Weird Worlds: Kepler 11

This week I decided to talk about some of the weird, wacky and real exoplanets that we have discovered. I am going to just focus on a few with possibly more to come at a later date.

Kepler 11

I have mentioned it in the past and the Kepler Mission is certainly the current poster-child of the planet-spotting community. It has been staring at a patch of sky near celestial north since 2009 and in that time has found 1235 potential planets, 16 of which have been confirmed and most of which require further investigation.

There are six confirmed planets in the Kepler 11 system (the star, which was too far away and hence dim to have a better name, is designated Kepler 11). The star is similar to our sun. The planets orbiting it, however, are nothing like our solar system. Five of the planets are within what would be the orbit of Mercury if they were in our solar system. The outermost (or at least, the outermost discovered so far) is just outside the orbit of Mercury. They are also all relatively small, on the scale of previously discovered exoplanets, but much larger than our rocky worlds. They range in mass from 2.3 times the mass of Earth to slightly less than the mass of Jupiter (about 300 times the mass of Earth) and size from 1.93 Earth radii to 0.4 Jupiter radii or about 4.4 Earth radii (interestingly, the smallest isn't the lightest—Kepler 11-f is much less dense than Kepler 11-b). Their years range from 10.3 to 118.4 Earth days. For comparison, Mercury's year is about 88 Earth days.

Let's ignore the fact that all of these planets are too close to their sun to be habitable and have a think about what such a system would look like from within. From Earth, all the planets out to Uranus just look like bright stars which move across the sky. How different would the night sky look from a planet in the Kepler 11 system? For no particularly compelling reason, I'm going to work this out for Kepler 11-f which is the least massive and the second furthest out from the star.

First a picture. It's a (cropped) screenshot from this Exoplanet iPhone app, showing the Kepler 11 system. The planets aren't to scale with the star (they are very much inflated), but are to scale with each other.

Obviously the trails following the planets aren't real either, but are there just to give you an idea of the orbits. I like how the developer made it so only the side of the planet facing the star is lit up. Yay, realism.

Now some stats on the system, which I have mostly gotten from that Exoplanet iPhone app. Also, I'm going to abbreviate the names to Keb, Kec, Ked, Kee, Kef, Keg for Kepler 11-b through f. Because I can. (And if you're wondering, there's no Kepler 11-a because that designator is reserved for the star.)

• Keb: 
• 4.3 Earth masses, 
• 1.93 Earth radii, 
• orbit is 0.091 AU, 
• closest approach to Kef is 0.159 AU
• Kec: 
• 0.04 Jupiter masses = 12.7 Earth masses, 
• 3.09 Earth radii, 
• orbit is 0.106 AU, 
• closest approach to Kef is 0.144 AU
• Ked: 
• 6.10 Earth masses, 
• 0.31 Jupiter radii = 3.41 Earth radii, 
• orbit is 0.159 AU, 
• closest approach to Kef is 0.091 AU
• Kee: 
• 8.4 Earth masses, 
• 0.40 Jupiter radii = 4.4 Earth radii, 
• orbit is 0.194 AU, 
• closest approach to Kef is 0.056 AU
• Kef: 
• 2.3 Earth masses, 
• 2.56 Earth radii, 
• orbit is 0.25 AU
• Keg: 
• 0.95 Jupiter masses = 301 Earth masses, 
• 0.33 Jupiter radii = 3.6 Earth radii, 
• orbit is 0.462 AU, 
• closest approach to Kef is 0.212 AU

Now for some calculations. Using the formula from my very first blog post, I calculated how big the other planets would appear at their closest approach to Kef. Also how big the sun, Kepler 11 (or Kea, why not) would appear. For all of these, I'm going to list them in units of the diameter of the full moon, except for Kea which I list in units of the diameter of the sun (because it's a star. Actually the angular diameter of the sun and the moon are roughly equal, which is why we get such nice looking solar eclipses). Also, this wiki table is useful for comparing how big things are in Kef's sky with how big things are in our sky. For future comparison, Venus varies in size from 0.16'-1.1' where the ' indicates arcminutes and there are 60 arcminutes in a degree. At it's closest visible point, however, Venus is a crescent that size, and full only at it's farthest point. That's about a thirtieth (0.036) of the size of the full moon. Easily resolvable with a telescope, but not quite resolvable as a disc with the naked eye.

At their furthest from Kef, all 5 other planets are similar to the size of Venus at it's furthest (and also it's fullest since that's when they are on the opposite side of Kea to Kef). At their closest approaches, however, there's a bit more variation. Remember for all of these except Keg the planets would be crescents of this size and only Keg would be full. Furthermore, I do declare that 1 FM (full moon) = 0.5º, and is the units I've used below. Because I didn't think anything would be gained by copy-pasting  "times the size of the full moon as seen from Earth" five times. (This is totally how units are invented. ;-p ) I may have also included some of the values as fractions.

• Keb: 0.05 – 0.1 FM (max is a tenth)
• Kec: 0.08 – 0.2 FM (max is a fifth)
• Ked: 0.08 – 0.3 FM (max is approximately a third)
• Kee: 0.1 – 0.7 FM (max is around two thirds)
• Keg: 0.05 – 0.15 FM (max is almost a seventh)

I'm not really sure about Keb, Kec and Keg—I suspect they may just look like very bright stars—but the other two would definitely be visible as circles/crescents to the naked eye. The night sky of Kef would be a very different place to ours. I can't help but think that with such obvious neighbouring planets any intelligent life that evolved on Kef would work out celestial mechanics rather more quickly than we did. After all, we had to really pay attention to the sky to notice that some of the shiny points of light moved while others didn't. Not that life as we know it is likely to have evolved on Kef. Which brings me to the day sky.

Kef's sun, Kea, would be 4.7 times the size of Sol in our sky. Almost five times as big. (For those keeping track, that's the same as saying almost five times the size (width) of the full moon. That might actually be easier to visualise since it doesn't generally hurt to look at the moon.) It would also be around 22 times brighter than our sun, giving Kef 22 times as much energy as the sun gives Earth. Do you see why Kef might not be particularly habitable? Kind of like how you wouldn't want to live on Mercury, but more so.

Also, as you may have surmised from the first set of data I dumped, Kef isn't very dense. Density is given by mass divided by volume and volume is proportional to the radius cubed (actually, for a sphere, volume is ⁴/₃ π R³). So Kef is only 0.14 times the density of Earth and, if it had a solid surface, which is highly unlikely, it would have a surface gravity of around a third of Earth's (similar to Mars's), despite being more massive. It's actually about three quarters the density of water, which isn't that surprising because if it were made of water (and I have absolutely no idea what it's composition is), we wouldn't expect water to be liquid in those conditions. What's interesting is that of the other planets, the two innermost are comparable to Mars in density (less dense, but close), the next three, Ked-f are comparable to Saturn (Saturn actually lies between Kef and Kee with Ked being a bit denser) and the outermost, Keg, is ridiculously dense. Like, denser than Osmium, the densest natural element. I think what this really highlights is how we only have an idea of planet size from the amount of dimming we see when it passes in front of the sun. The mass of the planets is worked out from the gravitational tugs they exert on each other in multi-planet systems (for transiting planets like the ones Kepler is looking for, that is). I'm willing to believe the densities of the other 5 planets, but I think I'll wait for better data before believing Keg.

My original plan was to talk about a variety of weird worlds in this post, but I got a bit carried away with Kepler 11, it seems. Stay tuned for more weird worlds in the future.