Friday, March 7, 2014

Frame dragging in a two dimensional gravitational field

If a massive spinning body possesses a strong gravitational field, that body will have a torque field around it that will act on external coorbiting pairs of objects. The torque field will apply a simultaneous torque to the coorbits of each pair, causing the ellipticity of each coorbit to precess in the same sense of the directions of their primary planetary orbital rotations.

That is: if , say, the Earth and the moon orbit each other with ellipticity e, and if the spinning Sun had sufficiently high mass, it  would possess a strong torque field concomitant to its gravitational field. This solar torque field would act on the Earth/moon system such that the moon's slightly elliptic orbit, e, would precess slowly in the anticlockwise direction consistent with the system's overall orbit about the Sun. If an highly elliptic orbit of a moon of Mars was observed for a long time, the ellipticity of its orbit would be seen to precess too. If a satellite was placed in an elliptical orbit about Venus in the plane of rotation of either the Milky Way Galaxy or the plane of the Solar system (rotational plane of the Sun), this orbit would be seen to precess slowly, more than could be accounted for by conservation of angular momentum (or lack of it) due to its own elliptical circumsolar orbit or to tidal forces.

The Earth/moon system has already been observed to possess such an inexplicable odd precession. Mars has two moons which may interfere with observations of individual ellipticities. But, Venus has no moons. It would be ideal for emplacement of an artificial satellite with properly oriented orbital ellipticity.

But, the Sun may not have enough mass to cause relativistic frame dragging of this type. But, the galaxy possesses a supermassive black hole (SMBH) with its two dimensional gravitational field confined to the galactic plane, mainly. The spacetime gravitational properties of black holes are conserved. So the torque field of a supermassive black hole must be concentrated and intensified in the galactic plane (the rotational plane of the black hole) and not spread out thinly over a sphere. So, its high intensity must reflect this focussed concentration, especially because gravitation must decline as 1/r for a two dimensional field, not 1/r^2 as for an ordinary three dimensional field. So, the influence of this torque field may be felt all the way out to the Earth and beyond.

In other words, relativistic frame dragging may reach much farther in the case of rapidly spinning SMBHs and this must be taken into account when analyzing orbital precession rates involving pairs of coorbiting objects simultaneously orbiting black holes.

That is, the moon/earth binary system exhibits anomalous changes in orbital eccentricity[1]. Its orbital eccentricity and precession change in a way that cannot themselves be easily explained. One explanation refers to the proposed 2 dimensional (2-D) gravitational field effect of relativistic frame dragging by the central supermassive black hole at the center of our galaxy. The short range usually attributed to frame dragging is not relevant to 2-D frame dragging because the proposed condensing of the black hole 3-D gravitational sphere of influence to a 2-D entity extends the radius of the frame dragging effect many orders of magnitude so that it affects the stars and other co-rotating systems as far out as earth and even farther.

An analysis of data records collected with the Lunar Laser Ranging (LLR) technique performed with better tidal models was unable to resolve the issue of the anomalous rate of change in eccentricity de/dt  of the orbit of the Moon, which has a magnitude of de/dt = (5±210-12 yr -1. Cosmological explanations fail: none of these is successful in reproducing the effect, since their predicted rates of change in lunar eccentricity are too small by several orders of magnitude.

Frame dragging declines as around 1/r3 for a normal classic theoretical unperturbed black hole, it appears. But a real supermassive black hole may have 2-D frame dragging declining as 1/r2 or even 1/r. Relativistic analysis should provide an exact numerical estimate.

This suggests a critical test of the 2-D gravitational field proposal. The gist of the test is that anomalous changes in orbital eccentricity and orbital axis of rotation should be detectable in binary stars and perhaps even in the orbits of planetary moons such as Mars’ Phobos and Deimos.  The Mars system can be considered as a simple binary system because Mars’ moons are not massive enough to significantly affect each other and their relative distances a generally too far. A three body gravitational system may be too complex to analyze accurately.

There may be other candidates for planet/moon anomalous orbital precession and eccentricity if the many body model of gravitation obstacle could be overcome (with ultra precise measurements and supercomputer assistance, say). But, all the other planets either have many moons or else have no known moons (Venus and Mercury). We could put moons (satellites) into orbit around Venus (say) and track these orbits as precisely as with LLR.

[1]  Anomalous precession of the axis of orbital rotation of earth/moon system, the lingering anomalous secular increase of the eccentricity of the orbit of the Moon: further attempts of explanation of cosmological origin,  Lorenzo Iorio,, submitted to Arxiv on 26 Apr 2014)


1 comment:

Gary A Kent said...


The orbital path of one of a pair or group of orbiting objects which orbit a planet, star or black hole together. They coorbit as a group.