Data on S2

At closest approach on 18th May 2018 the distance of S2 from the central mass was 120 AU = 1.7952 ten power thirteen metres (Wikipedia article). Its semi major axis is 1.451 ten power fourteen metres. The velocity of S2 at closest approach to the central mass was measured to be 7,650 kilometres per second = 7.650 ten power six metres per second. This gives a velocity v at position r, and these data may be enough to calculate the orbit from m theory. If the orbit were Newtonian then v squared = MG (2 / r – 1 / a)

where M = 8.572 ten power 36 kgm; G = 6.67407 ten power – 11 in SI units; r = 1.7952 ten power thirteen metres; a = 1.451 ten power fourteen metres. This gives:

v squared = 5.852 ten power 13 m squared


MG (2 / r – 1 / a) = 5.9769 ten power 13 m squared

So the deviation from the Newtonian result can be described by Eq. (54) of Note 417(7) in terms of an m (r) function. Assuming that the initial v and r are those at closest approach on 18th May 2018, the orbit can be computed with the code written by Dr. Horst Eckardt. This would give the precession due to m theory. For self consistency I have used throughout the data given in the Wikipedia article. I assume that wiki got it right this time.

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