The general relativistic Poynting-Robertson effectThe Poynting-Robertson effect causes a small body like a dust particle orbiting a central mass like a star which is shining light or radiation radially outwards to experience not only a radially outward pressure force but also an azimuthal angular drag on its orbit, essentially due to the abberration of the arriving radiation in the local rest frame of the particle, which if rotating in a circular orbit, sees the radiation arriving from a slightly forward direction resulting in a net backwards force, which acts as a drag force on the orbit so that the particle will spiral inwards over the course of a long time.See:http://en.wikipedia.org/wiki/Poynting-Robertson_effectThis worksheet enables one to easily play with the geodesics of the exterior Schwarzschild or Kerr spacetime in the equatorial plane, with an additional Poynting-Robertson drag due to the radial outflow of photons pushing on dust particles.The details are discussed by Donato Bini, Andrea Geralico and Robert T. Jantzen in
"The general relativistic Poynting-Robertson effect" (2008),
http://www34.homepage.villanova.edu/robert.jantzen/research/bibabs.htm#123
for which this worksheet produced the figures.initializeA unit mass LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiTUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjFGJ0Y5Rjk= sets the scale once and for all, so that we are essentially using the dimensionless radius LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkmbWZyYWNHRiQ2KC1JI21pR0YkNiVRInJGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2JC1GLzYlUSJNRidGMkY1L0Y2USdub3JtYWxGJy8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGRC8lKWJldmVsbGVkR1EmZmFsc2VGJ0Y9 as the actual variable and the rotation ratio LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkmbWZyYWNHRiQ2KC1JI21pR0YkNiVRImFGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2JC1GLzYlUSJNRidGMkY1L0Y2USdub3JtYWxGJy8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGRC8lKWJldmVsbGVkR1EmZmFsc2VGJ0Y9 .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The horizon as a function of the rotation parameter:Pkklcmhvckc2ImYqNiNJImFHRiRGJDYkSSlvcGVyYXRvckdGJEkmYXJyb3dHRiRGJCwmSSJNR0YkIiIiLUklc3FydEdGJDYjLCYqJEYsIiIjRi0qJDkkRjMhIiJGLUYkRiRGJA==QyQ+SShwbG90aG9yRzYiZio2I0kiYUdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLUklcGxvdEdGJTYoLCZJIk1HRiUiIiItSSVzcXJ0R0YlNiMsJiokRjAiIiNGMSokOSRGNyEiIkYxL0kidEdGJTsiIiEsJEkjUGlHJSpwcm90ZWN0ZWRHRjcvSSdjb29yZHNHRiVJJnBvbGFyR0YlL0kmY29sb3JHRiVJJmJsYWNrR0YlL0kqdGhpY2tuZXNzR0YlRjcvSSpudW1wb2ludHNHRiUiJCsiRiVGJUYlRjo=For zero rotation, the limiting equilibrium radius is simple:QyU+SShSbGltaXQwRzYiZio2I0kiQUdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCQqJkkiTUdGJSIiIiwmRi9GLyomOSQiIiNGLiEiIyEiIkY1RjNGJUYlRiVGLy1GJDYjJCIiJ0Y1but for nonzero rotation a numerical solution for this radius must be found first:QyU+SSpSbGltaXRpbXBHNiJmKjYkSSJBR0YlSSJhR0YlRiU2JEkpb3BlcmF0b3JHRiVJJmFycm93R0YlRiUsJioqOSQiIiJJIk1HRiUhIiJJInJHRiUjRjAiIiMsKCokRjMiIiRGMComRjNGMDklRjVGMComRjpGNUYxRjBGNSNGOEY1RjAqJiwoKiRGM0Y1RjAqJEY6RjVGMComRjFGMEYzRjAhIiNGNCwmKiQsJkY/RjBGQEYwRjVGMCooRjpGNUYxRjBGM0YwISIlRjBGMkYlRiVGJUYwLUYkNiQiIiEkIiInRjI=so for zero rotation we use the simple