a function of the distance of Mercury and the Sun.
The purpose of this simulation is to study the movement of the planet Mercury when Venus is replaced by a virtual planet.
After one revolution of Mercury select ESC.
The display shows after one revolution that Mercury has a forward angle of 289.223 arc sec in one century.
Return to CHAPTER5.TXT
The purpose of this simulation is to study the movement of the planet Mercury when both Venus and Earth are replaced by a virtual planet.
After one revolution of Mercury select ESC.
The display shows after one revolution that Mercury has a forward angle of 383.201 arc sec in one century.
Return to CHAPTER5.TXT
After one revolution of Mercury select ESC.
The display shows after one revolution that Mercury has a forward angle of 549.540 arc sec in one century.
Return to CHAPTER5.TXT
After two revolutions of Mercury select ESC.
The following are the results of this test:
Phi counts distance density angle 0 75582 69674040 .205561 -383 151166 69674040 .205561 -38390 75573 69672316 .205606 549 151142 69666016 .205604 549 180 75583 69683192 .205697 1483 151168 69683192 .205697 1483
270 75592 69684918 .205652 550 151192 69691220 .205652 550
The same results are also displayed as a figure
Figure 1 shows:
The string of white dots represents the angle in arc sec in one century
for phi between 0 and 360 in increments of 15 degrees
For phi between 55 and 305 the angle is positive i.e. a forward movement.
The two strings of red dots represent the difference in distance after
one and two revolutions of Mercury for phi between 0 and 360 in increments
of 15 degrees.
For phi between 0 and 180 the distance becomes smaller.
Maximum is at phi is 90.
For phi between 180 and 360 the distance becomes larger.
Maximum is at phi is 270.
Return to CHAPTER5.TXT
The purpose of this simulation is to study the movement of the planet MERCURY when:
After two revolutions of Mercury select ESC.
The following are the results of this test:
Phi counts distance density angle 0 75583 69678501 .205627 526 151167 69678501 .205627 52690 75583 69678458 .205628 549.5 151166 69678301 .205628 549.5 180 75583 69678730 .205631 572.8 151167 69678730 .205631 572.8
270 75583 69678773 .205630 549.5 151168 69678931 .205630 549.5
The results are also displayed as a figure
Figure 2 shows:
The string of white dots represents the angle in arc sec in one century for phi between 0 and 360 in increments of 15 degrees For all values of phi the angle is positive i.e. forward movement.
The two strings of red dots represent the difference in distance after one and two revolutions of Mercury for phi between 0 and 360 in increments of 15 degrees.
Return to CHAPTER5.TXT
Following are the results for forward movement of Mercury for delta time is 50 seconds:
Special Planets angle eccentricity condition arc seconds 0 -.248 .205630 1 Venus 209.041 .205629 2 Venus Earth 384.014 .205629 3 All 550.333 .205629
The purpose of this simulation to see if and how the planet Venus influences the movement of the planet Mercury.
The center of the display shows the position of the Sun (one dot)
After each revolution the angle in arc seconds of the forward movement are displayed.
The result is the following:
The purpose of this simulation to see if and how the planet Venus influences the movement of the planet Mercury but only when Mercury is at aphelion i.e. furthest distance from the Sun
The following picture shows the position of Venus the Sun (S) and Mercury(M).
21 (-.934) 16 (-.766) 26 (-.801) 11 (-.245) 3 (-.897)6 (.8091) 8 (-.585)
1 (2.257) 13 (.1413)
24 (1.655) 18 (1.477)
19 (2.440) 23 (2.4711)
14 (1.212) SUN M 0 28 (1.38)
9 (0.004) 5 (2.036)
4 (-.524) 10 (.5891)
27 (-.357) 15 (-.299)
22 (-.632) 20 (-.616)
17 (-.678) 25 (-.677) 12 (-.6722) 2 (-.666) 7 (-.676)
Figure 2
Figure 2 shows that there are two areas (one around position 0 and one around
position 1) that the forward angle is positive.
