It will be shown that the Equation of time derivation of the equation of time ignore the barycentric motions of the Earth-Moon system and the Sun-Jupiter system, thereby demonstrating that the relative motions of the sun and earth are accounted for without the need to use the Newtonian barycenters. In this way, the real success of the equation of time demonstrates the S-J and E-M barycentres do not exist in the real and therefore invalidate the heliocentric model of the solar system.
The following analysis firstly investigates the effect of the relative velocity of the earth to the sun when the earth-moon barycenter motion is included. We then include the motions of the sun caused by the sun-Jupiter barycenter motion to show the variation in earth-sun relative velocities over the 12 year Jupiter orbital period and include in the analysis the combined velocity effects of the S-J and E-M motions at ¼ month intervals at t = 0, 3, 6, 9 and 12 years in the Jupiter period.
This investigation demonstrates that by ignoring the S-J and E-M barycenter motions, the equation of time should change from its standard values by -66s to +66s at times during the 12 year Jupiter period. It also shows the equation of time should vary over the 12 year Jupiter orbit, yet the standard equation of time excludes the Jupiter motion and in practice is assumed to be the same for any year. This is further strong evidence for the non existence of the S-J barycenter and hence an invalidation of the heliocentric system.
Velocity of the Earth center of mass relative to E-M barycenter
Barycenter of the Earth-moon system
D = M(moon)d(moon)/(M(earth) +M(moon) = 0.012 x 384405/(1.00 + 0.012) = 4641 kilometers from center of the earth
If the earth orbits the earth – moon barycenter every 27.3 days with respect to the fixed stars and for the sake of simplicity assume the orbit is circular then the earth moves around the E-M barycenter t = 3600 x 24 x 27.3 = 2,358,720 s over a distance of 6.14 x 4641 = 28,495.74 km with an average velocity of 28495.74/2,358,720 = 0.012 km/s = 43.49 km/hr
For the sake of simplicity, let’s assume –
1. The sun is stationary relative to the orbiting earth.
2. The earths orbit velocity is 30 km/s
3. The earths orbit radius to the sun is 1 AU
4. Assume the rotation speed of the earth around its axis is constant.
If we track the motion of the center of mass of the earth, we have the following configurations, with velocities –
T=0
S – E b M
Earth vcm = ↓0.0121 km/s
Earth vorbit = ↑30km/s
Resultant earth’s c of m velocity relative to the sun ↑ 29.988 km/s
T=1/4 month
…..M
…...b
S - E
Earth vcm = → 0.0121 km/s
Earth vorbit = ↑30km/s
Resultant earth’s c of m velocity relative to the sun ↑ 30.00 km/s
T = ½ month
S - M b E
Earth vcm = ↑ 0.0121 km/s
Earth vorbit = ↑30km/s
Resultant earth’s c of m velocity relative to the sun ↑ 30.012 km/s
T = ¾ month
S – E
……b
……M
Earth vcm = ← 0.0121 km/s
Earth vorbit = ↑30km/s
Resultant earth’s c of m velocity relative to the sun ↑ 30.00 km/s
T = 1 month
S – E b M
Earth vcm = ↓0.0121 km/s
Earth vorbit = ↑30km/s
Resultant earth’s c of m velocity relative to the sun ↑ 29.988 km/s
Therefore over one month, the center of mass orbital velocity of the earth relative to the stationary sun varies according to the following –
Time…………. Earth c of m velocity relative to stationary sun
(month)………(km/s)
0………………29.988
¼……………..30.00
½……………..30.012
¾……………..30.00
1………………29.988
For the sake of simplicity, we can reduce the E-M velocities down to the velocity of the center of the earth’s mass as shown in the table above. When this is done we can calculate the distance travelled according to rotation around the E-M barycenter with respect to the Earth’s constant daily rotation around the axis. Let a day equal = 24 x 3600 = 86,400s.
Earth radius = 6,384 km, v = 6.14 x 6,384/86,400 = 0.454km/s rotation velocity at the Earth-Sun plane (assumed to be along the line of the earths equator- which has no tilt in this example).
