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Three - GRAVITY SIMULATION

  Everything is energy in motion.
Pir Vilayat Inayat Khan  

This approach is based upon the assumption that gravity is caused by the acceleration of the nether. Since velocity is "relative" in the sense that it does not act as a force, it is acceleration that we feel, and gravity is already known to be felt as if it were acceleration.

If one accelerates in space, or if one travels in a vehicle that rotates so as to form artificial gravity, there is a force very like gravity that one feels. On the other hand, if one travels in a vehicle that is not rotating and is not accelerating, one has the feeling of falling, and there is no noticeable feeling of gravity. Furthermore, the vehicle "coasts" along without any force to cause it to change its velocity relative to the universe around it.

When we are in a gravity funnel, we are subjected to nether that is accelerating at all points within it. If we fall, we have the same feeling that an astronaut has in space, and we call it "free-fall". This is when we are allowing the acceleration of the nether to carry us along with it.

The spreadsheet presentation which follows is a simulation for gravity. Using it allows you to see gravity in action - at least in a mathematical sense. With this spreadsheet, you can alter each unkown one at a time until you discover for yourself that the only way to make them all fit together correctly is via the use of the equations and concepts presented in this book. Eventually, you will feel comfortable with the actions of nether.

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If you are not familiar with spreadsheets, you may wish to skip part of this chapter and any subsequent parts of the book that mention work with spreadsheets. The simulation is designed for someone who is interested in truly understanding gravity. For this understanding, the exercise of creating the spreadsheet is there for you to use. Mental work is required, but the rewards are worth the effort for those who wish to know. Remember that you may always come back to this part at a later date.

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Because some spreadsheets have a limited number of symbols available, for the most part, capital letters will be used as major symbols and small letters will act as subscripts.

--- Cell A1:     "Gravity"     Title of the spreadsheet.

Cell B1:     " - (1/2)"     Be sure to use the minus sign.

--- Cell C1:    " = V exp"     This tells what is in cell B1. It is the exponent to be used to alter the inward velocity of the nether to see what happens as the radius increases. Where V is a velocity found in sphere above the earth's surface, V= Ve * [F^(-.5)]. This means that V = Ve * (1/sqrt F).

Cell D1:    "1"     This is the mass ratio mr for an earth location. It may be altered when you wish find effects of different masses as have other celestial bodies.

--- Cell E1:     " = mr"    This tells what is in cell D1.

Cell F1:     "7"     This is the factor, F, for multiplying altitude. The use of 2 for F will make sphere "s" twice the value of Re. The use of 3 for F will make sphere "s" three times the value of Re, and so on. Seven is being used now merely to provide a reference for checking the spreadsheet.

--- Cell G1:     " = F"     This tells what is in cell F1.

Cell H1:     "3.141592654"     This is our limited value of pi.

--- Cell I1:     " = pi"     This tells what is in cell H1.

Cell B2:     " - (3/2)"     Be sure to use a minus sign.

--- Cell C2:     " = M exp"     This tells what is in cell B2. It is the exponent that will be used to alter Mass or nether density to see what happens as the radius increases. If Mass is M, then M = Me * [F^(-3/2)] or M = Me / [F^(3/2)].

Cell D2:     "1/2"     This is one-half and .5 may be substituted.

--- Cell E2:     " = mr exp V"     This tells what is in cell D2. It is the exponent to be used to alter the velocity when the mass ratio is changed. Velocity increases as the square root of the mass increase.

Cell F2:     "1/2"     This is one-half and .5 may be substituted.

--- Cell G2:     " = mr exp M"     This tells what is in cell F2. It is the exponent to be used to alter the Mass or nether density to see what happens when the mass ratio is changed. Mass of the nether changes as the square root of the mass increase. If mr is 5, for instance,
M = Me * sqrt 5.

Cell B3:     "3950.19 * 5280"     This will show as 20,857,003. It is the radius of the earth at the poles in feet.

--- Cell C3:     " = Planet R"     This tells what is in cell B3.

Cell E3:     "32.25777559"     This is earth's gravity at the poles in feet /second /second.

--- Cell F3:     " = Planet G"     This tells what is in cell E3.

Cell A5:     "SPHERES:"     Classification for a line of spheres.

--- Cell B5:     "PLANETARY SURFACE (e)"     Head of a column.

Cell D5:     "ABOVE SURFACE (a)"     Head of a column.