In two other areas (one around position 3 and one around position 17) the
forward angle is slightly negative.
The area around position 0 shows the position of Venus when Venus and Mercury are close together (at the same time).
The area around position 1 shows the position of Venus when Venus and Mercury were close together at the beginning of the revolution of Mercury.
In the other areas Mercury and Venus are during one revolution of Mercury never close together.
In position 1, 5, 6, 9, 10, 13 and 14 the forward angle is positive.
In position 2, 3 and 4 the forward angle is negative.
The results are also displayed in two figures:
This display has the same layout as figure 2.
May be what you see goes to quick ? Repeat the same test but change the wait time to 1 second.
The display more or less looks like:
y x x . x y y y . x y y y y y . x y y y y y y y y x . x . y x . x . x . x . x . x . x . x . x . x . x . . t=100 yearsFigure 1
Horizontal represents the time Vertical represents the angle a of Mercury
The position were the two lines meant indicate one century.
The value for the forward movement of Mercury influenced by Venus in arc seconds in one century is:
This means if you want to do an accurate simulation delta time has to be at least 100 seconds or less.
Return to CHAPTER5.TXT
The purpose of this simulation to see how the planet Earth influences the movement of the planet Mercury.
The center of the display shows the position of the Sun (one dot)
Around the Sun are shown
After each revolution the angle in arc seconds of the forward movement are displayed.
The result is the following:
The result of the simulation can the best studied from figure 5 and 25.
The value for the forward movement of Mercury influenced by Venus and the Earth in arc seconds in one century is:
Return to CHAPTER5.TXT
The purpose of this simulation to see if and how the planet Venus and the Earth influences the movement of the planet Mercury.
The result of the simulation can the best studied from figure 6 and 26.
The value for the forward movement of Mercury influenced by Venus and the Earth in arc seconds in one century is:
This result shows that the forward movement of Mercury influenced by Venus and the Earth is equal to the sum of Mercury influenced by Venus (par 3) and Mercury influenced by the Earth (par 4) i.e. 290 + 93 = 383
Return to CHAPTER5.TXT
The purpose of this simulation to see if and how the planets Venus, Earth, Mars, Jupiter and Saturn influences the movement of the planet Mercury.
The influence of the three outer planets is very small. See also the program SUNRAD test 5.
The result of the simulation can the best studied from figure 7 and 27.
The value for the forward movement of Mercury influenced by Venus, Earth Mars, Jupiter and Saturn in arc seconds in one century is:
Accordingly to (See Literature 7 page 198) this value should be 531 arc seconds in one century.
Return to CHAPTER5.TXT
In this section in 2 tests the movement of Mercury is simulated.
In both tests the influence of the planets Earth, Mars, Jupiter and Saturn is simulated by making Venus 1.9 times as heavy.
In test 1 the initial distance is 69680000 km and c = 300000 km/sec
This is the same conditions as figure 5 of the program Mercury.
In test 2 the initial distance is 90000000 km and c = 12000000 km/sec.
This is the same conditions as figure 13 of the program Mercury.
The following table shows the results
Program PLANETS (Sun & 2 planets) Program MERCURY (virtual planet) rev distance angle1 angle2 time distance angle1 angle2 0 69678618 2000 69465718 1.94 1465 478 69470796 1.94 1466 4000 68831603 3.87 1465 952 68836844 3.87 1465.6 6000 67797640 5.76 1463 1417 67801365 5.76 1464.1 8000 66393539 7.58 1459 1871.1 66395780 7.60 1462.6 50000 19301578 28.95 1532 6804.6 18956047 29.21 1554
rev = revolutions of Mercury. distance in km angle 1 is in degrees. angle 2 in arc sec in one century. time in years
Time of 1 revolution
The above results show that the influence of the planets Earth, Mars, Jupiter and Saturn initially can be simulated by making Venus 1.9 times as heavy, but becomes less accurate for shorter distances from the Sun.