Time………….…Earth c of m v rel to sun…..Difference…………Time difference
(month)………..(km/s)……………………...over 24 hrs(km).…………..(s)
0………………29.988…………………………-1,036.8…………...+34.57
¼……………..30.00…………………………..0…………………..…0
½……………..30.012…………………………1,036.8……............-34.55
¾……………..30.00…………………………..0…………………..…0
1………………29.988…………………………-1,036.8………..…..+34.57
The column entitled “Difference” is the derived as follows –
Let the earth’s center of mass velocity be the average velocity of the earth orbiting through space due to the E-M motion. vcom = 0.0121 km/s. The orbital velocity of the Earth around the sun is then the total of the orbital velocity around the sun of 30km +- the E-M barycenter velocity component. The difference is then distance obtained through the addition of the E-M barycenter velocity component over 24 hours.
Time difference is the difference in time between the earth motions without and with the E-M barycenter velocity component for a point on the earth’s earths equator to be facing the same point in space. From the above table we see a sinusoidal variation in the times required for the earth to return to the same point at the sun.
The velocity effect of the 12 year Jupiter orbital period.
We can also add in the 12 year Jupiter-Sun barycenter with the sun orbiting the barycenter at 0.011 km/s. In this way we can arrive at time differences for parts of the month, throughout Jupiter’s orbit period as follows –
At year 0, when the barycenter is between the sun and the earth, the sun moves to the left of the earth.
S <- v = 0.011 km/s
B
E -> v = 30km/s orbit
J ->
At this time in the Jupiter cycle an observer will see the sun move due to its barycentric motion by 0.011 x 60 x 60 x 24 = 950 km in 24 hours relative to the Earth. Therefore, if we assume the earths orbital velocity around the sun is 30km/s, the time difference for a point on the earth’s equator to reach the same point in space, as caused by the S-J motion is 950/30 = -31.66s
Time………….…Time difference……. Time difference……Total time difference
(month)………..E-M(s)…………….. S-J (s)……………..(s)
0………………+34.57………………..-31.66……..………..+2.90
¼……………..0……………………….-31.66………..……..-31.66
½……………..-34.55…………………-31.66…………….+2.90
¾……………..0……………………….-31.66………..…….-31.66
1………………+34.57………………..-31.66………..…….+2.90
At year 3, when the barycenter is between Jupiter and the sun, the sun will seem to not move at all relative to the earth.
↓S _ B _ J ↑...........sun v = 0.011 km/s towards the earth
E -> v = 30km/s orbit
Time………….…Time difference……. Time difference……Total time difference
(month)………..E-M(s)…………….. S-J (s)……………..(s)
0………………+34.57………………..0……………..………+34.57
¼……………..0……………………….0………………..…….0
½……………..-34.55…………………0……………..………-34.55
¾……………..0……………………….0………………..…….0
1………………+34.57………………..0……………..……….+34.57
At year 6, when the barycenter is between Jupiter and the sun, the sun will seem to move to the left from the earth.
J <-
B
S ->…………. sun v = 0.011 km/s
E -> v = 30km/s orbit
Time………….…Time difference……. Time difference……Total time difference
(month)………..E-M(s)…………….. S-J (s)……………..(s)
0………………+34.57………………..+31.66……..………..+66.23
¼……………..0……………………….+31.66……..………..+31.66
½……………..-34.55…………………+31.66……..………..-2.89
¾……………..0……………………….+31.66……..………..+31.66
1………………+34.57………………..+31.66……..………..+66.23
At year 9, when the barycenter is between Jupiter and the sun, the sun will move away from the earth and appear to be stationary to the earth bound observer.
↓ J _ B _ S ↑........... sun v = 0.011 km/s away from the earth
________ E→ v = 30km/s orbit
Time………….…Time difference……. Time difference……Total time difference
(month)………..E-M(s)…………….. S-J (s)……………..(s)
0………………+34.57………………..0…………..……………+34.57
¼……………..0……………………….0…………..……………0
½……………..-34.55…………………0…………..…………...-34.55
¾……………..0……………………….0…………..….………...0
1………………+34.57………………..0…………..….………...+34.57
At year 12, when the barycenter is between the sun and the earth, the sun moves to the left from the earth.
S <- v = +0.011 km/s
B
E -> v = 30km/s orbit
J ->
At year 12, we have the same problem discussed at year 0.
Time………….…Time difference……. Time difference……Total time difference
(month)………..E-M(s)…………….. S-J (s)……………..(s)
0………………+34.57………………..-31.66…..…………..+2.90
¼……………..0……………………….-31.66…..…………..-31.66
½……………..-34.55…………………-31.66…..…………..-66.21
¾……………..0……………………….-31.66…..…………..-31.66
1………………+34.57………………..-31.66…..…………..+2.90
From the above tables, it is evident that when incorporating the S-J and E-M motions into the relative velocities of the sun and the earth, the time required for the earth to return to a fixed point in space varies according to the time in the Jupiter period and the E-M orbital period.