plotQyU+SSZwbG90Qkc2ImYqNiNJIkFHRiVGJTYkSSlvcGVyYXRvckdGJUkmYXJyb3dHRiVGJS1JJXBsb3RHRiU2JywkKiZJIk1HRiUiIiIsJkYyRjIqJjkkIiIjRjEhIiMhIiJGOEY2L0kmdGhldGFHRiU7IiIhLCRJI1BpRyUqcHJvdGVjdGVkR0Y2L0knY29vcmRzR0YlSSZwb2xhckdGJS9JJmNvbG9yR0YlSSVibHVlR0YlL0kqdGhpY2tuZXNzR0YlRjZGJUYlRiVGMi1GJDYjJCIiJ0Y4but for nonzero rotation the radius must be found numerically first. The critical condition is 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:PkklQ1JJVEc2ImYqNiNJImFHRiRGJDYkSSlvcGVyYXRvckdGJEkmYXJyb3dHRiRGJCoqLCgqJEkickdGJCIiIyIiIiokOSRGL0YwKiZJIk1HRiRGMEYuRjAhIiMjRjBGLywmKiQsJkYtRjBGMUYwRi9GMCooRjJGL0Y0RjBGLkYwISIlRjBGLiMhIiJGLywoKiRGLiIiJEYwKiZGLkYwRjJGL0YwKiZGMkYvRjRGMEYvIyEiJEYvRiRGJEYkWe test out this condition:LUklcGxvdEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYkNyUtSSVDUklUR0YnNiMkIiInISIiIiIiJCIiKUYvL0kickdGJzskIiM9Ri8iIzU=Qyw+SSJhRzYiJCIiJiEiIiIiIj5JIkFHRiUkIiIqRihGKS1JJ2Zzb2x2ZUdGJTYkLy1JJUNSSVRHRiU2I0YkKiZGK0YpSSJNR0YlRigvSSJyR0YlOywmRjZGKS1JJXNxcnRHRiU2IywmKiRGNiIiI0YpKiRGJEZARihGKSIjXUYpPkYkLkYkRig+RisuRitGKA==So we need to find the solution outside the horizon up to some convenient radius:QyU+SSZyY3JpdEc2ImYqNiRJIkFHRiVJImFHRiVGJTYkSSlvcGVyYXRvckdGJUkmYXJyb3dHRiVGJS1JJ2Zzb2x2ZUc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYkLy1JJUNSSVRHRiU2IzklKiY5JCIiIkkiTUdGJSEiIi9JInJHRiU7JCIjPUY8IiNdRiVGJUYlRjotRiQ2JCQiIipGPCQiIiZGPA==and then plot a circle with that radius:QyU+SSdwbG90QUJHNiJmKjYkSSJBR0YlSSJhR0YlRiU2JEkpb3BlcmF0b3JHRiVJJmFycm93R0YlRiUtSSVwbG90RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNigtSSZyY3JpdEdGJTYkOSQ5JS9JJnRoZXRhR0YlOyIiISwkSSNQaUdGMCIiIy9JJ2Nvb3Jkc0dGJUkmcG9sYXJHRjEvSSZjb2xvckdGJUklYmx1ZUdGJS9JKnRoaWNrbmVzc0dGJUY+L0kqbnVtcG9pbnRzR0YlIiQrIkYlRiVGJSIiIi1GJDYkJCIiJyEiIiQiIiZGTw==deqsThese are taken from the article by Bini, Geralico and Jantzen: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PkkmZXFyX0tHNiIvLUklZGlmZkclKnByb3RlY3RlZEc2JC1JInJHRiQ2I0kidEdGJEYtKiwsKCokRioiIiMiIiIqJEkiYUdGJEYxRjIqJkkiTUdGJEYyRipGMiEiI0YyLUkjbnVHRiRGLEYyLUkkc2luRzYkRihJKF9zeXNsaWJHRiQ2Iy1JJmFscGhhR0YkRixGMiwoKiRGKiIiJEYyKiZGKkYyRjRGMUYyKiZGNEYxRjZGMkYxIyEiIkYxRipGRg==PkkoZXFwaGlfS0c2Ii8tSSVkaWZmRyUqcHJvdGVjdGVkRzYkLUkkcGhpR0YkNiNJInRHRiRGLSomLCYqKi1JI251R0YkRiwiIiItSSRjb3NHNiRGKEkoX3N5c2xpYkdGJDYjLUkmYWxwaGFHRiRGLEYzLUkickdGJEYsRjMsKCokRjsiIiNGMyokSSJhR0YkRj9GMyomSSJNR0YkRjNGO0YzISIjI0YzRj9GMyomRkNGM0ZBRjNGP0YzLCgqJEY7IiIkRjMqJkY7RjNGQUY/RjMqJkZBRj9GQ0YzRj8hIiI=QyQ+SSVERVFTRzYiPCZJJ2VxbnVfS0dGJUkoZXFwaGlfS0dGJUkmZXFyX0tHRiVJKmVxYWxwaGFfS0dGJSEiIg==LUklc3Vic0clKnByb3RlY3RlZEc2JS9JIkFHNiIkIiInISIiL0kiYUdGKCIiIUklREVRU0dGKA==Qyg+SSVURVNURzYiLUknZHNvbHZlR0YlNiYtSSZ1bmlvbkclKnByb3RlY3RlZEc2JC1JJXN1YnNHRis2JS9JIkFHRiUkIiIiISIjL0kiYUdGJSIiIUklREVRU0dGJTwmLy1JI251R0YlNiNGNyQiIiMhIiIvLUkkcGhpR0YlRj1GNy8tSSJyR0YlRj0iIiUvLUkmYWxwaGFHRiVGPUY3PCYtRjw2I0kidEdGJS1GQ0ZNLUZGRk0tRkpGTS9JJXR5cGVHRitJKG51bWVyaWNHRisvSSdvdXRwdXRHRiVJLmxpc3Rwcm9jZWR1cmVHRiVGMz5JJHJfbkdGJS1JJWV2YWxHRis2JEZQRiRGMy1GWTYjIiImRjM=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYuLUkjbWlHRiQ2JVEkcl9uRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEqJmNvbG9uZXE7RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtRiw2JVElZXZhbEYnRi9GMi1JKG1mZW5jZWRHRiQ2JC1GIzYoLUYsNiVRInJGJ0YvRjItRlM2JC1GIzYlLUYsNiVRInRGJ0YvRjIvJStleGVjdXRhYmxlR0Y9RjlGOS1GNjYtUSIsRidGOUY7L0Y/RjFGQEZCRkRGRkZIL0ZLUSYwLjBlbUYnL0ZOUSwwLjMzMzMzMzNlbUYnLUYsNiVRJVRFU1RGJ0YvRjJGW29GOUY5LUY2Ni1RIjtGJ0Y5RjtGYG9GQEZCRkRGRkZIRmFvRk0tSSdtc3BhY2VHRiQ2Ji8lJ2hlaWdodEdRJjAuMGV4RicvJSZ3aWR0aEdRJjAuMGVtRicvJSZkZXB0aEdGYHAvJSpsaW5lYnJlYWtHUShuZXdsaW5lRidGKy1GUzYkLUYjNiUtSSNtbkdGJDYkUSI1RidGOUZbb0Y5RjlGaG8tRjY2LVEifkYnRjlGO0Y+RkBGQkZERkZGSEZhby9GTkZib0Zbb0Y5circular