Isaac Newton's three laws of force and motion.
These laws work for bodies moving much slower than the speed of light. For similar actions operating near the speed of light Einstein's special theory of relativity takes over. This is a very valuable concept and explains many peculiarities which affect atomic particles. However, at Solar System speeds the time discrepancy is not as great. Earth's velocity with respect to the Sun 3.0304 x 10^4 meters per second plus-or-minus .5 meters per second for the Earth's surface; the speed of light is 3 x 10^8 meters per second. This evaluates to a factor of 1 x 10^-4 slower than light. Figuring in the velocity of the Sun through the galaxy, the speed of the galaxy through the universe, the rotational spin of the Earth, and a body moving on Earth; I believe it is possible that relative to somewhere in the universe, a body could be moving faster than the speed of light. But I'm no Einstein and I am only an observer on this planet.
The point of Einstein's formula is its evaluation as the relativistic velocity approaches the speed of light. Because, we can not divide by zero we have a problem. As v approaches c the effect of the formula on time, mass and energy is to approach infinite. Einstein's theory does apply to the Electric Effect of the solar system because Electric Effects can move at the speed of light.
Planets move very slowly with respect to each other and the speed of light. Gravity is a slow force. Newton developed a gravitational law and it can be stated as: Every particle of matter in the universe attracts every other particle with a force which is directly proportional to the product of the masses of the particles and inversely proportional to the square of the distance between them.
Newton gave proof to the situation of a homogeneous sphere's gravitational force is the same as the entire mass were concentrated in a point at its center. The mass and weight relationships were defined and G = 6.670 x 10^-11 newton meters squared per kilogram squared.
Typical forces of gravity:
The Sun and Earth is 3.5111 x 10^22 Newtons
The Moon and Earth is 1.8326 x 10^20 Newtons
So, if there is an attraction between the two bodies, then why do they stay apart
It is best to describe the term velocity now.
Generally, special relationships are made in three dimensional space. The change in relationship of one body to another through time is velocity. Thus, the change of relationship of bodies in space is:
Where V is the total velocity and Vx, Vy and Vz are the dimensional velocities in three dimensional space.
Where L is the total angular momentum and Lx, Ly, and Lz are the dimensional momentums.
In a plane one of the velocity values is zero, thus, it drops out. It can be shown that the angular acceleration is equal to the square of the velocity divided by the radius:
Acceleration of the moon is 0.002739 meters per second squared toward Earth. Now, Newton second law can be applied to find the force required for this acceleration. F = m A This term is call centripetal force. This is the same force one gets when they tie an object to a cord and whips the body around in circles. The force holds the object at the end of the cord. This force refers to an effect which results in a change in the direction of the velocity of a body rather than a change in the magnitude of the velocity.
The centripetal force on the Sun is 3.5434 x 10^22 Newtons and on the Moon is 1.7904 x 10^20 Newtons.
These values are very close to the ones determined by the use of gravitational forces of two bodies when one considers the masses and human errors which are involved. Because of the discrepancy between the forces of gravity and the way the Earth and Moon really work, it took years to establish a reasonable theory of planetary motion. Along came Johann Kepler, who decided to abandon the idea that a circle was the only perfect curve which the planets must follow. Kepler came up with three of his own laws which satisfied observations.
Newton applied these laws to his theory and showed that the masses were actually involved and obtained an expression.
Although the theory of relativity created slight modifications in these laws, together with Newtons universal gravitation laws, forms the basic structure the entire celestial mechanics.
Graphing the planets and moons on a log-log graph using ratio of cube of the mean distance between the bodies to square of the sidereal period shows a line with a slope of 3/2 on which all the planets and moons resides. A major revelation. Later a graph of all satellites shows them to be in a straight line too.
