Too often we are told that relativity is a theory more accurate than Newtonian physics in describing movement of material object in space. It is so? With the closed-loop movements about some massive objects being so overwhelmingly found existing among celestial objects, and with the appearance of the close loops ranging from some extremely elongated shape to some near perfect circles of any size, we must imagine that only the more accurate theory can render the equation to do the job of describing them all. Unfortunately to relativity, for the purpose of accurately describing the loci of all these movements, Newtonian physics takes over the job; no equivalence whatsoever can be found from relativity. Indeed, we even wonder if a close loop equation can be derived with relativity. Let's look at the diagram below.
In this diagram, A is a massive gravitational body, and B is a free material body moving around A.
At both of the virtual equilibrium points, the gravitational force between A and B is exactly equal to the centrifugal force developed on B because of B's movement. Once established and if all physical parameters are free from any foreign interference, Rve is a constant. In the set-in picture of the diagram, vvt is the tangential component of v, B's instantaneous speed at any point, and vvr is the corresponding centripetal component. In the conic section equation, vTve is the tangential component of B's speed at the virtual equilibrium point, and vRve is the corresponding centripetal component.
Detailed derivation of the above conic section equation is skipped here, as it is quite involved. However, if any reader is interested, he/she can request the derivation work sent to him/her. Please just leave us a message by clicking the "Contact Us" on the menu bar.
During B's movement, if material is added or removed from B, its orbit around A must alter. Depending on the material quantity and the manner the materials are added or removed, curves with precession, or spiral, or open loop may result. It is so because multiple moving curves introduced by the material variation are superimposed.
On the other hand, if everything on B stays the same, but only A's material quantity changes, B's orbit will change, too. Suppose our sun loses 1/4 of its mass, what would happen to the orbits of all its planets? Ever since the solar system is established, how much mass has our Sun ejected into the space and thus lost? Should it then be a surprise that the orbit of Mercury, which is the closest planet to the sun, has to show advanced precession on its orbit in correspondence with the loss of the sun's mass? If the sun's mass continues to lose, the Mercury's precession continues to advance until someday the loss exceeds a threshold value. Then, Mercury will move away from the sun with an open loop trajectory. The moving away may never happen because the sun may have become a red giant and devour Mercury before too much mass is lost. If someone must insist that such precession can only be explained with general relativity, regardless of how special relativity's concept of speed limit being invalid, how would he explain the Moon's spiral orbit about the Earth? How is general relativity capable of shedding some light on the explanation? Shouldn't it have been possible that the Moon's spiral movement was resulted because excessive angular momentum was invested to the Moon during the early history of its movement? Besides, the Earth's mass quantity constantly changes during its entire history, too.
For the derivation of the above equation guided by Newton's laws, please refer to the last part of the article Dark Matter??? in this website.