--- Cell F5:     "MULTIPLE ABOVE (s)"     Head of a column.

Cell H5:     "OVER MULTIPLE (h)"     Head of a column.

--- Cell A7:     "MV/G=K:"     What will be in a line to the right.

Cell A8:     " MVA/10^15:"     The 10^15 is 10 to the 15th power.

--- Cell D9:     " = (Ve dif / Ge ave) / (Vs dif / Gs ave)"

Cell A10:     "Sph. Radii:"     What will be in line 10.

--- Cell B10:     "B3"     This is the radius of the earth again.

Cell C10:     " = Re"     This tells what is in cell B10.

--- Cell E10:     " = Ra"     This tells what will be in cell D10.

Cell G10:     " = Rs"     This tells what will be in cell F10.

--- Cell I10:     " = Rh"     This tells what will be in cell H10.

Cell A11:     "Sph. Areas:"     What will be in line 11.

--- Cell B11:     "4 * H1 * (B10^2)/1000000000000"     This is 4piRe²/10 to the 12th.

Cell C11:     " = Ae/10^12"     This tells what is in cell B11.

--- Cell E11:     " = Aa/10^12"     This tells what will be in cell D11.

Cell G11:     " = As/10^12"     This tells what will be in cell F11.

--- Cell I11:     " = Ah/10^12"     This tells what will be in cell H11.

Cell C12:     "100"     The number of feet between spheres e and a.

--- Cell D12:     " = He"     This is what is in cell C12.

Cell G12:     "100"     The number of feet between spheres s and h.

--- Cell H12:     " = Hs"     This is what is in cell G12.

Cell D10:     "B10 + C12"     This is Re plus He to arrive at Ra.

--- Cell F10:     "B10 * F1"     This is Re multiplied by F for an altitude well above the planetary surface.

Cell H10:     "F10 + G12"    This is Rs plus Hs to arrive at Rh.

--- Cell A13:     "Known G:"     What will be in line 13.

Cell B13:     "D1 * E3"     This is mr times Ge.

--- Cell C13:     " = Ge"     This is what is in cell B13.

Cell E13:     " = Ga"     This is what will be in cell D13.

--- Cell G13:     " = Gs"     This is what will be in cell F13.

Cell I13:     " = Gh"     This is what will be in cell H13.

--- Cell A14:     "Average G:"     What will be on line 14.

Cell D14:     " = Ge ave"     This is what will be in cell C14.

--- Cell H14:     " = Gs ave"     This is what will be in cell G14.

Cell A15:     "(V-V), Vdif:"     What will be on line 15.

--- Cell D15:     " = Ve dif"     What will be in cell C15.

Cell H15:     " = Vs dif"     What will be in cell G15.

--- Cell D16:     " = Ve dif / Ge ave"     What will be in cell C16.

Cell H16:     " = Vs dif / Gs ave"     What will be in cell G16.

--- Cell A17:     "Formula V:"     What will be on line 17. This means that each V will be determined by T, from equation 5, times G.

Cell C17:     " = Ve"     What will be in cell B17.

--- Cell E17:     " = Va"     What will be in cell D17.

Cell G17:     " = Vs"     What will be in cell F17.

--- Cell I17:     " = Vh"     What will be in cell H17.

Cell A18: "Exponent V:" - What will be on line 18. This means that each V other than Ve will be determined by the V exponent formula.

--- Cell C18:     " = Ve"     What will be in cell B18.

Cell E18:     " = Va"     What will be in cell D18.

--- Cell G18:     " = Vs"     What will be in cell F18.

Cell I18:     " = Vh"     What will be in cell H18.

--- Cell A19:    "Average V:"     What will be on line 19.

Cell D19:     " = Ve ave"     What will be in cell C19.

--- Cell H19:     " = Vs ave"     What will be in cell G19.

Cell A20:     "Ve mls/sec:"     What will be in cell B20.

--- Cell A21:     "Masses:"     What will be on line 21.

Cell B21:     "1 * (D1^F2)"     The number one is nether Mass at sea level which is our standard. Nether Mass or density varies from place to place, so we must arbitrarily choose a standard. D1 is the mass ratio, that which is the mass of another body divided by the mass of earth. It is to the power found in cell F2 which is .5. D1 and F2 are needed here to show how a change in mass ratio influences nether Mass.