Because Newtons laws were based on bodies for the exertion of gravity they did not explain why gravity acted on an electromagnetic wave. Thus, Einstein came up with his theory of gravitation. Einstein assumed gravity is a physical effect produced by the curvature of a four dimensional space-time continuum. Einstein's field equations require that the gravitational field has a finite velocity of propagation which is the same for all electromechanical waves.
Thus, the gravitational field has independent dynamic degrees of freedom which permit waves to exist in two modes. This then requires energy. An estimate of the energy radiated by the Earth-Sun gravitational system per year amounts to 10^16 ergs or about a million kilowatts. This represents about 10^-15 of the Earth mechanical energy from the time the Earth was created.
Except for the concept of a energy cost for gravity, Einstein's gravitational theory follows the Newtonian gravitational laws.
There seems to be only one discrepancy. That is when satellites are orbited they return shortly and crash quickly into the Earth's atmosphere when compared to the time a celestial body stays in orbit.
The discrepancy can be explained by two factors:
Personally, I believe both account for the discrepancies.
Given a finite value of the force of gravity, there is the limits of gravity's effect. One can calculate this limit and it is Escape Velocity which is the velocity required by an object to escape the gravitational force of another object.
This is derived by finding the necessary velocity to stabilize an orbiting satellite. Ignoring things like friction from the atmosphere, non-uniformity of the Earth's mass, the effect of drag and a few other things one can calculate the necessary horizontal velocity to maintain an orbit. Baring complications this formula generally works like this:
If the satellites horizontal velocity is less than Vh the satellite crashes. If the satellite's velocity is in excess of Vh and less than Vh * ( 2 )^0.5 then the satellite maintains an elliptical orbit. If the satellite's velocity exceeds Vh * ( 2 )^0.5 then the satellite leaves the Earth's gravitational force and goes into free space.
It would seem that a satellite can be inserted into orbit relatively accurately because there is a square root of two factor between escape and a stabilized orbit.
Thus, it can be concluded that if a satellite does not maintain orbit there must be some drag or other component force slowing down the vehicle. There is one easy way of solving this problem, and, that is to add a small force opposite the drag. Thus, maintaining the orbital velocity. However, the addition of force does not help astrosatellites as the Earth's Moon or the Sun's Earth. These are also subject to drag or other component forces slowing down the body. So, how do celestial bodies stay orbiting?
Its been said that deep space has little to stop the motion of the Planets and Moons. However, experiments with orbiting satellites prove otherwise. The solar wind's affect on a Comet's tail is tremendous. Any material which can move a Comet's tail the way the tail gets moved is not to be neglected. Personally, I believe it is foolish naivety to neglect this force. Adding the collision force to the path of a body is one thing, but, adding an electric break to the body is another. The energy required to sustain the plasma sheet tear in the solar wind is more than enough to break an astrobody.
Thus, from this there is only one conclusion. That is the solar system's bodies are powered. There must be a force opposite the retarding forces just like the force added to man's satellites to keep them in orbit. At this point one can ask, if the system is powered how much power is the system getting.
About all that can be said about the energy to supply the force at this time is that it is small compared to the net kinetic energy of planets and moons. Kepler's, Einstein's and Galilo's astronomical observations prove the theory of a falling body astronomically matches a falling body at the Earth' surface, so it seems mass and mass attraction are primary forces moving the solar system. All other forces are probably secondary forces or at best minor forces. However, these forces are applied to these bodies over tremendous times lengths.
Einstein connected gravitation (mass attraction), mass and energy to waves.
Energy decreases at the rate proportional to:
Thus, the total energy reaching the Earth is the area of reception times the net energy output divided by four pi times the distance squared. Using the mean distance from the Sun the total radiant energy available at the surface of the Earth is 1386 joules per square meter per second. This value is 1.99 calories per square centimeter per minute which corresponds to measured values that range between 1.94 and 1.99 calories per square centimeter per minute. Assuming the Earth is far enough from the Sun to call it a point source we can find the total energy by the Earth's area as a circle 1.27 x 10^14 square meters times the energy per square meter or 1.77 x 10^17 joules per second, or 1.52 x 10^22 joules per day.
