Due to a number of things I’ve been confused and uncertain of late, my research has gone in a lot of strange and disparate directions. My discovery of, “Stability of Satellites Around Close-in Extrasolar Planets”, had obvious connection to my work on the Yaccatrice/Sky Moon system orbiting Cintilla. I haven’t had a chance to dig too deeply into this one, but initial impressions give good reason for optimism. Early in the article, it gives a critical orbital semimajor axis for the outermost stable orbit around a body itself orbiting another body. This critical orbit is a constant fraction of the Hill radius for the body being orbited with respect to the larger body it in turn is orbiting…

That’s confusing. Sorry. In order to have a stable orbit around a planet, a moon must orbit within a fraction of 0.36 of the Hill radius of the planet. Yaccatrice orbits Sky Moon at about half this distance. Good sign! Also, looking at figure three on page 1092(the pages are journal pages, the article isn’t that verbose), I note that for a planet to have an Earth-mass moon orbiting in the habitable zone of a 0.3 Solar mass star it would need to have a mass of about 2 Jupiters. Sky Moon only has a mass of about 1.5 Jupiters, but Yaccatrice, for it’s part only has a mass of about 0.6 Earths. Since the minimum mass for the planet seems to be related to the mass of the moon raised to the 3/8 power then the planet Yaccatrice orbits should be at least 0.818 as massive as a planet suitable to retain an Earth-mass moon. If I’m reading the graph right and a planet of just less than 2 Jupiter masses is capable of retaining an Earth mass moon on the order of 5 billion years, then Sky Moon would have to have a mass of about 520 Earth masses. More actually, because Barnes and O’Brien are assuming the radius to be about the same as that of Jupiter and the required mass is proportional to the 15/8ths power of planet radius. I may have to promote Sky Moon to be a large gas giant of around 600 Earth masses to make Yaccatrice work.

On the one hand, that means more work. On the other hand, that means a well-grounded and supportable case for the realism of my planet. On the gripping hand, I have a closed function to use to determine masses in these close-in systems. Okay…

I also like this article because it references two text books I have in my own personal library, Hansen and Kawaler’s Stellar Interiors and Hubbard’s Planetary Interiors. I’ll have to see if Amazon carries these and add them to the World Builder’s Bookshelf :).

Another article of interest, referenced from the previous article was Holman and Wiegert’s, “Long-Term Stability of Planets In Binary Systems.” If I scanned over the previous article, I’ve barely more than looked at this one. All I can say is this one looks really promising for at least a good sanity check of orbits in binary systems and seems to give some good closed equations or inequalities describing required stellar and planetary parameters in such systems.

Some additional related links that I have yet to properly peruse or more than cursorily observe.

Exoplanetary formation in S–type binary star systems,” Turrini, Barbieri et al. 2006.

Formation and Detectability of Terrestrial Planets around α Centauri B,” Guedes, Rivera et al. ????.

Formation and detectability of Earth-like planets around Alpha-Centauri B,” Davis. 2007.(note: The Cambridge journals site seems to be a bit persnickety so persistence is in order. Once you have the document… Save it!… They may not let you back in…)

Terrestrial Planet Formation in Binary Star Systems,” Quintana. 2007.

The stability of planets in the Alpha Centauri system,” Wiegert & Holman. 1996.

Dynamical Stability of Earth-Like Planetary Orbits in Binary Systems,” David, Quintana et al. 2003.

And one of those little things you just run across while googling for something else, “The Odds for Life on a Moonless Earth,” Redd. 2011.

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