Contents
MODIFYING THE SPREADSHEET
for
PLANETS
There is another way to look at how gravity works. First, copy the spreadsheet you have for gravity so that you do not spoil what you already have. Choose a planet other than Earth and find it's radius, its mass as compared to Earth's, and its supposed gravity. Now do the following to the copy of the spreadsheet for gravity.
Cell A1: Alter the title to read "PLANETS".
--- Cell B4: Enter the radius of the planet in feet.
Cell D1: Enter the mass ratio of the planet. Note: Leave E3 as it is with earth's gravity in it.
Cell D4: Enter "(B3/B4)^2". This is earth's radius divided by the other planet's radius, the quantity squared.
--- Cell E4: Enter " = (R/R)^2". This tells what is in cell D4.
Cell F4: Enter "(B3/B4)^(1/2)". This is the square root of the earth's radius divided by the other planet's radius.
--- Cell G4: Enter "sqrt (R/R)". This tells what is in cell F4.
Cell C3: Remove what is there and enter " = Earth R". This tells what is in cell B3.
--- Cell C4: Enter " = Planet R".
Cell B10: Change what is there to "B4". You are merely replacing the earth radius with the other planet's radius.
--- Cell B13: Add " x D4". You are multiplying what is already there by the value in D4.
Cell B18: Add "x F4". You are multiplying what is already there by F4.
--- Cell A16: Enter "KG/M = V:". This tells what will be in cell B16.
Cell B16: Enter "B7 x B13/B21".
--- Cell B21: Add "x ((B3/B4)^(3/2))". Here you are multiplying what is already there by the increase in nether Mass due to the change in radius.
--- Change cells C10, C11, C13, C17, C18, C21, D9, D12, D14, D15, D16, and D19 so that all "e" for earth subscripts are changed to "p" for planet.
Some values may have so many numbers that they exceed the cell spaces of the spreadsheet, in which case you might divide these values by powers of ten.
To check your work, use the approximate figures for one of the planets listed below and see if you arrive at the correct results. The mass ratio means the planet's mass as compared to Earth's. The radius is in miles and must be converted to feet by multiplying by 5,280. The gravity and nether V are the figures you will find from the spreadsheet if you did your work correctly. They are very approximate as compared to precise figures that may be published for gravity. Gravity is given in feet per second per second. The nether V means the incoming nether velocity in feet per second at the planet's surface if the velocity could be expressed as such (remember that acceleration is the actual effect).
- Planet -
(or moon) / Mass Ratio / Radius / Gravity / Nether V
Mars - - - - - - .11 - - 2,100 - - 12.555 - - 16,686Jupiter - - - 318 - - - 44,400 - - 81.195 - - 195,114
Moon - - - - - .0123 - - 1,081 - - 5.298 - - - 7,776
CROSSCHECKS FOUND
in the
SPREADSHEETThe two rows or lines called 17 and 18 crosscheck each other for the values of V found in them.
Line 17 uses the formula G[(2R/G)^(1/2)] = V throughout. This technique makes use of the formula at four different locations.
Line 18 confirms line 17 by using a different method to obtain the same results. At B18, we find the square root of (Re/Rp) times the velocity for nether at earth's surface times the square root of the mass ratio. This equation should be broken into two parts to be understood; (1) the square root of the mass ratio times Ve, corrects Ve to what it would be at the surface of the subject planet if the radius of the planet were the same as the radius of Earth; and (2) Multiplying by the square root of (Re/Rp) adjusts the velocity to the radius of the subject planet and gives us Vp, the "velocity" of the nether at the surface of the planet.
At D18, Vp is adjusted by one over the square root of Ra/Rp in which Ra is the radius of a sphere above the planetary surface. This gives us the value for Va. At F18 and H18 the same thing is accomplished. If all is done correctly, B17=B18, D17=D18, F17=F18, and H17=H18. This means than the values for the "Velocities" found in line 17 are equal to those found in line 18. This way, method one crosschecks method two and vice-versa.
A third crosscheck is used for Vp at cell B16 where KG/M=Vp when K is MV/G.
The crosscheck found between lines 17 and 18 is especially significant because it establishes the validity of the formula to find Vp for any planet, sun, or moon.
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