## The Earth's precession & spin as it relates to Joshua’s long day around 1400 BC and the sun and it's shadow going backwards 10 marks around 701 BC.

I believe the Earth precessed around 180 degrees in 12 hours resulting in the long day of Joshua. I believe this caused the Sun and moon to appear to stand still for about a day to observers in Canaan. I also believe the Earth precessed around 180 degrees in 5.5 hours in 701 BC which caused the sun and it's shadow to actually go backwards in the sky around 120 degrees. Imagine my surprise and thankfulness when I read Immanuel Velikovsky author of "Worlds In Collision" figured this out many years before I did. Thankfulness because I felt this was confirmation of the conclusions I felt God had led me to. At presentthis article does not elaborate on what probably caused the force that caused the Earth to precess rapidly resulting in Joshua's long day and century's later the sun and thus the shadow of the sun dial to go backwards.

If you want to see a detailed yet simplified explaination of the forces that cause the present precession of the Earth I suggest you read C Johnson's "Precession of Gyroscopes and of the Earth." The major players are the sun and the moon. C Johnson, a Theoretical Physicist, calculates what sums up be to a total average torque on the equatorial bulge of the Earth bythe moon and the Sun of 4.54 e22 kg-m squared/s.I had been doing my math wrong but then discovered the Earth's present precession rate (7.7 e-12 radians/s) times the Earth's spin rate (7.3 e-5 radians/s) times the figures Johnson uses or calculated as the moment of inertia or I of the entire Earth (8.07 e37 kg-m squared/s) = 4.53 e 22 kg-m squared/s.According to this formula 4.53 e 22 kg-m squared/s is the force that would be necessary to cause the present precession of the Earth.This is almost exactly what C Johnson calculated is the average combined precessional force of the Sun and moon on the Earth.

This article explains the torque or force that is believed to be necessary to cause the present precession of the Earth. It also calculates the torques or forces that would probably have to have been present to cause Joshua’s long day and later the sun-dial to turn backwards 10 marks. Copyrighted 4/15/2015 and 5/02/2023 by Wayne Mckellips. Updated 5/02/2023. Eventually, I hope to be able to explain how God caused the precessions that made the sun and moon stand still as observed from Canaan for about a day around 1400 BC and later the Sun to go backwards in the sky around 120 degrees around 701 BC.

The formula for a solid sphere's moment of inertia is r squared times mass times 2 divided by 5. Let’s do it for the Earth. 6.371 e 6 meters squared equals 4.05 e 13 meters squared. That times 5.97 e 24 kg equals 2.42 e 38. That times 2 equals 4.84 e 38. That divided by 5 equals 9.68 e 37 km-meter squared. However, the earth is not a solid sphere. So it's I or moment of inertia is actually around 8.0 e37 kg-meter squared.

There are 2pi radians in 360 degrees. That is, if you take the radius of a circle and multiply it by 2 times pi the product will be the exact length of the circumference of the circle.

The radius of the Earth is around 6,378,000 meters. However, there is more material around the Earth’s equator than there is around the Earth’s poles. This extra material around the Earth’s equator’s I (moment of inertia) is around 3.3 e 35 kg-meter squared or perhaps as low as 2.6 e35 kg-m squared. (I got that by taking the previous A amount from the C amount.) It is thought the precession of the Earth results from a torque or force that acts on the extra material around the Earth's equator. If the sun is exactly level with the Earth's equatorial bulge, the sun cannot grab ahold of the Earth's equatorial bulge. However, the more North or South the Sun is relative to the Earth's equatorial bulge the more the sun can grab unto both the closest and furtherest parts of Earth's equatorial bulge. The center of the Earth is the pivotal point.

The Earth take 86,164 seconds to spin or rotate once around its axis. That’s how many seconds there are in a sidereal day. 86,164 seconds divided by 2 pi = 13,713. 1 divided by 13,713= 7.292 e -5 radians per second. That means, as the Earth spins it moves through 7.3 e -5 of an Earth radian per second. To check the math we'll take 7.29 e -5 radians times 86,164 seconds. That gives us the 6.28 radians the Earth spins through in one sidereal day.

The Earth is tilted around 23.5 degrees. The tilt of the Earth precesses or revolves through a complete circle in around 25,800 years. Since there are 365.25 days in a Earth year, I used 86,164 seconds per sidereal day times 365.25 days times 25,800 years to get around 811,962,145,800 seconds in 25,800 years. That many seconds divided by 2pi= 129,227,489,050. 1 divided by that quotient = 7.738 e -12 radians per second. That means, as the Earth precesses it moves through that much of a radian per second.

The torque or force needed to cause the Earth’s rotational axis to precess through a complete circle in around 25,800 years is “(the moment of inertia of the entire Earth as the whole Earth has to be moved),” times (the number of radians the Earth moves through per second as it spins), times (the number of radians the Earth moves through per second as it precesses). Let's try it. (8.0 e37 kg-meter squared) times (7.3 e -5 r/s) times (7.7 e -12 r/s) = 4.5 e 22 kg-m squared/s.

If the Earth precessed 180 degrees in 12 hours, we should be able to figure its precession rate. Let's do that. 86,164 seconds divided by 2 tells us there are 43,082 seconds in half a sidereal day. 43,082 seconds divided by pi of 3.14159 = 13,713. Now 1 divided by 13,713 = 7.29 e -5 radians/s. Let's check the math. 7.29 e -5 r/s times half a day in seconds or 43,082 = 3.14 radians. So the torque or force needed to cause that precession rate would have been (7.3 e -5 r/s {the precesson rate} times 7.3 e -5 r/s {the spin rate} times 8.0 e 37 kg-m squared According to this formula,4.26 e 29 kg-m squared/s would have been the torque or force required to make the Earth complete a 180 degree spin axis precession in 12 hours.