The total linear kinetic energy of the Earth is given by one half mass times the square of velocity, or 6.669 x 10^31 joules.
To put this in another form; if the world started from standstill, all the energy received was converted to forward motion, and the system could possibly work; there would be enough energy to accelerate the Earth to its present velocity in 12 million years. This is a sizable amount of energy. Even at .2 percent efficiency the Sun's energy can be responsible for the Earth's orbit in the amount of time the Earth is believed to have existed. The one thing that can be said is that there is more than enough energy to be possible.
What would be the effect on an astrobody if the energy per square meter were changing as a function of distance? The answer to this question is the proof of my theory. There should be two effects occurring; the transitional velocity changing and the rotational velocity changing.
The change in energy also is affected by the source of the energy. It has been shown that the Sun's output does change drastically during periods of activity. If the Sun's output changes then it is reasonable to say the energy reaching the Earth will also change. This is the case. It has been shown that Sun spots affect the Earth's spin. This affect is very minor. One such example of data that the Sun affect the Earth's spin occurred and was measured in August 1972. Following a rather great solar storm the length of the day did change.
By taking the maximum distance from the Sun and subtracting the minimum distance from the Sun the Earth has a variance in distance of 4.98 x 10^9 meters one can equate a total energy difference which is incident on the circumference of the Earth. Or, 1.4 x 10^25 joules per year. The maximum daily change is about 9 x 10^18 joules per day.
Unfortunately kinetic energy for a rotational body is not as easy to calculate as it is for transitional energy. For the Earth, it is complicated by various masses at different radii from the axis and it is a fluid mass.
The Earth has four mass inertias; the atmosphere, crust, mantle, and the core. Atmosphere being very small, the best estimates or a density of 3-6 grams per cubic centimeter for mantle-crust material and 10-17 grams per cubic centimeter for the core. For these calculations of energy 3.5 grams per cubic centimeter for the mantle, and 14 for the core will be used. The average is 5.515 grams per cubic centimeter.
Inertia for a sphere is given by:
Inertia for the core is given directly by this expression, and inertia for the mantle is found by subtracting the cores portion of inertia from the mantle's total inertia for the mantle's density, and the two are added together for the Earth's total inertia.
Core inertia is 1.06579 x 10^37 kgm m^2, Mantle inertia is 5.9247 x 10^37 kgm m^2. Total inertia is 6.9904 x 10^37 kgm m^2. Average density inertia is 9.75725 x 10^37 kgm m^2.
The kinetic energy which is stored in the rotation of the Earth is:
The Earth rotates at 1 revolution in 86164.091 seconds. The daily radian rate is 7.2912 x 10^-5 radians per second. The kinetic energy stored in rotation is 1.8586 x 10^29 joules for the inertia given by the separate inertial components. It so happens that the Earth has a time difference in rotation. The Earth is about 60 milliseconds different in time of rotation between June and October. The maximum seasonal variation is about 0.44 milliseconds in one day. To find out the necessary difference in energy to account for the change in time is to simply solve the kinetic energy problem for one time period and then again for a period milliseconds longer or shorter, and subtract the two. The result is the energy required to change the inertia of the Earth for a given change in the daily period.