geodesic velocitiesFor the nonrotating case LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5Rjk= the circular geodesic speed is simple:QyU+SSdudV9nZW9HNiJmKjYjSSJyR0YlRiU2JEkpb3BlcmF0b3JHRiVJJmFycm93R0YlRiUtSSZldmFsZkclKnByb3RlY3RlZEc2Iy1JJXNxcnRHNiRGLkkoX3N5c2xpYkdGJTYjKiZJIk1HRiUiIiIsJjkkRjdGNiEiIyEiIkYlRiVGJUY7LUYkNiMiIiU=For the rotating case we have corotating (plus) and counterrotating (minus) velocities:Qyc+SShudV9nZW9wRzYiZio2JEkickdGJUkiYUdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLUkmZXZhbGZHJSpwcm90ZWN0ZWRHNiMqKCwoKiQ5JSIiIyIiIiomRjRGNi1JJXNxcnRHNiRGL0koX3N5c2xpYkdGJTYjKiZJIk1HRiVGNjkkRjZGNiEiIyokRj9GNUY2RjYtRjk2IywoRkFGNkYzRjZGPUZAISIiLCZGNEY2KiZGP0Y2LUY5NiMqJkY/RjZGPkZFRjZGNkZFRiVGJUYlRkUtRiQ2JCIiJSIiIUY2LUYkNiRGTSQiIiZGRQ==Qyc+SShudV9nZW9tRzYiZio2JEkickdGJUkiYUdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLUkmZXZhbGZHJSpwcm90ZWN0ZWRHNiMqKCwoKiQ5JSIiIyIiIiomRjRGNi1JJXNxcnRHNiRGL0koX3N5c2xpYkdGJTYjKiZJIk1HRiVGNjkkRjZGNkY1KiRGP0Y1RjZGNi1GOTYjLChGQEY2RjNGNkY9ISIjISIiLCZGNEY2KiZGP0Y2LUY5NiMqJkY/RjZGPkZFRjZGRUZFRiVGJUYlRkUtRiQ2JCIiJSIiIUY2LUYkNiRGTSQiIiZGRQ==procedure 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 and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEoR0VPcGF0aEYnLyUlYm9sZEdRJmZhbHNlRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLyUnZmFtaWx5R1EwVGltZXN+TmV3flJvbWFuRicvJSVzaXplR1EjMTJGJ0YvL0Y2USdub3JtYWxGJw==This procedure generalizes the geodesic equation solution to the "radial" radiation pressure case. Its output is the list 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, while the inputs after the time variable are the initial data 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 (order changed, no good reason) and the two parameters LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkobWZlbmNlZEdGJDYmLUYjNiYtSSNtaUdGJDYlUSJBRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiLEYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GMTYlUSJhRidGNEY3Rj5GPi8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJ0Y+ for drag and rotation. Initially purely azimuthal initial data set LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEnJiM5NDU7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUkjbW5HRiQ2JFEiMEYnRjJGMkYyLUkjbW9HRiQ2LVEiPUYnRjIvJSZmZW5jZUdGMS8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0YxLyUqc3ltbWV0cmljR0YxLyUobGFyZ2VvcEdGMS8lLm1vdmFibGVsaW1pdHNHRjEvJSdhY2NlbnRHRjEvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZSRjotRj82LVEifkYnRjJGQkZERkZGSEZKRkxGTi9GUVEmMC4wZW1GJy9GVEZZRjI=. The procedure LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEoR0VPcGF0aEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIn5GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTEY5instead just delivers the sequence LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2JVEickYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInRGJ0YvRjIvRjNRJ25vcm1hbEYnRj0tSSNtb0dGJDYtUSIsRidGPS8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0ZFLyUqc3ltbWV0cmljR0ZFLyUobGFyZ2VvcEdGRS8lLm1vdmFibGVsaW1pdHNHRkUvJSdhY2NlbnRHRkUvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GLDYlUScmIzk4MTtGJy9GMEZFRj1GNS1GLDYjUSFGJ0Y9, so that 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
