File:MOND vs Newtonian rotation.gif
Summary
| 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
\[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
I, the copyright holder of this work, hereby publish it under the following license:
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