If the Earth precessed 180 degrees in 5 and ½ hours, we should be able to figure its precession rate as 1.5865 e -4 r/s. That's 60 seconds times 60 minutes times 5.5 hours = 19,800 seconds. 19,800 divided by pi of 3.14159 equals 6,303. 1 divided by 6,303 equals 1.5865 e -4 r/s. Let's check the math. 1.5865 e -4 r/s times 19,800 = 3.14 radians. So the torque or force needed to cause that precession rate would have been (1.5865 e -4 r/s {the precession rate} times 7.3 e -5 r/s {the spin rate} times 8.0 e 37 kg-m squared. According to this formula,9.265 e 29 newton meters or kg-m squared/s would have been the torque or force required to make the Earth complete a 180 degrees spin axis precession in 5 and ½ hours.

The Earth’s mass is 5.972 e 24 kg. Its “sphere of influence” is around 9.24 e 8 meters. The radius of the Earth is 6.378 e 6 meters. The sun’s mass is 1.989 e 30 kg. The earth is an average of 1.5029 e 11 meters from the Sun's center. Venus’s mass is 4.869 e 24 kg. Mars’ mass is 6.4219 e 23 kg. The gravitational constant (G) = 6.67 e -11. The mass of Venus times the mass of the Earth times (G) = 1.939 e 39 kg. The mass of the Sun times the mass of the Earth times (G) = 7.9228 e 44 kg. On July 6 of 2010 the Earth was at its aphelion, furtherest point from the Sun at 152,097,701 km. On Jan 3rd of 2010 the Earth was at its perhelion, closest point to the sun at 147,098,074 km. The Earth's summer solstice was June 21 in 2010. Earth's winter solstice was Dec 21 in 2009. During the solstice is when the Sun is most NOrth or South of the 23.45 degree tilt of the Earth. That is also when the Sun has its greatest pull on the band of extra material around the Earth's equator. Note, the value of gravitational constant (G) is currently uncertain beyond the first three digits.

To determine the Sun's pull on the Earth one multiples the mass of the Sun in kg times the mass of the Earth in kg times the gravitational constant (G) and then devides that figure by the distance the center of the Sun is from the center of the Earth in meters squared. So the formula is Force = [(M1) (m2) (G)] / [(distance in meters) squared]. (M1) (m2) (G) is 7.9228 e 44 kg. On June 21 of 2010 the seperating distance was approximately 151,713,114,308 meters. On Dec 21 of 2009 the seperating distance was approximately 147,133,190,214 meters. To determine the precessional torque of the sun on the Earth on those days one needs to square the distance then devide it into (M1) (m2) (G) then multiply that answer by the sine of 23.45 degrees which is the angle of the equatorial belt of extra material around the Earth relative to the gravational pull of the Sun on the Earth on those days. The sine of 23.45 is .3979. Then we then need to multiply that answer by 2 since the Sun is pulling on both the parts of the Equatorial belt closest to it as well as the parts of the belt furthest from it which results in the Sun's precessional pull on the Earth. This tells us on June 21 of 2010 during the summer solstice the precessional torque on the Earth was approximately 2.74 e 22 kg - m squared/s. On Dec 21 of 2009 during the winter solstice the Sun's pull on the Equatorial belt resulting in a precessional pull on the Earth was approximately 2.91 e 22 kg -m squared/s. Adding those two forces together and deviding by two we get a maximum precessional torque from the sun of 2.826 e 22 kg -m squared/s in 2010. I believe C. Johnson the theoretical physicist who wrote the excellent article on the precession of gyroscopes and the Earth got 2.87 e 22 nt m, in his example. So we got pretty close to the same answer using different methods. Note, the distance the sun is from the Earth at perihelion, and aphelion, and Autumnal or Vernal equinox, and Summer or winter solstice vary from year to year.

The reason this is important is because now we know we can also use the method I just used to calculate the maximum precessional torque Venus could have on the Earth when it was the Earth's Sphere of Influence distance (SoI) approximately 9.24 e 8 meters from the Earth. When the Sun and moon just stood still for about a day as viewed from Canaan I believe Venus was slightly further than the Earth's SoI as the Earth apparently did not move further away from the Sun. In 701 BC I believe Venus was within the Earth's SoI resulting in the Earth's system as a result of that encounter with Venus moving further away from the Sun. I believe that is when the Earth went from a 360 day Earth year to a 365 1/4 day Earth year. Mars also moved out to where it is today. Venus moved in closer to the Sun to where it is today. So in 1400 BC there was no exhange of angular momentum between Venus and the Earth system but in 701 BC there was an exchange in angular momentum between Venus and the Earth system. When Noah's flood occurred around 9,600 BC. I believe there was an exchange of angular momentum between Venus and the Earth system resulting in the Earth's year going from 290 days to 360 days.

To compute the maximum possible torque of Venus on the Earth if it was near the Earth's SoI distance from Earth we could use the following formula. {[(Mass Earth) (Mass Venus) (G)] divided by [(distance in meters) squared]} times 2. Remember the sine of an angle cannot be greater than 1. Sothe maximum possible torque force of Venus on the Earth, at the Earth's SoI distance of 9.24 e 8 m is 4.54 e 21 kg - m squared/s.AS we previously calculatedthe torque needed to cause the rapid precession of the Earth in 1400 BC and 701 BC was X to a power of 29 nt meters/s so obviously there must have been another force involved which caused the rapid precession of the Earth those two times.I hope to cover that force at a later date in time.

Biblical text for Joshua's long day. Joshua 10:12-14. Biblical text for the shadow of the sundial going backwards. Isaiah 38:7-9. 2nd Kings 20:11. 2nd Chronicles 32:31.

Copyright 2/20/2023 by Wayne Mckellips.

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