[Morwen]

Well, the case of Eärendil surely is not the "normal" astrology, as it was only one rare occassion. Similarly in Frodo's case, I always considered this star rather being there to evoke the image of the Eye of Sauron (it is said there that it seemed to Frodo like an eye), of course I don't think it was THE Eye, but rather Frodo's subconscious stirred after the recent events transformed this star in his mind to the sign of something scary (reminds me of Lovecraft's "Polaris" and things like "What the Moon brings" here - Frodo's state of mind clearly was not perfectly okay at that time).

I'm not suggesting that the appearance of Gil-Estel was "normal" merely that it was thought significant (as it was).

The Hunter's Moon waxed round in the night sky, and put to flight all the lesser stars. But low in the South one star shone red. Every night, as the Moon waned again, it shone brighter and brighter. Frodo could see it from his window, deep in the heavens, burning like a watchful eye that glared above the trees on the brink of the valley.
FotR, The Ring Goes South

I agree that the comparison of the star to an eye is meant to evoke the image of Sauron's Eye. However, Frodo is actually supposed to be observing a bright red star, one that grows ever brighter and such a symbol has been used to signify times of turmoil. There may not be in Middle Earth a practice of observing the movements of the planets and stars to predict events on a personal level. But odd happenings in the heavens may be taken to predict general events and be seen as signs of hope (Gil-Estel) or war (bright red star).