Thanks for the replies. I will look on it later. It seems that you refer to point masses when volume distributions have to be considered.
David David Jonsson, Sweden, phone callto:+46703000370 On Wed, Mar 3, 2010 at 4:42 PM, Stephen A. Lawrence <[email protected]> wrote: > > > On 03/03/2010 10:27 AM, Stephen A. Lawrence wrote: > > I don't really understand how tidal and retarded effects can cancel. > > > > Tidal effects are only detectable on extended bodies, and the "tidal > > force" generally (always?) has nonzero divergence. > > Actually I think that's wrong -- I don't think it's *divergence* that I > mean here; the tidal forces "diverge vertically" and "converge > horizontally" and the result is the net divergence stays zero. > > Just fished around a bit on the Web. You've got tidal forces when the > Weyl tensor is nonzero. See, for instance: > > http://www.answers.com/topic/weyl-curvature > http://en.wikipedia.org/wiki/Congruence_%28general_relativity%29 > > That's from GR but the same general concept is going to apply to > Newtonian gravity as well, since the theories are essentially identical > anyplace where conditions are mild enough for humans to live comfortably > (surface of the Sun, or anyplace inside the orbit of Mercury, are > examples of places where it's not "comfortable"). > > I don't think retarding the gravity field results in a nonzero Weyl > tensor, and in "small field" conditions these tensors are going to be > combining more or less linearly, so, again, I don't see how the effects > of retardation can cancel tidal forces. > > > > > > On the other hand, the retarded gravity effect typically manifests > > itself as a rotation of the acceleration vector versus what you'd > > calculate given the (calculated) current position of the gravitating > > body. It's detectable by its action on point particles, which don't > > accelerate as Newtonian theory would predict. > > > > But the divergence of retarded gravity is still zero where the mass > > density is zero. > > > > So, again, I don't see how they can cancel. > > > > I also question this assertion: > > > > [DJ:] > >> If either of these effects are acting on a body its orbit will become > >> unstable. > > > > I don't understand what you mean by this. Tidal forces act on all > > planets, without exception, if they're in orbit. But as long as the > > planet's own gravity is larger than the tidal forces acting on it, that > > doesn't result in instability in its orbit. In fact the effect of tidal > > forces can be to "lock" a planet into a particular orbit and rotation > > rate -- in other words, tidal forces can make the orbit *more* stable. > > > > > > On 03/01/2010 04:13 PM, David Jonsson wrote: > >> Hi > >> > >> My own posting today on Usenet. > >> > >> I would be glad if someone could help me with how to calculate this for > >> some examples to see if there is any reason in it. > >> > >> David > >> > >> David Jonsson, Sweden, phone callto:+46703000370 > >> > >> > >> ---------- Forwarded message ---------- > >> From: *David Jonsson* <[email protected] > >> <mailto:[email protected]>> > >> Date: Mon, Mar 1, 2010 at 6:41 PM > >> Subject: Can retarded gravity be counteracted by tidal acceleration? > >> To: [email protected] <mailto:[email protected]> > >> > >> > >> Could the accelerating tidal effects > >> http://en.wikipedia.org/wiki/Tidal_acceleration > >> be cancelled by retarded gravity effects > >> http://en.wikipedia.org/wiki/Speed_of_gravity ? > >> > >> If either of these effects are acting on a body its orbit will become > >> unstable. Tidal forces are almost always accelerating and the retarded > >> gravity effect is decelerating an astronomical body. Maybe there are > >> conditions when the two effects balances each other and maybe these > >> conditions form the structure known as the Titius series which is > >> purely empirical and not yet explained > >> http://en.wikipedia.org/wiki/Titius–Bode_law > >> . > >> Exoplanets give new cases to test this idea. Moons, rings and pulsars > >> could also be tested against this idea. > >> > >> David > >> > > > > > >
