Hi and Good day!

My question revolves around two observations / discoveries pertaining to orbit shape, strong equivalence principle and falling bodies problem in realm of General Relativity?

First observation is regarding system of three stars orbiting close to the Milky way central black hole known as Sagittarius A* (Sgr A*) which is four million times that of the sun. The closest known star to Sgr A*, named S2, orbits around Sgr A* in its highly elliptical orbit.

Quote from article:

"Newton predicted that a star should follow the same elliptical orbit through space over and over again. But according to relativity, when the star swings in close to the black hole, it overshoots slightly, shifting the center line of the orbit by a tiny amount. This also means that the orbit is a slightly different shape at closest approach compared to its path farthest from Sgr A*."

So apart from tracing elliptical path, it also over shoots slightly shifting the centre line of orbit by tiny amount.

Complete details can be found at:

http://www.sciencemag.org/news/2017/08/star-hurtling-toward-massive-black-hole-may-seal-deal-einstein-s-general-theory

Second observation is regarding trio (three star system)which includes a pulsar in orbit with a nearby white dwarf. A second white dwarf orbits farther from said pulsar and nearby dwarf system.

Quote from article:

"But the strong equivalence principle is more stringent and difficult to test than the weak version. According to the strong equivalence principle, not only do different materials fall at the same rate, but so does the energy bound up in gravitational fields. That means that an incredibly dense, massive object with a correspondingly strong gravitational field, should fall with the same acceleration as other objects. We’re asking, ‘How does gravity fall?’” says astronomer Anne Archibald of the University of Amsterdam, who presented the preliminary result at the meeting. “That sounds weird, but Einstein says energy and mass are the same.” That means that the energy bound up in a gravitational field can fall just as mass can. If the strong equivalence principle were violated, an object with an intense gravitational field would fall with a different acceleration than one with a weaker field. scientists measured the timing of signals from a pulsar — a spinning, ultradense collapsed star that emits beams of electromagnetic radiation that sweep past Earth at regular intervals. The pulsar in question, PSR J0337+1715, isn’t just any pulsar: It has two companions (SN: 2/22/14, p.8). The pulsar orbits with a type of burnt-out star called a white dwarf. That pair is accompanied by another white dwarf, farther away. If the strong equivalence principle holds, the paired-up pulsar and white dwarf should both fall at the same rate in the gravitational field of the second white dwarf. But if the pulsar, with its intense gravitational field, fell faster toward the outermost white dwarf than its nearby companion, the pulsar’s orbit would be pulled toward the outermost white dwarf, tracing a path in the shape of a rotating ellipse. Scientists can use the timing of a pulsar’s signals to deduce its orbit. As a pulsar moves away from Earth, for example, its pulses fall a little bit behind its regular beat. So if J0337+1715’s orbit were rotating, signals received on Earth would undergo regular changes in their timing as a result. Archibald and colleagues saw no such variation. That means the pulsar and the white dwarf must have had matching accelerations, to within 0.16 thousandths of a percent."

Hence, the bottom line is that no trace of elliptic path found as the time period of pulse (period between flashes is just 2.73 milliseconds) received from pulsar remained constant (as received on earth based receiver). It has also been deduced that this system have matching accelerations.

Complete details can be found at:

https://www.sciencealert.com/einstein-general-relativity-three-body-dead-stars-psr-j0337-1715

https://www.sciencenews.org/article/trio-dead-stars-uphold-key-part-einsteins-theory-gravity.

In case of first observation S2 is falling towards Sgr A* which is black hole and traces highly elliptic path around it . Moreover as it crosses close to black hole the path centre line also deviates. In second case however, which is also a strong gravitation system consisting of pulsar and two dwarfs, no elliptic behavior and deviation from centre line observed as the inner (pulsar +nearby dwarf) come close to outer dwarf. Both observations are actually free falling object systems however, the observation made about path traced in two cases is different.

Referring again to second observation, once taking into consideration pulsar EM pulse time period measurement which has found to be invariant (as measured on earth), no reference is made to gravitational time dilation as the pulsar is located in the centre with dwarfs orbiting around it. The EM pulse time period should get a tiny fraction disturbed in gravitational potential of system.

Sorry for the lengthy post,

Thanking in anticipation,

Best Regards.

Saad Sharjeel