--- Cell C21:     " = Me"     This is what is in cell B21.

Cell D21:    "B21 * ((D10/B10)^B2)"

--- Cell E21:     " = Ma"     This is what will be in cell D21.

Cell F21:     "B21 * ((F10/B10)^B2)"

--- Cell G21:     " = Ms"     This is what will be in cell F21.

Cell H21:     "B21 * ((H10/B10)^B2)"

--- Cell I21:     " = Mh"     This is what will be in cell H21.

Cell D11:     "4 * H1 * (D10^2)/1000000000000"     This the area of sphere (a).

--- Cell F11:     "4 * H1 * (F10^2)/1000000000000"     This is the area of sphere (s).

Cell H11:    "4 * H1 * (H10^2)/1000000000000"     This is the area of sphere (h).

--- Cell D13:     "B13 * ((B10/D10)^2)"     This gravity at sphere (a), based upon the inverse square law.

Cell F13:     "B13 * ((B10/F10)^2)"     This is gravity at sphere (s).

--- Cell H13:    "B13 * ((B10/H10)^2)"     This is gravity at sphere (h).

Cell C14:    "((1/((D10/B10)+1)) * B13) + ((1 - (1/((D10/B10)+1))) * D13)"     This is the average gravity between the lower two spheres.

--- Cell G14:    "((1/((H10/F10)+1)) * F13) + ((1 - (1/((H10/F10)+1))) * H13)"     This is the average gravity between the upper to spheres.

Cell B17:     "((2 * B10/B13)^(1/2)) * B13"     This is the square root of the quantity 2Re /Ge, which comes from Re/(Ge /2), times Ge. This square root is the time it takes to fall the distance Re when accelerated by a constant Ge. Time multiplied by acceleration is velocity. mr and its V exponent are a factor for masses other than earth's.

--- Cell D17:     "((2 * D10/D13)^(1/2)) * D13"     This is Va, the velocity of the nether when it passes through sphere (a).

Cell F17:     "((2 * F10/F13)^(1/2)) * F13"     This is the velocity of the nether as it passes through sphere (s).

--- Cell H17:     "((2 * H10/H13)^(1/2)) * H13"     This is the velocity of the nether as it passes through sphere (h).

Cell B18:     "36682.43527 * (D1^D2)"     This line depends upon the formula for Ve. Whereas formula V's will be altered automatically by the formula, line 18 V's must use a base of formula Ve * sqrt(mr).

--- Cell D18:     "B18 * ((D10/B10)^B1)"     Va is computed by multiplying it by its increase in radius times the V exponent. The resulting figure should be equal to D17.

Cell F18:     "B18 * ((F10/B10)^B1)"     Vs=Ve(Rs/Re)^Vexp

--- Cell H18:     "B18 * ((H10/B10)^B1)"     Same method as D18 and F18.

Cell C19:     "(B18+D18)/2"     Average V for spheres (e) and (a).

--- Cell G19:     "(F18+H18)/2"     Average V for spheres (s) and (h).

Cell B20:     "B17/5280"     Changed feet/sec to miles/sec.

--- Cell C15:     "(B17-D17) * (C19/C12)"     This is (Ve-Va)(Vave/H).

Cell G15:     "(F17-H17) * (G19/G12)"     This is (Vs-Vh)(Vave/H).

--- Cell C16:     "C15/C14"     This is a ratio that should be very close to one. It will not be exact because there must always be too large a difference between the spheres due to the limitations of the spreadsheet (number integers it can use and show).

Cell G16:     "G15/G14"     Essentially like Cell C16.

--- Cell C9:     "C16/G16"     This ratio should be very close to one.

Cell B7:     "B21 * B17/B13"     This is the K value which uses M at sea level on earth as a standard. This value will change if a different standard is used, but will remain essentially the same for any celestial body at any point on its surface and at any altitude above its surface. It is slightly less than 256pi times the square root of two, and might well be exactly that value if the additional length due to the spiral effect of the nether flow were taken into account.

--- Cell D7:     "D21 * D17/D13"     Should be same value as cell B7.

Cell F7:     "F21 * F17/F13"     Should be same value as cell B7.

--- Cell H7:     "H21 * H17/H13"     Should be same value as cell B7.

The following are divided by 1000 when they are labeled as being divided by 10 to the 15th power. The inputs to them have already been divided by 10 to the 12th power and that is why the apparent discrepancy occurs.

