m(r) theory with constant m

It was shown in UFT419 that this type of theory is enough to describe the orbit of S2. In this note the equations of motion with constant m(r):= mu are defined to be Eqs. (14) and (15). It would be very interesting to graph the orbits as a function of mu. In general they produce precessing orbits, and it will be interesting to see if there is both forward and retrograde precession for constant mu. In the low velocity limit Eqs. (14) and (15) reduce to Eqs. (22) and (23), in which there is an effective central mass defined by Eq. (25). This equation can be taken as defining the concept of mass itself in terms of its associated spherical spacetime. So mass becomes mu squared with M taken as the unit kilogram. Mass is therefore spherical spacetime itself. In this limit it is shown that mu defines any Newtonian type orbit. The orbit can be thought of in a new way, it is caused by mu and not by the anthropomorphic idea of M. For constant mu the orbit that gives the observed velocity curve of a whirlpool galaxy is defined by Eq. (40), a spiral which depends on the choice of mu. As many spirals as observed in a galaxy can be produced by a choice such as (42), a sum of mu sub 1, mu sub 2, …. mu sub n. Finally if m(r) depends on r, any galaxy and any number of spiral arms, or any more general shape, can be found by integrating Eq. (40) numerically using the Maxima integrator on a desktop.


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