can be used in the parametrized curve plot.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However, the circular orbits inside LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEickYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjZGJ0Y5LUY2Ni1RIn5GJ0Y5RjtGPkZARkJGREZGRkgvRktRJjAuMGVtRicvRk5GVy1GLDYlUSJNRidGL0YyRjk= are unstable, as this example shows:LUklcGxvdEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYkJi1JJEdFT0dGJzYpSSJ0R0YnIiIhLUknbnVfZ2VvR0YnNiMiIiVGMkYuRi5GLjYjIiIiL0YtO0YuIiQrIg==We fix a more useful procedure for the parametrized curve plotting.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QyUtSShHRU9wYXRoRzYiNikiIzUiIiEkIiIjISIiIiIlRigkIiInRitGKCIiIi1GJDYpRidGKEYpRixGKEYoRig=QyQtSSVwbG90RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiY3JC1JKEdFT3BhdGhHRig2KUkidEdGKCIiISQiIiMhIiIiIiVGLyQiIidGMkYvL0YuO0YvIiUrNS9JJ2Nvb3Jkc0dGKEkmcG9sYXJHRicvSSp0aGlja25lc3NHRihGMS9JJmNvbG9yR0YoSSZibGFja0dGKCIiIg==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 figure 1Now we test it for a value of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnL0YwUSdpdGFsaWNGJ0Yv.QzI+SSJBRzYiJCIiJyEiIiIiIj5JImFHRiUiIiFGKS9JKXJob3Jpem9uR0YlLUklcmhvckdGJTYjRitGKS9JKnJjcml0aWNhbEdGJS1JJnJjcml0R0YlNiRGJEYrRik+SSRycjBHRiUiIiVGKS1JJ251X2dlb0dGJTYjRjhGKS1JKGRpc3BsYXlHRiU2JC1JKHBsb3Rob3JHRiVGMS1JJnBsb3RCR0YlNiNGJEYpPkkmcmluZ3NHRiVJIiVHRiVGKA==QzItSSVwbG90RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiY3JC1JKEdFT3BhdGhHRig2KUkidEdGKCIiISQiIiMhIiIiIiVGL0kiQUdGKEkiYUdGKC9GLjtGLyIkKyYvSSdjb29yZHNHRihJJnBvbGFyR0YnL0kqdGhpY2tuZXNzR0YoRjEvSSZjb2xvckdGKEkmYmxhY2tHRihGMj5JI3AwR0YoSSIlR0YoRjItRiQ2JjckLUYsNilGLkYvJCIiJkYyRjNGL0Y0RjVGNkY5RjxGPkYyPkkjcDFHRihGQ0YyLUYkNic3JC1GLDYpRi5GLyQiIilGMkYzRi9GNEY1RjZGOS9JKm51bXBvaW50c0dGKCIlK11GPEY+RjI+SSNwMkdGKEZDRjItSShkaXNwbGF5R0YoNidGQkZMRlhJJnJpbmdzR0YoL0kldmlld0dGKDckOyEjNSIjNUZqbiIiIj5JKnBsb3RmaW5hbEdGKEZDRjI=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circular geodesic is unstableMaybe we should express this in fractions of the circular geodesic velocity, but the circular geodesic at this radius is unstable.LUklcGxvdEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYmNyQtSShHRU9wYXRoR0YnNilJInRHRiciIiEtSSdudV9nZW9HRic2I0kkcnIwR0YnIiIlRi5GLkYuL0YtO0YuIiQrJC9JJ2Nvb3Jkc0dGJ0kmcG9sYXJHRiYvSSp0aGlja25lc3NHRiciIiMvSSZjb2xvckdGJ1EpRGFya0dyYXlGJw==QyUtSSdudV9nZW9HNiI2I0kkcnIwR0YlIiIiJi1JKEdFT3BhdGhHRiU2KSIkKyMiIiFGIyIiJUYuRi5GLjYjIiIjJust before 5 revolutions it falls in.LUklcGxvdEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYmLUkkc2luR0YkNiMmLUkoR0VPcGF0aEdGJzYpSSJ0R0YnIiIhLUknbnVfZ2VvR0YnNiNJJHJyMEdGJyIiJUYxRjFGMTYjIiIjL0YwO0YxIiQrJC9JKnRoaWNrbmVzc0dGJ0Y4L0kmY29sb3JHRidRKURhcmtHcmF5Ric=NiUsJC1JJ251X2dlb0c2IjYjSSRycjBHRiYkIiIkISIiRiQsJEYkJCIjNkYrQzItSSVwbG90RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiY3JC1JKEdFT3BhdGhHRig2KUkidEdGKCIiISwkLUknbnVfZ2VvR0YoNiNJJHJyMEdGKCQiIiQhIiIiIiVGL0kiQUdGKEkiYUdGKC9GLjtGLyIkKyYvSSdjb29yZHNHRihJJnBvbGFyR0YnL0kmY29sb3JHRihJJmJsYWNrR0YoL0kqdGhpY2tuZXNzR0YoIiIjRjc+SSNwMEdGKEkiJUdGKEY3LUYkNiY3JC1GLDYpRi5GL0YxRjhGL0Y5RjpGO0Y+RkFGREY3PkkjcDFHRihGSUY3LUYkNic3JC1GLDYpRi5GLywkRjEkIiM2RjdGOEYvRjlGOi9GLjtGLyIlKzVGPkZBRkQvSSpudW1wb2ludHNHRigiJStdRjc+SSNwMkdGKEZJRjctSShkaXNwbGF5R0YoNidGSEZQRmpuSSZyaW5nc0dGKC9JJXZpZXdHRig3JDshIzUiIzVGYm8iIiI+SSpwbG90ZmluYWxHRihGSUY3LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzY2LUkjbWlHRiQ2JVElcGxvdEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzY1LUY2NiYtRiM2LC1GLDYlUShHRU9wYXRoRidGL0YyLUY2NiQtRiM2NS1GLDYlUSJ0RicvRjBRJmZhbHNlRicvRjNRJ25vcm1hbEYnLUkjbW9HRiQ2LVEiLEYnRkovJSZmZW5jZUdGSS8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0ZJLyUqc3ltbWV0cmljR0ZJLyUobGFyZ2VvcEdGSS8lLm1vdmFibGVsaW1pdHNHRkkvJSdhY2NlbnRHRkkvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1JI21uR0YkNiRRIjBGJ0ZKRkwtRl9vNiRRJDEuMUYnRkotRk02LVEifkYnRkpGUC9GU0ZJRlRGVkZYRlpGZm5GaG4vRlxvRmpuLUYsNiVRJ251X2dlb0YnRkhGSi1GNjYkLUYjNiUtRiw2JVEkcnIwRidGSEZKLyUrZXhlY3V0YWJsZUdGSUZKRkpGTEZlby1GX282JFEiNEYnRkpGTEZeb0ZMLUYsNiVRIkFGJ0ZIRkpGTC1GLDYlUSJhRidGSEZKRmRwRkpGSkZMLUYsNiVGR0YvRjItRk02LVEiPUYnRkpGUEZob0ZURlZGWEZaRmZuL0ZpblEsMC4yNzc3Nzc4ZW1GJy9GXG9GZXFGXm8tRk02LVEjLi5GJ0ZKRlBGaG9GVEZWRlhGWkZmbi9GaW5RLDAuMjIyMjIyMmVtRidGaW8tRl9vNiRRJTEwMDBGJ0ZKRmRwRkpGSi8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJ0ZMLUYsNiVRJ2Nvb3Jkc0YnRi9GMkZhcS1GLDYlUSZwb2xhckYnRkhGSkZMLUYsNiVRJmNvbG9yRidGL0YyRmFxLUYsNiVRJmJsYWNrRidGL0YyRkwtRiw2JVEqdGhpY2tuZXNzRidGL0YyRmFxLUZfbzYkUSIyRidGSkZMLUYsNiVRKm51bXBvaW50c0YnRi9GMkZhcS1GX282JFElNTAwMEYnRkpGZHBGSkZKLUZNNi1RIjpGJ0ZKRlBGaG9GVEZWRlhGWkZmbkZkcUZmcUZlby1GLDYlUSNwMkYnRi9GMi1GTTYtUSomY29sb25lcTtGJ0ZKRlBGaG9GVEZWRlhGWkZmbkZkcUZmcS1GLDYlUSIlRidGL0YyRl10LUknbXNwYWNlR0YkNiYvJSdoZWlnaHRHUSYwLjBleEYnLyUmd2lkdGhHUSYwLjBlbUYnLyUmZGVwdGhHRl51LyUqbGluZWJyZWFrR1EobmV3bGluZUYnLUZNNi5GZ29GL0YyRlBGaG9GVEZWRlhGWkZmbkZobkZpby1GLDYlUShkaXNwbGF5RidGL0YyLUY2NiQtRiM2Ly1GLDYlUSNwMEYnRi9GMkZMLUYsNiVRI3AxRidGL0YyRkxGYHRGTC1GLDYlUSZyaW5nc0YnRi9GMkZMLUYsNiVRJXZpZXdGJ0YvRjJGYXEtRjY2Ji1GIzYtLUZNNi1RKiZ1bWludXMwO0YnRkpGUEZob0ZURlZGWEZaRmZuRmpxL0Zcb0Zbci1GX282JFEjMTBGJ0ZKRmdxRmR3RkxGYHdGZHdGZ3FGZHdGZHBGSkZKRl9yRmJyRmRwRkpGSi1GTTYtUSI7RidGSkZQRlJGVEZWRlhGWkZmbkZobkZmcUZlby1GLDYlUSpwbG90ZmluYWxGJ0YvRjJGY3RGZnRGXXRGZHBGSg==But in fact at this radius the circular orbit is unstable, and in this case it falls into the hole after a few revolutions and numerical error intervenes...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Enough of this detour.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 figures 2a, 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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVElR3JBWUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKiZjb2xvbmVxO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUkjbXNHRiQ2I1EpRGFya0dyYXlGJy1GNjYtUSI6RidGOUY7Rj5GQEZCRkRGRkZIRkpGTS8lK2V4ZWN1dGFibGVHRj1GOQ==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Now we do a sequence of 6 initial speeds.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 to clean 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=10 figure 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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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 figures 4a, 4bNow we test it for a nonzero rotation.