In test 2 the influence of the planets Earth, Mars, Jupiter and Saturn is simulated by making Venus 1.9 times as heavy (i.e. identical as test 1) but now compared with the same conditions as figure 13 of the program Mercury. In figure 13 the initial distance is 90000000 km and c = 12000000 km/sec.
The following table compares the results
Program PLANETS (Sun & 2 planets) Program MERCURY (virtual planet) rev distance angle1 angle2 time distance angle1 angle2 0 90024773 90024921 1000 90008991 1.75 1795.9 478 90022658 1.28 1315.7 2000 90000990 3.50 1793.5 952 90015830 2.57 1315.7 3000 89981839 5.22 1782 1417 90004445 3.85 1315.3 4000 89963340 6.99 1791 1646 89988514 5.13 1314.9
The above results show that the concept to simulate the influence of the planets Earth, Mars, Jupiter and Saturn, by making Venus 1.9 times as heavy, is not accurate and that a more complex model is required (assuming that the virtual planet concept is correct, which is the subject of the next test)
Return to CHAPTER5.TXT
In this section in 2 tests the movement of Mercury is simulated.
In both tests the influence of the planets Venus, Earth, Mars, Jupiter and Saturn is simulated.
In test 1 the initial distance is 69680000 km and c = 300000 km/sec
This is the same conditions as figure 5 of the program Mercury.
In test 2 the initial distance is 90000000 km and c = 12000000 km/sec.
This is the same conditions as figure 13 of the program Mercury.
The following table shows the results
Program PLANETS (Sun & 6 planets) Program MERCURY (virtual planet) rev distance angle1 angle2 time distance angle1 angle2 0 69678618 2000 69465840 1.944 1464.1 478.2 69470796 1.94 1466 4000 68832036 3.87 1465 952.2 68836844 3.87 1465.6 6000 67796662 5.76 1463 1417.8 67801365 5.76 1464.1 8000 66391178 7.60 1462.7 1871.1 66395780 7.60 1462.6 50000 19007090 29.20 1552 6772.3 18956047 29.21 1554
rev = revolutions of Mercury. distance in km
angle 1 is in degrees. angle 2 in arc sec in one century. time in years
Time of 1 revolution
The results of both tests are almost identical!
In test 2 the influence of the planets Venus, Earth, Mars, Jupiter and Saturn is simulated but now compared with the same conditions as figure 13 of the program Mercury. In figure 13 the initial distance is 90000000 km and c = 12000000 km/sec.
The following table compares the results
Program PLANETS (Sun and 6 planets) Program MERCURY (virtual planet) rev distance angle1 angle2 time distance angle1 angle2 0 90024773 90024921 200 90016834 .24 1237 70.3 90024833 .26 1315 400 90016553 .53 1369 140.7 90024564 .51 1315 600 90021916 .78 1327 211 90024111 .77 1315 800 90014065 1.02 1315 281.4 90023476 1.03 1315 1000 90013902 1.32 1352 351.7 90022658 1.28 1315 1200 90018306 1.55 1328 422.1 90021657 1.54 1315 1400 90011024 1.82 1334 492.4 90020474 1.79 1315 1600 90012626 2.11 1349 562.8 90019109 2.05 1315 1800 90012179 2.32 1324 633.1 90017561 2.31 1315 2000 90007531 2.63 1347 703.5 90015830 2.57 1315 2200 90006682 2.84 1325 773.8 90013917 2.82 1315 2400 90003159 3.14 1341 844.1 90011812 3.08 1315 2600 90002539 3.38 1330 914.5 90009545 3.34 1315 2800 89997421 3.68 1346 984.8 90007086 3.59 1315 3000 89993097 3.89 1330 1055.1 90004445 3.85 1315
rev = revolutions of Mercury. distance in km angle 1 is in degrees. angle 2 in arc sec in one century. time in years
The results are almost identical meaning that the virtual planet concept is a very good (and practical) substitute for 5 planets Venus, Earth, Mars, Jupiter and Saturn.
