The purpose of this simulation is to show how two objects move around each other. This movement is studied under different conditions.
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.
For Mercury the basic movement is an ellipse.
The purpose of this test is to demonstrate the movement of Mercury around the Sun for v = 0
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 -1.07Return to CHAPTER5.TXT
The purpose of this test is to study the behaviour of Mercury when the shape of the Sun is not round.
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
Return to CHAPTER5.TXT
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 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 -471490 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.
Return to CHAPTER5.TXT
The purpose of this test is to study the behaviour of the movement of the Earth when :
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 -4725The following are the results for delta t of 100 seconds and v = 19.7 km/sec using the modified initial conditions.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
angle revolutions counts distance eccentricity arcsec 0 1 75582 69674040 .205561 -933 2 151166 69674040 .205561 -93390 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.
Return to CHAPTER5.TXT
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.
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
Return to CHAPTER5.TXT
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.
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
Return to CHAPTER5.TXT
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.
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
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
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.
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.
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.
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
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.
Return to CHAPTER5.TXT
The movement of the Earth around the Sun is a circle i.e. eccentricity is 0.
The movement of the planets is also studied.
The purpose of this test is to demonstrate the movement of the Earth around the Sun for v = 0
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 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
For the planet Venus c = 300000 km/sec (v=35) the values are the following:
107999999 108000000 108000001 108000002
For the planet Mars c = 300000 km/sec (v=24) the values are the following:
227999999 228000000 228000000 228000000
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)
For the planet Saturn c = 300000 km/sec (v=9) the values are the following:
1429999999 1430000329 1430000659 1400000988
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"
The previous results can be mathematical described accordingly to the following rules.
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.
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+) * (r²-r0²)
This leaves the major problem: Is the "instability" of jupiter acceptable and accordingly to observations.
Return to CHAPTER4.TXT
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
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
The following are the results of this test:
delta t = 400 sec delta t = 100 secangle 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 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.
Return to CHAPTER4.TXT
The purpose of this test is to study the behaviour of the movement of the Earth when:
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 14955012990 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 14960004590 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.
Return to CHAPTER4.TXT
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 22472422690 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 22464945390 1 102284 224562084 2 204676 224724228
180 1 102386 224636869 2 204881 224798999
270 1 102284 224562107 2 204676 224724249
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.
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
The result of the test is that the revolution time is 189 million years. v of Sun is 249 km/sec
Return to CHAPTER4.TXT
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.
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.
Return to PROVE.TXT
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
The purpose of this test is to show the behaviour of the pulsar with no extra parameters set.
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.
Return to CHAPTER6.TXT
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.
angle revolutions time distance arcsec 0 3039989 0 1 26791.36 3040038 -939 2 53583.34 3040087 -941 3 80375.90 3040136 -942angle 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
Return to CHAPTER6.TXT
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.
v revolutions time distance arcsec 0 3040001 100 1 26791.54 3040049 86.38 2 53583.7 3040098 88.92v 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
Return to CHAPTER6.TXT
The purpose of this test is to observe the behaviour of the pulsar for different values of c i.e. speed of gravity propagation.
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 948.91c 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.
Return to CHAPTER6.TXT
The purpose of this test is to show the behaviour of the pulsar when the mass of the pulsar m1 is modified.
After S = 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 35.75mass 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 3039999mass m0 m1 revolutions time distance arcsec 1D+22 -1 1 7 3039999
Return to CHAPTER6.TXT
The purpose of this test is to show the behaviour of the pulsar for different values of oblateness
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.
Return to CHAPTER6.TXT
The purpose of this test is to show the behaviour of the pulsar when a virtual planet is included.
mass mull revolutions time distance arcsec 1 1 26791.24 3040000 3.63 2 53582.46 3040000 1.23 3 80373.7 3040000 0.96mass 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
Return to CHAPTER6.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 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