The net energy required for inertia change for various time changes are:
| Seconds | Milliseconds | Energy in Joules |
| 0.00001 | 0.01 | 6.9 x 10^19 |
| 0.00005 | 0.05 | 2.7 x 10^20 |
| 0.0001 | 0.1 | 4.1 x 10^20 |
| 0.0002 | 0.2 | 8.3 x 10^20 |
| 0.0003 | 0.3 | 1.2 x 10^21 |
| 0.0004 | 0.4 | 1.6 x 10^21 |
| 0.0005 | 0.5 | 2.0 x 10^21 |
| 0.001 | 1.0 | 4.3 x 10^21 |
| 0.005 | 5.0 | 2.2 x 10^22 |
| 0.060 | 60.0 | 2.5 x 10^23 |
For a 60 millisecond rotational difference requires 2.5 x 10^23 joules. This energy is necessary no mater where it comes from. Some scientist have suggested it is the seasonal winds. Because the atmosphere is not as dense as the Earth itself is and three quarters of the atmospheres mass is between 3000 meters and the surface this is not practical. Basically, the atmosphere would have to circle the Earth 39 times faster than the Earth rotates to change it by 10^20 joules in one day. This is about a 40,000 mile an hour wind. Another consideration was the change in angular velocity by a change in inertia by the affect of the gravity change from elliptic.
My calculations were very low. The author of one of the book I got the formula, calculated g/g = 1.5 x 10^-11 then stated / = 2.6 x 10^-9 per year which I didn't understand because it should have been 1.95 x 10^-11. Any way, the author stated that this would not account for the change in spin as the spin change was 6.96 x 10^-7 per year. I agreed with that. My factor was 10^-13 which is very low so the author had a best case scenario. Any how, the error in spin by a gravitation change at best will only account for less than a hundredth of the spin variation. Something other than gravity must cause it.
The time of the variance is important too. It has been shown that the rotational speed is maximum during the summer and minimum during the winter with the maximum acceleration during the spring and the maximum deceleration during the autumn. That is if you are living in the Northern hemisphere. The daily change in rotational period is not going to be explained by Newton's or Kepler's gravitational laws because the gravitational change variance should be the other way around.
To account for daily changes of a maximum period of .5 milliseconds in one day can not be accounted for by a change in radiation due to the change in distance. For a maximum daily change in distance would only account for 9 x 10^18 joules which is only a small portion of the necessary 2 x 10^21 joules. So, thermal heat energy from standard radiation can't account for the required energy.
It should be noted that there is more than enough kinetic energy to account for the change in rotational time. Ke=10^30 joules is the daily change. However, this change is at the expense of potential energy and would follow Newton's and Kepler's laws. Which should slow down the tangential velocity and this doesn't happen.
There is the theory, as the Earth gets closer to the Sun it heats up and expands. Thus, the Earth's rotation slows down. However, the difference in absorbed heat is so slight that it would not account for the necessary expansion, and also, we would be able to measure the Earth's expansion. Since, the Earth's expansion is far less than the amount required for the rotation energy required to change the velocity, it is a very unlikely theory.
Another scenario I read about was that mass was moved toward the poles. If this occurred it would for sure change the spin. However, it would also change the size of the poles but at the very least the density. A mass movement toward the poles significant enough to alter the spin would easily be detected by seismic readings. No such occurrence can be detected.
There is a difference in distance rates of change between the Earth and Sun for each day. As an elliptically orbiting body, the Earth's distance from the Sun is not the same each day. Thus, there is a rate of change in distance from the Sun. If an electric field were present, then the rate of change through the field, would yield a rate of change of some type of vectored force. Studies have shown that a 2 volt per kilometer electric field exist in the solar space about the Earth.
A typical computer run of the change in distance and the change in energy utilizing the electric square law relationship for a typical 365 day year may be found.
Applying the simple mathematical relationships for the change in distance of an elliptically orbiting body shows up a rate change proportional to the energy required to cause the change. When slippage caused by a weak frictional forces between the Earth's core and crust are taken into consideration, the variance in the Earth's rotation speeds seems to correspond to the rate of change of distance between the Earth and Sun.
Considering solar space has a 2 v/km electric field, the Earth's core material iron, even super heated has good electro magnetic properties, would support the theory that there is some sort of electromagnetic interaction between Earth and solar space. As the rate of change of distance between the Earth and Sun increases or decreases there is going to be a change in induced electro magnetic affects. These affects should be measurable. These affects should be cyclic.
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