Bearing in mind, by implication of the above conditions, the place of hiding of the binary star needs to conform with the general plane of the planets in our SolarSystem - i.o.w. in a defined locale. Our entire SS, no less, is required to revolve around the object, which needless to say, demands gravity associated with a HUGE mass - that we are led to believe is conveniently cloaked by invisibility ;-) The perigee of, not only the Sun's parabolic path but our whole SolarSystem along with it, respective said object, will impose certain limits pertaining distance - governed by relevant physics. These factors, in combination, determine the DarkStar to be located a looong way out - accordingly pushing the parameter of our Sun's required parabolic orbit even further. Matters that Tommy the TimeTravellingTurtle ought to have contemplated prior to embarking on his fictitious journey.
Now, let's venture top of the World - upward, where respective of the Poles, the stars -- continuous from equatorial / ecliptic plane region -- envelop Earth in all directions and extend over the Poles. The view, perpendicular to the plane of the ecliptic, reveal evidenced circular precession related star motion around the pole of the ecliptic (centered on the EclipticPole) - portraying such to be consistent with -- axial rotation -- established trend and not compatable, in the least, with what the orbital action inferred above, would produce. Emphasized on previous occasions, the particular pattern of changing coordinates demand a binary object located in close proximity - stars don't lie (thumping the book ;-) Genesis 1:14
You can't have it both ways -- the binary proposal creates its own CheckMate abberation -- where XY lateral motion is contradictory as well as with Z axis. Considering velocity of travel associated with orbital distance -VS- the perceivable circumpolar rate invokes more of the bizarre. I did not even address true Polar wander, which may not be obvious in the short term, however foresee the problem going really haywire exponentially with time. Our magnificent shiny star is as rock-steady stationary as ever. The exotic claims put out by the BinaryResearch... Institution :-D cannot be seriously entertained.
ps. Investigate apsidal precession for a mind-bending puzzle of its own unique kind... an interesting proposal, more so than the binary bull... however, falsifiable also by star pattern.
Edited 6 time(s). Last edit at 24-Aug-19 18:36 by hendrik dirker.