However, when calculating the Equation of Time, only the effects of the ellipse and the tilt of the earth are taken into account and the S-J and E-M effects are taken into account.
The mathematical expression of the equation of time can be written as
Δt=(M-v)+( λ- α)/wE
Δt = ts − t is the time difference between solar time ts (essentially time measured by a sundial) and mean solar time t (essentially time measured by a mechanical clock). The first term in parentheses is the time difference due to the eccentricity of the Earth's orbit, and the second term is the time difference due to the inclination of the Earth's rotational axis with respect to its orbital plane. This formulation ignores perturbations due to the moon and other planets, as well as the very small variations in the orbital and rotational parameters with time. http://en.wikipedia.org/wiki/Equation_of_time
Note that the Equation of time is used to determine standard time from the sundial time –
The equation of time expresses the relationship between the sundial and standard time, and the standard time is then available from the sundial by applying the proper value, plus or minus, from the equation of time. But such conversion yields true standard time only if the sundial is on the standard meridian. One must know one's distance east or west of the standard meridian in order to make the remaining correction to the sundial time.
The Earth turns through one time zone in an hour. The time zone is 15 degrees wide (one twenty-fourth of 360 degrees), so each degree of longitude within the time zone is equivalent to four minutes of time (60 min./15o). This then is the correction to make for each degree of longitude away from the standard meridian: minus if east or plus if west of the standard meridian
As an example, suppose that you are located at longitude 155 degrees west. What is the correction to arrive at standard time for your time zone? The standard meridian is the 150 degree west meridian, so you are located 5 degrees west of that. Every degree is 4 minutes of time, so the sun passes overhead at your longitude 4 x 5 = 20 minutes later than at the standard meridian. Thus, you must add 20 minutes from your sundial time to get the standard zone time. This, of course, is in addition to the time that must be added or subtracted according to the equation of time. See Appendix B for additional examples.http://www.cso.caltech.edu/outreach/log/NIGHT_DAY/equation.htm
So according to Wicki and Caltech, the equation of time is derived using only the effects of the elliptical orbit and the earth tilt to determine the time lag during the year between the apparent solar time and the mean solar time. Apparently the equation of time is well known and works quite well in practice. Yet the equation has been shown above to not include the Earth-Moon barycenter motion every month or the Sun-Jupiter barycentric motion over 12 years. The Wicki and Caltech sites assume the equation of time does not vary from one month to the next due to the E-M motion, or one year to the next over 12 years, due to the S-J motion.
Evidently the Equation of time, like other astronomical mathematical equations, assumes Newton’s and Keplar’s formulas and physics, yet those same equations, which assume the barycentric motion of the planets to be an accurate model of orbital mechanics, are routinely ignored when the observations of the sun’s location do not match the theory.
Ignoring the Earth-Moon and Sun-Jupiter barycenter motions in the equation of time is no small anomaly in the maths. This indicates that the barycentric motions, which produce time differences from that predicted by the equation of time of between -66s to +66s indicates the E-M and S-J motions simply do not exist in the real. This singular observation indicates the immediate solar system of the sun-earth-moon-Jupiter act in a way that is not compatible with Newtonian mechanics, but is very compatible with geocentrism. According to a geocentric model, the equation of time can be derived assuming an elliptical orbit of the sun, or a circular orbit with a variable sun orbit velocity over the year, without the need for the Earth-moon barycenter motion or the sun Jupiter barycentric motion.
Any way we look at the equation of time, it’s practical success indicates heliocentrism is an invalid model of the solar system. As it is invalid, then either Newtonian barycenter motion is invalidated and a geocentric solar system can be valid. As science points towards a geocentric universe form other experimental failures to find any Earth motion, through space, then it is no surprise to the geocentrist that the equation of time is derived by ignoring the relative velocity changes associated with the E-M and S-J barycenters, simply because –
1. The barycentric motions don’t exist in the real,
2. The universe is really geocentric,
3. Gravity is not caused by mass attraction, but by the aether flow
4. The real cause of planetary orbits is the celestial winds.
Conclusion - The standard derivation of the equation of time is further compelling evidence for a stationary earth in a geocentric universe.
JM
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