﻿ Explication Excel sheets simulation gravity

# Explication Excel sheets

 Sheet 1 (reference) In this sheet the data from Solfue (2013) are rewritten in the form I will use in later sheets. Also, in this sheet l calculate my point of reference. Column A The disk of 50 kpc is being divided in 1000 rings, each with a width of 0,05 kpc Column C For each individual disk the absolute mass has been calcultated with a small programm in Matlab. These masses add op to the total mass of the disk (C1010) of 12,92 * 10^40 kg. Column D Mass density of the ring (mass per area) Column E Check: the density of a ring is divided by the density of the ring 2.4 kpc outward. Given Solfues data this value has to be 2. The data in column E are the date calculated by the Matlab program, and they are recalculated in excel column N Column G Values for perpendicular acceleration as calculated by the Matlab program. In this reference case this is the value of 2PI*G*density, as explained in the text.. This value is checked by excel in column Q. Column I The acceleration from column G causes the upper- and lower bound of the cilindrival volume to move inward, the 'dent'. In this column the absolute change in volume is calculated for each ring. Since this is the reference case, alle these volumes together make up for the total change in volume caused by the mass of the disk (I1010), in other words: since 'the dent' takes care of all the change in volume, there is no need for the rim to move inward. The values in column I are checked in Excel in column S. Sheet 2 (data) In this sheet the data are assembled for the perpendicular acceleration for points at different heights above/below the eq-plane, at several distances from the centre of the disk. Values have been calculated in Matlab. The paramaters chosen are: 5000 rings of 0,01 kpc width, each divided in 2000 segments. For each value calculated there were 10.000.000 points involved. However, things colud be done in a higher resolution if needed. Column A Radius is divided in rings of 0,5 kpc each. The value of radius = 0,05 kpc is added in row 5. In later sheets the data from this sheet will be interpolated tot rings of 0,05 kpc each. Column C Values for perpendicular accelartion of the reference case, taken from sheet 1. Column F Perpendicular accelaration at height 0,50 kpc above and below the eq-plan, as calculated in Matlab. Column G The percentage of 'missing volume'. If the perpendicular acceleration is less the in the reference case, the 'dent' is not as deep, and this results in less volume change compared to the reference case. Since the inward distance covered is a linear function of a, half the acceleration results in half the volume change. The data in this column will be the basis for interpolation in the next sheets. Column I and J Same as columns F and G, but for a height over/below of 0,4 kpc. Column L and M Same as columns F and G, but for a height over/below of 0,3 kpc. Column O and P Same as columns F and G, but for a height over/below of 0,25 kpc. Column R and S Same as columns F and G, but for a height over/below of 0,20 kpc. Column U and V Same as columns F and G, but for a height over/below of 0,125 kpc. From here on the resolution becomes a problem. Values move away from the tendencies on higher altitudes. This is probably due to my crude way of modelling. From here on the model becomes less realistic, since all mass of the disk has to be distributed over some heighth of the disk: the milkyway is not flat. Sheet 3 - 7 For the different altitudes of the data-sheet the resultant radial acceleration is being calculated, and as a consequence the resulting rotational velocity. Column A Radius, distance from the centre in rings of 0,05 kpc Column B Perpendicular acceleration in the reference-case, copied from sheet 1 Column C Volume change in the reference-case, copied from sheet 1 Column G Percentage missing volume, taken from sheet 2 Column H Interpolation from column G, to get back o the smaller rings Column J Absolute missing volume in m^3, product of column G and column E (corrected for percentage term) Column L Same as column J, but cumulative Column N area of the rim. This is calculated from the radius and the height above/below the eq-plane. Note that when this height is 0.nnn kpc, the height of the rim is 2 x 0.nnn kpc. Column P Distance travelled = missing volume (column L) divided by the erea of the rim (column N) Column R Distance travelled in 1 second = 1/2 a t^2. Therefore the value of a (acceleration) = 2 x the value of column P Column T and U Acceleration caused by the bulge - independently of the accelaration caused by the disk. Column U rewrites column T, to adapt for the order of magnitude, so the two accelerations can easyly be added Column Y Sum of accelerations from columns R and U Column AB From classical Newtonian dynamics: a = (v^2)/r. Since a (column Y) and r (column A) are known, v can be calculated Sheet 8: graphics Some results of the precious sheets are represented as rotation curves