Cell B8:     "B21 * B17 * B11/1000"     This is the figure for total momentum or total mass per second passing through a particular sphere. It must be the same for all spheres used for a particular body.

--- Cell D8:     "D21 * D17 * D11/1000"     Should be the same value as cell B8.

Cell F8:     "F21 * F17 * F11/1000"     Should be the same value as cell B8.

--- Cell H8:     "H21 * H17 * H11/1000"     Should be the same value as cell B8.

Note that total momentum for each level is the same. In other words the amount of Mass passing through each sphere during each second is the same amount of Mass passing through any other sphere during each second. This is MVA, Mass times velocity times area of sphere.

Set up in equations for total momentum, W,

Me Ve Ae = Wet

Ma Va Aa = Wat

Ms Vs As = Wst

Mh Vh Ah = Wht

and Wet = Wat = Wst = Wht

The foregoing equalities must be correct for all values of F and for all values of mr for any particular body. However, when the mass ratio is changed, the values for momentum also change even though the equalities remain.

To find the velocity of the nether for any spherical body at any point at or above its surface, first find the gravity at that point from its mass ratio and the inverse square law. Second, find the mass using the formula:
M = [mr^(1/2)] [(Ra/Rs)^(-3/2)] In this formula, Ra is the higher of the two radii used. Then V=K/GM.

One easier way to find a nether velocity is to use the formula:
V= [(2R/G)^2] G

The radius of the earth is shortest at the poles and is 13 miles greater at the equator. Gravity is less at points away from the northern latitudes. Gravity is easily discovered with extreme accuracy using a pendulum. The dimensions of the earth are not so easily found and may be subject to some error.

If we set K equal to precisely 256 pi times the square root of two and then change Re to accommodate the new K value, the new Re turns out to be 3,951.667 miles, not far off of the value normally used, 3,950.19. This seems too nearly perfect to be a coincidence and the geometric properties do not explain it. However, our ancient system of weights and measures, including the frequencies of the musical scale, were designated by someone, and they are often very strong clues as to what some of the ancient people knew.

If we assume that this is not simply a code given to us by the ancient people, then there is a natural law at work. In fact, a natural law may be the answer even if this is a code.

Two things make a substantial difference in the calculation of the nether flow constant. One is the value for gravity and the other is the radius (which has a unique curvature). Given a particular body size, a larger surface gravity indicates that the body has a larger mass. Given a particular value for gravity, a larger body size indicates that the body has a larger mass. The point is that the planetary radius adjusts the distance from the center of mass and it adjusts the curvatures of the imaginary spheres.

Remember that we could use a value other than Re to calculate the nether flow constant, but then G and V would be different. The nether flow constant would be the same, but the G we would measure would be found at a place other than the surface of the earth, and this is not very convenient. If we are to use the G found at the surface of a planet, then the radius for the planet's surface is the most convenient one we can use. Using another R, such as one a mile above the surface, would give us a different value for K. We could use such a thing, but the consequent equations would be unnecessarily complicated. So the best value we can use for the radius is that for the planetary surface. For earth, that value is Re.

Going a bit farther in manipulating the equations to see what we have found:

(1/2) Ve² = Re Ge

This is an energy equation and should have an M term with it.

(1/2) MVe² = Re Ge

If we let M = 1,

Ve² = 2 Re Ge

Ve = sqrt (2 Re Ge)

This is the easiest equation to use to find a velocity and works on all levels for any spherical body:

Primary Velocity Equation:

V = sqrt (2 R G)

K may be considered the same as T when T is the time in which an object falls a distance of R while being accelerated by the G located at distance R from a center of mass. The following shows how to find K easily.

V = KG

Squaring both sides:

V ² = (KG) ²

From primary velocity equation:

V ² = 2RG

Equivalencies:

(KG) ² = 2RG

Dividing both sides by G ²:

K ² = 2R/G

Taking the square root of both sides:

K = sqrt (2R /G)

Primary K Equation: K = sqrt (2R /G)

So now we know that
V = sqrt (2 R G) and K = sqrt (2R /G). These equations are considerably more convenient for our use in finding the velocity at any planetary surface or the planet's K. For a any body, mr is accounted for by G, so we have:

V = sqrt (2RG) and K = sqrt (2R/G)

 

A moment's insight is sometimes worth a life's experience.
Oliver Wendell Holmes
 

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