File:MOND vs Newtonian rotation.gif
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MOND_vs_Newtonian_rotation.gif (369 × 314 pixels, file size: 2.47 MB, MIME type: image/gif, looped, 101 frames, 10 s)
Captions
Captions
Toy model for rotation of a disk with exponential mass distribution: Newtonian gravity vs MOND
Summary[edit]
| Description |
English: MOND is a possible explanation for the observed v(r) curve for stars in a galaxy (which is incompatible with Newtonian gravity).
The observed behaviour is explained by assuming that Newton's second law (F=m a) is modified for very small values of a. |
| Date | |
| Source | https://twitter.com/j_bertolotti/status/1283363962780815361 |
| Author | Jacopo Bertolotti |
| Permission (Reusing this file) |
https://twitter.com/j_bertolotti/status/1030470604418428929 |
Mathematica 12.1 code[edit]
\[Rho]0 = 5 ; Rs = 10; a0 =.; G = 1; M[r_] := \[Rho]0 (1 - Cosh[r] + Sinh[r]);(*Exponential mass distribution*)
\[Omega]newton[pos_] := Sqrt[(G M[r])/Norm[pos]^3];
\[Omega]MOND[r_, a0_] := Evaluate[FullSimplify[Sqrt[Evaluate[ a /. Solve[(G M[r])/Norm[r]^2 == a/Sqrt[1 + a0^2/a^2], a][[4]] ]/ Norm[r]]] ]
rmax = 10;
\[Delta]r = 0.1;
a0 = 20;
p0 = Table[
Grid[{
{
Plot[\[Omega]newton[r]*r, {r, 0, rmax}, ImageSize -> Small, PlotRange -> {0, 4}, Axes -> False, Frame -> True, FrameTicks -> None, FrameLabel -> {{"v", ""}, {"r", "Newtonian gravity"}}, LabelStyle -> {Bold, LightGray}, PlotStyle -> {White}, Background -> Black]
,
Plot[\[Omega]MOND[r, a0]*r, {r, 0, rmax}, ImageSize -> Small, PlotRange -> {0, 4}, Axes -> False, Frame -> True, FrameTicks -> None, FrameLabel -> {{"v", ""}, {"r", "MOND"}}, LabelStyle -> {Bold, LightGray}, PlotStyle -> {White}, Background -> Black]
}, {
Graphics[{
Flatten@Table[{
Orange,
Disk[{0, 0}, r + \[Delta]r, {0 + \[Omega]newton[r] t, \[Pi] + \[Omega]newton[r] t}],
Black,
Disk[{0, 0}, r, {0 + \[Omega]newton[r] t, \[Pi] + \[Omega]newton[r] t}],
Purple,
Disk[{0, 0}, r + \[Delta]r, {\[Pi] + \[Omega]newton[r] t, 2 \[Pi] + \[Omega]newton[r] t}],
Black,
Disk[{0, 0}, r, {\[Pi] + \[Omega]newton[r] t, 2 \[Pi] + \[Omega]newton[r] t}]
}, {r, rmax - \[Delta]r, \[Delta]r/10, -\[Delta]r}]
}, PlotRange -> 1.1 {{-rmax, rmax}, {-rmax, rmax}},
Background -> Black]
,
Graphics[{
Flatten@Table[{
Orange,
Disk[{0, 0},
r + \[Delta]r, {0 + \[Omega]MOND[r, a0] t, \[Pi] + \[Omega]MOND[r, a0] t}],
Black,
Disk[{0, 0}, r, {0 + \[Omega]MOND[r, a0] t, \[Pi] + \[Omega]MOND[r, a0] t}],
Purple,
Disk[{0, 0}, r + \[Delta]r, {\[Pi] + \[Omega]MOND[r, a0] t, 2 \[Pi] + \[Omega]MOND[r, a0] t}],
Black,
Disk[{0, 0}, r, {\[Pi] + \[Omega]MOND[r, a0] t, 2 \[Pi] + \[Omega]MOND[r, a0] t}]
}, {r, rmax - \[Delta]r, \[Delta]r/10, -\[Delta]r}]
}, PlotRange -> 1.1 {{-rmax, rmax}, {-rmax, rmax}},
Background -> Black]
}}, Background -> Black]
, {t, 0, 10, 0.1}];
ListAnimate[p0]
Licensing[edit]
I, the copyright holder of this work, hereby publish it under the following license:
 
|
This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication. |
| The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.
|
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 10:05, 16 July 2020 | | 369 × 314 (2.47 MB) | Berto (talk | contribs) | Uploaded own work with UploadWizard |
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