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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW9HRiQ2LVEiI0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLUkjbWlHRiQ2JVEzYSYjODc4ODsmIzg3MjI7MC41RicvJSdpdGFsaWNHUSV0cnVlRicvRjBRJ2l0YWxpY0YnLyUrZXhlY3V0YWJsZUdGNEYvLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzY6LUkjbWlHRiQ2JVElcGxvdEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzY1LUY2NiYtRiM2MS1GLDYlUSRHRU9GJ0YvRjItRjY2JC1GIzYyLUYsNiVRInRGJy9GMFEmZmFsc2VGJy9GM1Enbm9ybWFsRictSSNtb0dGJDYtUSIsRidGSi8lJmZlbmNlR0ZJLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRkkvJSpzeW1tZXRyaWNHRkkvJShsYXJnZW9wR0ZJLyUubW92YWJsZWxpbWl0c0dGSS8lJ2FjY2VudEdGSS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUkjbW5HRiQ2JFEiMEYnRkpGTC1GX282JFEkMC4yRidGSkZMLUZNNi1RIn5GJ0ZKRlAvRlNGSUZURlZGWEZaRmZuRmhuL0Zcb0Zqbi1GX282JFEiNEYnRkpGTEZeb0ZMLUYsNiVRIkFGJ0ZIRkpGTC1GLDYlUSJhRidGSEZKLyUrZXhlY3V0YWJsZUdGSUZKRkotRjY2Ji1GIzYlLUZfbzYkUSIxRidGSkZjcEZKRkovJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRidGTEY+RkEtRjY2Ji1GIzYlLUZfbzYkUSIyRidGSkZjcEZKRkpGXHFGX3FGTC1GLDYlRkdGL0YyLUZNNi1RIj1GJ0ZKRlBGaG9GVEZWRlhGWkZmbi9GaW5RLDAuMjc3Nzc3OGVtRicvRlxvRl9yRl5vLUZNNi1RIy4uRidGSkZQRmhvRlRGVkZYRlpGZm4vRmluUSwwLjIyMjIyMjJlbUYnRmlvLUZfbzYkUSUxMDAwRidGSkZjcEZKRkpGXHFGX3FGTC1GTTYtUSomdW1pbnVzMDtGJ0ZKRlBGaG9GVEZWRlhGWkZmbkZkci9GXG9GZXItRl9vNiRRIzEyRidGSkZhckZdc0ZMRmVvRmlyRl1zRmFyRl1zRkxGZW8tRiw2JVEnY29vcmRzRidGL0YyRltyLUYsNiVRJnBvbGFyRidGSEZKRmNwRkpGSi1GTTYtUSI6RidGSkZQRmhvRlRGVkZYRlpGZm5GXnJGYHJGZW8tRiw2JVEjcDBGJ0YvRjItRk02LVEqJmNvbG9uZXE7RidGSkZQRmhvRlRGVkZYRlpGZm5GXnJGYHItRiw2JVEiJUYnRi9GMkZmcy1JJ21zcGFjZUdGJDYmLyUnaGVpZ2h0R1EmMC4wZXhGJy8lJndpZHRoR1EmMC4wZW1GJy8lJmRlcHRoR0ZndC8lKmxpbmVicmVha0dRKG5ld2xpbmVGJy1GY3Q2JkZldEZodEZbdS9GXnVRJWF1dG9GJ0YrLUY2NiQtRiM2KS1GNjYmLUYjNjFGPi1GNjYkLUYjNjJGRUZMRl5vRkwtRl9vNiRRJDAuNUYnRkpGTEZlb0Zqb0ZMRl5vRkxGXXBGTEZgcEZjcEZKRkpGZXBGTEY+Rlx2RmJxRkxGaXFGW3JGXm9GYXJGZnJGY3BGSkZKRlxxRl9xRkxGYHNGW3JGY3NGY3BGSkZKRmZzRmVvLUYsNiVRI3AxRidGL0YyRlx0Rl90RmZzRmJ0RmB1RmJ0RmVvRmNwRko=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzY2LUkjbWlHRiQ2JVElcGxvdEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzY5LUY2NiYtRiM2MS1GLDYlUSRHRU9GJ0YvRjItRjY2JC1GIzYyLUYsNiVRInRGJy9GMFEmZmFsc2VGJy9GM1Enbm9ybWFsRictSSNtb0dGJDYtUSIsRidGSi8lJmZlbmNlR0ZJLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRkkvJSpzeW1tZXRyaWNHRkkvJShsYXJnZW9wR0ZJLyUubW92YWJsZWxpbWl0c0dGSS8lJ2FjY2VudEdGSS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUkjbW5HRiQ2JFEiMEYnRkpGTC1GX282JFEkMC4yRidGSkZMLUZNNi1RIn5GJ0ZKRlAvRlNGSUZURlZGWEZaRmZuRmhuL0Zcb0Zqbi1GX282JFEiNEYnRkpGTEZeb0ZMRl5vRkwtRiw2JVEiYUYnRkhGSi8lK2V4ZWN1dGFibGVHRklGSkZKLUY2NiYtRiM2JS1GX282JFEiMUYnRkpGYHBGSkZKLyUlb3BlbkdRIltGJy8lJmNsb3NlR1EiXUYnRkxGPkZBLUY2NiYtRiM2JS1GX282JFEiMkYnRkpGYHBGSkZKRmlwRlxxRkwtRiw2JUZHRi9GMi1GTTYtUSI9RidGSkZQRmhvRlRGVkZYRlpGZm4vRmluUSwwLjI3Nzc3NzhlbUYnL0Zcb0ZcckZeby1GTTYtUSMuLkYnRkpGUEZob0ZURlZGWEZaRmZuL0ZpblEsMC4yMjIyMjIyZW1GJ0Zpby1GX282JFEkMTAwRidGSkZgcEZKRkpGaXBGXHFGTC1GTTYtUSomdW1pbnVzMDtGJ0ZKRlBGaG9GVEZWRlhGWkZmbkZhci9GXG9GYnItRl9vNiRRIzEyRidGSkZeckZqckZMRmVvRmZyRmpyRl5yRmpyRkxGZW8tRiw2JVEnY29vcmRzRidGL0YyRmhxLUYsNiVRJnBvbGFyRidGSEZKRkwtRiw2JVEmY29sb3JGJ0YvRjJGaHEtRiw2JVElZ3JheUYnRi9GMkZgcEZKRkotRk02LVEiOkYnRkpGUEZob0ZURlZGWEZaRmZuRltyRl1yRmVvLUYsNiVRJHAwMEYnRi9GMi1GTTYtUSomY29sb25lcTtGJ0ZKRlBGaG9GVEZWRlhGWkZmbkZbckZdci1GLDYlUSIlRidGL0YyRmlzLUknbXNwYWNlR0YkNiYvJSdoZWlnaHRHUSYwLjBleEYnLyUmd2lkdGhHUSYwLjBlbUYnLyUmZGVwdGhHRmp0LyUqbGluZWJyZWFrR1EobmV3bGluZUYnLUZmdDYmRmh0Rlt1Rl51L0ZhdVElYXV0b0YnRistRjY2JC1GIzYtLUY2NiYtRiM2MUY+LUY2NiQtRiM2MkZFRkxGXm9GTC1GX282JFEkMC41RidGSkZMRmVvRmpvRkxGXm9GTEZeb0ZMRl1wRmBwRkpGSkZicEZMRj5GX3ZGX3FGTEZmcUZocUZeb0ZeckZjckZgcEZKRkpGaXBGXHFGTEZdc0ZocUZgc0ZMRmNzRmhxRmZzRmBwRkpGSkZpc0Zlby1GLDYlUSRwMTFGJ0YvRjJGX3RGYnRGaXNGYHBGSg==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYsLUkjbWlHRiQ2JVElcGxvdEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYxLUY2NiYtRiM2MS1GLDYlUSRHRU9GJ0YvRjItRjY2JC1GIzYyLUYsNiVRInRGJy9GMFEmZmFsc2VGJy9GM1Enbm9ybWFsRictSSNtb0dGJDYtUSIsRidGSi8lJmZlbmNlR0ZJLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRkkvJSpzeW1tZXRyaWNHRkkvJShsYXJnZW9wR0ZJLyUubW92YWJsZWxpbWl0c0dGSS8lJ2FjY2VudEdGSS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUkjbW5HRiQ2JFEiMEYnRkpGTC1GX282JFEkMC44RidGSkZMLUZNNi1RIn5GJ0ZKRlAvRlNGSUZURlZGWEZaRmZuRmhuL0Zcb0Zqbi1GX282JFEiNEYnRkpGTEZeb0ZMLUYsNiVRIkFGJ0ZIRkpGTEZeby8lK2V4ZWN1dGFibGVHRklGSkZKLUY2NiYtRiM2JS1GX282JFEiMUYnRkpGYHBGSkZKLyUlb3BlbkdRIltGJy8lJmNsb3NlR1EiXUYnRkxGPkZBLUY2NiYtRiM2JS1GX282JFEiMkYnRkpGYHBGSkZKRmlwRlxxRkwtRiw2JUZHRi9GMi1GTTYtUSI9RidGSkZQRmhvRlRGVkZYRlpGZm4vRmluUSwwLjI3Nzc3NzhlbUYnL0Zcb0ZcckZeby1GTTYtUSMuLkYnRkpGUEZob0ZURlZGWEZaRmZuL0ZpblEsMC4yMjIyMjIyZW1GJ0Zpby1GX282JFEkMTAwRidGSkZgcEZKRkpGaXBGXHFGTC1GLDYlUSdjb29yZHNGJ0YvRjJGaHEtRiw2JVEmcG9sYXJGJ0ZIRkpGTC1GLDYlUSZjb2xvckYnRi9GMkZocS1GLDYlUSVncmF5RidGL0YyRkwtRiw2JVEqdGhpY2tuZXNzRidGL0YyRmhxLUZfbzYkUSIzRidGSkZgcEZKRkotRk02LVEiO0YnRkpGUEZSRlRGVkZYRlpGZm5GaG5GXXJGZW8tRiw2JVEkcDIyRidGL0YyLUZNNi1RKiZjb2xvbmVxO0YnRkpGUEZob0ZURlZGWEZaRmZuRltyRl1yLUYsNiVRIiVGJ0YvRjItRk02LVEiOkYnRkpGUEZob0ZURlZGWEZaRmZuRltyRl1yRmBwRko=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYwLUkjbWlHRiQ2JVElcGxvdEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYxLUY2NiYtRiM2MS1GLDYlUSRHRU9GJ0YvRjItRjY2JC1GIzYyLUYsNiVRInRGJy9GMFEmZmFsc2VGJy9GM1Enbm9ybWFsRictSSNtb0dGJDYtUSIsRidGSi8lJmZlbmNlR0ZJLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRkkvJSpzeW1tZXRyaWNHRkkvJShsYXJnZW9wR0ZJLyUubW92YWJsZWxpbWl0c0dGSS8lJ2FjY2VudEdGSS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUkjbW5HRiQ2JFEiMEYnRkpGTC1GX282JFEkMC44RidGSkZMLUZNNi1RIn5GJ0ZKRlAvRlNGSUZURlZGWEZaRmZuRmhuL0Zcb0Zqbi1GX282JFEiNEYnRkpGTEZeb0ZMLUYsNiVRIkFGJ0ZIRkpGTC1GLDYlUSJhRidGSEZKLyUrZXhlY3V0YWJsZUdGSUZKRkotRjY2Ji1GIzYlLUZfbzYkUSIxRidGSkZjcEZKRkovJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRidGTEY+RkEtRjY2Ji1GIzYlLUZfbzYkUSIyRidGSkZjcEZKRkpGXHFGX3FGTC1GLDYlRkdGL0YyLUZNNi1RIj1GJ0ZKRlBGaG9GVEZWRlhGWkZmbi9GaW5RLDAuMjc3Nzc3OGVtRicvRlxvRl9yRl5vLUZNNi1RIy4uRidGSkZQRmhvRlRGVkZYRlpGZm4vRmluUSwwLjIyMjIyMjJlbUYnRmlvLUZfbzYkUSUxMDAwRidGSkZjcEZKRkpGXHFGX3FGTC1GLDYlUSdjb29yZHNGJ0YvRjJGW3ItRiw2JVEmcG9sYXJGJ0ZIRkpGTC1GLDYlUSpudW1wb2ludHNGJ0YvRjJGW3JGZnJGTC1GLDYlUSZjb2xvckYnRi9GMkZbci1GLDYlUSZncmVlbkYnRi9GMkZjcEZKRkotRk02LVEiOkYnRkpGUEZob0ZURlZGWEZaRmZuRl5yRmByRmVvLUYsNiVRI3AyRidGL0YyLUZNNi1RKiZjb2xvbmVxO0YnRkpGUEZob0ZURlZGWEZaRmZuRl5yRmByLUYsNiVRIiVGJ0YvRjJGaHMtSSdtc3BhY2VHRiQ2Ji8lJ2hlaWdodEdRJjAuMGV4RicvJSZ3aWR0aEdRJjAuMGVtRicvJSZkZXB0aEdGaXQvJSpsaW5lYnJlYWtHUShuZXdsaW5lRictRmV0NiZGZ3RGanRGXXUvRmB1USVhdXRvRictRiw2JVEoZGlzcGxheUYnRi9GMi1GNjYkLUYjNjYtRiw2JVEkcDAwRidGL0YyRkwtRiw2JVEkcDExRidGL0YyRkwtRiw2JVEkcDIyRidGL0YyRkwtRiw2JVEjcDBGJ0YvRjJGTC1GLDYlUSNwMUYnRi9GMkZMRlt0RkwtRiw2JVEocGxvdGhvckYnRi9GMi1GNjYkLUYjNiUtRiw2JUZicEYvRjJGY3BGSkZKRkwtRiw2JVEldmlld0YnRi9GMkZbci1GNjYmLUYjNi0tRk02LVEqJnVtaW51czA7RidGSkZQRmhvRlRGVkZYRlpGZm5GZHIvRlxvRmVyLUZfbzYkUSI3RidGSkZhckZgeEZMRlx4RmB4RmFyRmB4RmNwRkpGSkZccUZfcUZjcEZKRkpGY3BGSg==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2MC1GLDYlUSVwbG90RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNjEtRjs2Ji1GIzYxLUYsNiVRJEdFT0YnRjRGNy1GOzYkLUYjNjItRiw2JVEidEYnL0Y1USZmYWxzZUYnL0Y4USdub3JtYWxGJy1JI21vR0YkNi1RIixGJ0ZPLyUmZmVuY2VHRk4vJSpzZXBhcmF0b3JHRjYvJSlzdHJldGNoeUdGTi8lKnN5bW1ldHJpY0dGTi8lKGxhcmdlb3BHRk4vJS5tb3ZhYmxlbGltaXRzR0ZOLyUnYWNjZW50R0ZOLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictSSNtbkdGJDYkUSIwRidGT0ZRLUZkbzYkUSQwLjhGJ0ZPRlEtRlI2LVEifkYnRk9GVS9GWEZORllGZW5GZ25GaW5GW29GXW8vRmFvRl9vLUZkbzYkUSI0RidGT0ZRRmNvRlEtRiw2JVEiQUYnRk1GT0ZRLUYsNiVRImFGJ0ZNRk8vJStleGVjdXRhYmxlR0ZORk9GTy1GOzYmLUYjNiUtRmRvNiRRIjFGJ0ZPRmhwRk9GTy8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJ0ZRRkNGRi1GOzYmLUYjNiUtRmRvNiRRIjJGJ0ZPRmhwRk9GT0ZhcUZkcUZRLUYsNiVGTEY0RjctRlI2LVEiPUYnRk9GVUZdcEZZRmVuRmduRmluRltvL0Zeb1EsMC4yNzc3Nzc4ZW1GJy9GYW9GZHJGY28tRlI2LVEjLi5GJ0ZPRlVGXXBGWUZlbkZnbkZpbkZbby9GXm9RLDAuMjIyMjIyMmVtRidGXnAtRmRvNiRRJTEwMDBGJ0ZPRmhwRk9GT0ZhcUZkcUZRLUYsNiVRJ2Nvb3Jkc0YnRjRGN0Zgci1GLDYlUSZwb2xhckYnRk1GT0ZRLUYsNiVRKm51bXBvaW50c0YnRjRGN0ZgckZbc0ZRLUYsNiVRJmNvbG9yRidGNEY3RmByLUYsNiVRJmdyZWVuRidGNEY3RmhwRk9GTy1GUjYtUSI6RidGT0ZVRl1wRllGZW5GZ25GaW5GW29GY3JGZXJGam8tRiw2JVEjcDJGJ0Y0RjctRlI2LVEqJmNvbG9uZXE7RidGT0ZVRl1wRllGZW5GZ25GaW5GW29GY3JGZXItRiw2JVEiJUYnRjRGN0ZddC1JJ21zcGFjZUdGJDYmLyUnaGVpZ2h0R1EmMC4wZXhGJy8lJndpZHRoR1EmMC4wZW1GJy8lJmRlcHRoR0ZedS8lKmxpbmVicmVha0dRKG5ld2xpbmVGJy1GanQ2JkZcdUZfdUZidS9GZXVRJWF1dG9GJy1GLDYlUShkaXNwbGF5RidGNEY3LUY7NiQtRiM2Ni1GLDYlUSRwMDBGJ0Y0RjdGUS1GLDYlUSRwMTFGJ0Y0RjdGUS1GLDYlUSRwMjJGJ0Y0RjdGUS1GLDYlUSNwMEYnRjRGN0ZRLUYsNiVRI3AxRidGNEY3RlFGYHRGUS1GLDYlUShwbG90aG9yRidGNEY3LUY7NiQtRiM2JS1GLDYlRmdwRjRGN0ZocEZPRk9GUS1GLDYlUSV2aWV3RidGNEY3RmByLUY7NiYtRiM2LS1GUjYtUSomdW1pbnVzMDtGJ0ZPRlVGXXBGWUZlbkZnbkZpbkZbb0Zpci9GYW9GanItRmRvNiRRIzUwRidGT0Zmci1GZG82JFEjMTBGJ0ZPRlFGYXhGaHhGZnJGZXhGaHBGT0ZPRmFxRmRxRmhwRk9GT0ZocEZPRitGaHBGTw==Now we switch the sign of the rotation: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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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 figures 5a, 5bNow we increase LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=.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Note the precession of the elliptical-like orbit.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Now the ellipse itself is shrinking as the drag forces the orbit inwards.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For the geodesic speed, the orbit slowly decays.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We should add a formula for the period of the circular orbit,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If the velocity is much smaller, the orbit basically just drops into the hole.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Here are two such drop in geodesic orbits compared to the circular geodesic orbit.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Hmm.