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Fig. 1


Interpolating functions ν(β) = [1 + (1 + 4β-1)1 / 2] / 2 (dot-dashed line) and ν(β) = [1−exp(−β1 / 2)] -1 (solid line) as functions of heliocentric distance Ξ. βgN/a0 is approximated with , i.e. vectors of external and internal Newtonian gravity are assumed to be perpendicular to each other for simplicity. The two topmost horizontal dashed lines are the values ν-functions asymptote to under the condition Ξ → ∞ (then ), the downmost ν = 1 marks the Newtonian limit. Vertical dashed lines from left to right indicate the aphelia of Neptune and Sedna and the distances where GM/ Ξ2 = ge = 1.9a0 and GM/ Ξ2 = a0. The dotted line is β− 1 / 2 = [(GM/ Ξ2) /a0] − 1 / 2, the deep-MOND limit of ν(β), in the case of no external field.

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