The big improvement is speed of the simulation.
One revolution of Mercury with program (delta time = 400):
PLANETS with Venus * 1.9 takes about 10 seconds. PLANETS with 5 planets takes about 50 seconds. MERCURY with virtual planet takes about 4 seconds.
Return to CHAPTER5.TXT
This simulation is to demonstrate the movement of Mercury when:
The Sun moves around in our Galaxy in one big circle.
The following figure shows the position of the Sun (S) and the planet Mercury (M) at four positions:
a: phi = 90 B: phi = 180 (Sun moves away from M) c: phi = 270 D: phi = 0 (Sun moves towards M)^ <--S M . B (phi = 180). . . . . . . . . . . . . . . . ^ ^ ^ S M G--> v S M C (phi = 270) A (phi = 90) V . . . . . . . . . . . . . . . ^ S--> M D (phi = 0) Figure 3
G = Center of Galaxy Mass = 110000000000 * Mass of Sun S = Sun Distance S - G is 25000 light years. M = MERCURY v = speed of the Galaxy.
For this configuration the speed of S is 249.091 km/sec.
The following are the results of this test:
phi count distance density angle 0 75734 69678608 .204106 -11105 151470 69678590 .204106 -1110590 75519 69598990 .205341 581.4 150914 69519468 .205313 580.5 180 75432 69678613 .207151 12489 150865 69678598 .207151 12489 270 75646 69758344 .205917 585.9 151422 69838176 .205945 586.6
Return to CHAPTER5.TXT
This simulation is to demonstrate the movement of Mercury when:
The following are the results of this test:
phi count distance density angle 0 75874 69678592 .202705 -21568 151750 69678529 .202705 -2156790 75659 69599599 .20394 -10151 151194 69520675 .20391 -10159 180 75571 69678616 .20575 1502 151143 69678616 .20575 1502 270 75785 69757720 .20451 -10131 151699 69836918 .20454 -10123
Return to CHAPTER5.TXT
This simulation is to demonstrate the movement of Mercury when:
The following are the results of this test:
phi count distance density angle 0 75590 69678616 .205556 -16.226 151181 69678615 .205556 -16.21390 75585 69676624 .205587 278.45 151168 69674633 .205586 278.406 180 75582 69678616 .205632 573.322 151166 69678616 .205632 573.316 270 75588 69680607 .205601 278.545 151180 69682599 .205602 278.566
Return to CHAPTER5.TXT
This simulation is to demonstrate the movement of Mercury when:
Return to CHAPTER5.TXT
In order to simulate the different conditions the parameter selection display is used
From the Parameter Selection Display the following parameters can be changed:
0 = Select test display1 = 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 gravity propagation. Standard value is 300000 km/sec
6 = Delta time in seconds between each calculation cycle. Standard value is 100
7 = Eccentricity of Mercury. Standard value = 0.20563
8 = Speed of Sun. Standard value = 0
9 = Angle Phi of Sun in degrees. Standard value = 0
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 for phi from 0 to 360. c = 300000. v = 0,10 and 20 4 = Test with Mercury and Venus 5 = Test with Mercury, Venus and Earth. 6 = Test with Mercury and all the planets except Pluto. 7 = Test for phi from 0 to 360. c = 12000000. v = 19.7 10: phi = 180, v = 200 11: phi = 170, v = 200 12: phi = 190, v = 200 13: phi = 180, v = 200 14: phi = 0 , v = 200 15: phi = 180, v = 50 16: phi = 180, v = 400 17: phi = 180, v = 19.7
14 = Virtual Planets Condition 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
15 = # of calculation cycles saved. Standard value = 0 0 = No calculation values saved.