# Orbit of a double planet

In a system where 2 planets of similar mass are orbiting around a common barycenter, would the following configuration considered stable on the long run?

• They orbit at 1,6 AU from their star
• The star is a F8 and is 19% more massive than the Sun
• One planet is the same size and mass than Earth, but the other is 10% more massive
• They are located roughly at 90 000 km form their common barycenter
• They are tidally locked to each other
• Their double planet system is tilted at 25 degrees, so they can have seasons

Is it flawless?

Note that the concept is not mine (source) but I want to know if it works.

• It seems fine, at a glance. The star stats are typical, the orbital radius is fine, the masses aren't unnatural, the semi-major axis is okay, the tilt is plausible, and tidal locking is possible in this setup. I think the answer is a simple "yes". I can't speak for whether or not some of the calculated numbers in the link work out, but all this seems fine. – HDE 226868 Aug 2 '15 at 19:23

Okay, let's look at this:

We have a yellow-white F8 star somewhat larger than our sun, with the planets orbiting at 1.6 AU. This is in the correct ballpark for the worlds to be in the habitable zone of such a star. However, please note the somewhat higher UV output of the star.

A point to consider is that during the spring and autumn equinoxes, there could be repeated solar eclipses over the course of a number of local days - which, given the mass of the larger world as 7.1768*10^24kg (being 1.2 times that of Earth at 5.98×10^24kg) and the distance of 180,000km, would be 8d 0h 37m 5.59s. If I'm wrong, and the orbital separation is 90,000, the orbital period/day length would be 2d 20h 6m 2.97s. The latter would be more hospitable, though either way, there would be a large difference between day-time and night-time temperatures either way. Given the details given in http://www.cartographersguild.com/showthread.php?t=28951, it would appear that a day length of 62h and an orbital separation of 90,000km is the correct figure. Using the stated planetary mass from that page and the larger world's geosynchronous orbital radius of 89,238km, we get an orbital period/day length of 2d 14h 6m 6.86s. This is around 6h different from the value obtained using the figures in the OP's question so please note the importance of exact figures.

For the planets to be tidally locked at 180000km separation is also plausible, and even more so at 90,000km, given their mass. That their plane of common orbit is tilted 25° could be a problem - the sun 's gravity would be trying to pull this back into the plane of the ecliptic, but it isn't beyond the bounds of possibility.

One point is made in the referenced thread, that:

Deianira may not be relevant to the story, but it is relevant to the planetary info because the two planets are tidally locked to one another, orbiting a common barycenter. This is the closest celestial body that Eurydice has to a moon, which means, at least by my friend's and my estimates, that the core of Eurydice is going to be as much as twice as hot as that of Earth due to increased gravitational pull from this very large planet that it is tidally locked to.

This fails to take into account the factor that the worlds are tidally locked when considering the effect of tidal effects on core heating. Since the operative factor is being tidally locked, there is no varying vector of gravitational attraction to apply varying forces to the worlds such that they would be causing a constant change in shape, and the presence of the opposing world would not contribute to core heating at all, as opposed to twice that of the earth/moon system. In order for the presence of such a large "moon" to have any effect on core heating, the worlds would have to be not tidally locked, and the degree of heating would depend on the perceived orbital times.

Anyway, with a solar day of 62h, there are going to be colder nights and hotter days than on earth. Depending on various environmental factors, you could well get frost every night, even in the tropics.

• Their local sun's tide will be trying to slow down the orbits of these planets so the differences between the double planet tide and stellar tides will cause tidal heating and eventually lead to the orbital decay of the planets. – Jim2B Aug 3 '15 at 2:27
• @Jim2B That's an incredibly slow process though, look at how slowly our moon's orbit is changing for example. – Tim B Aug 3 '15 at 7:59
• True but the more rapid the orbit, I think the more rapid the orbit the more of an effect the solar tide will have. On the other hand, the brighter star means they'll be further away and tides vary by $\frac{1}{r^3}$. – Jim2B Aug 3 '15 at 18:17