Feb 232017
 

I figured what the world was lacking was a simple line drawing diagram showing the worlds of the TRAPPIST-1 system to actual scale. The worlds are to scale in both diameter and orbital radii.

Considering some additions. The main one: comparison of how big the primaries are in the skies of the secondaries. Suggestions?

 

Note: TRAPPIST-1 is the headlining image on Google today. It’s actually pretty cute.

UPDATE:

Here’s what things look like from other things. On the far left is how Jupiter looks in the sky of the four Galilean moons, compared to how Luna looks from Earth and Earth looks from Luna. One the top right is how the TRAPPIST-1 star looks from its various planets. Note that even though the star is *dinky,* it is gigantic in the sky  of its planets due to proximity. For all of them, the star is bigger than the moon as seen from Earth (and thus bigger than Sol in Earths sky).

At lower left is how some of the planets look from some of the other planets at closest approach. Note that virtually all closest approaches are *substantially* bigger in the sky than the moon in Earths sky, though none are as big as the Earth in Lunas sky.

Note that all three of these views are to the same scale. Jupiter from Io would be an amazing and quickly fatal sight.

Here’s just the planet-to-planet view:

 Posted by at 8:28 pm
  • fsdg dfgsgd

    The WSJ article about this had a quote from one of the scientists involved that said you would see wandering planets in the sky that were about the size of the moon. Combine this with the MOST EXCELLENT comments in one of your previous posts about how most of the daytime sky might be black with stars, and you get a picture more amazing than any I remember seeing in sci-fi/fantasy art. Wow.

  • se jones
    • publiusr

      While the rest of the universe yells “get your hot Jupiters”
      trappist has to be the cat lady of Earth sized worlds…I want a rocky planet tax–share the wealth lady–you have a hoarding problem

      • se jones

        >cat lady of Earth sized worlds

        You are a wordsmith extraordinaire

        • publiusr

          I try–although I can be trying at times….

  • se jones

    Speaking of gravity wells and great views from night skies: JWST, TESS, WFIRST & CHEOPS should all be able to tease* out signals from some of the larger moons** in the TRAPPIST-1 system (depending on observer time allotted, orbital inclinations of the moons and in the case of TESS, getting a mission extension ’cause I doubt TRAPPIST-1 is in its catalog of 200k brightest local stars)

    *professional drivers only. Do not attempt at home.
    **estimate only, results may vary.

    • Herp McDerp

      I doubt that these planets have any moons large enough to be detectable. Perturbations from the other planets and (especially) tidal interactions with the primary would pretty much guarantee that the moons’ orbits would be disrupted. Each planet’s Hill sphere is going to be pretty small.

      If TRAPPIST-1 has planets in larger orbits — especially more massive planets — they might have moons … but we’d have to be extremely lucky to see any transits by such planets. Scott’s scale diagram of the system shows how lucky we are to see anytransits at all; tip the plane of the orbits by even one degree, and we’d miss most of them.

      • se jones

        I thought of that, but the accepted theories of planet formation leading to this sort of system, require the inward migration of the planets from their initial states. The star has high metallicity, giving better odds of any moons being rocky (or even metallic like Psyche?) which reduces the Roche radius.
        You may be right, but nature is full of surprises. Much modeling is called for.

        “…extremely lucky to see any transits”. You bet, but luck was on our side, so we *do* see this system edge on. Odds are also good that any moons will orbit their primary in a plane close to the TRAPPIST-1 ecliptic plane. As the primaries orbit the star, at *some* point (twice) each orbit (year) we could get transits if the line of nodes is close to our line of sight. I say “close” because any moons would, of necessity, be close to their primary thus giving us better odds of transits.

        Every observation depends on S/N, and this TRAPPIST-1 systems is just about “best case” for S/N, with a dim star, in our local hood, good geometry, short orbital periods, and lots of ideal new instruments coming online in the near future.

        • Herp McDerp

          i>I say “close” because any moons would, of necessity, be close to their primary thus giving us better odds of transits.

          They would have to be, to stay within the planet’s Hill sphere … but they wouldn’t stay there for very long. The orbits of any moons in this system will evolve very rapidly due to fierce star-planet-moon tidal effects. In general, if the moon’s orbital period is the same as or faster than the planet’s day, the moon will spiral inward (e.g., Phobos); if the planet rotates faster than the moon orbits, the moon will spiral outward (e.g., Luna).

          Still, we should look … because as you say, Nature is full of surprises. We once “knew” that Mercury was a one-face world, asteroids didn’t have satellites, Jupiter didn’t have rings, Pluto was probably an escaped moon of Neptune, novae were caused by stellar collisions, and planetary systems would always have their jovian planets located beyond the “snow line” … There’s no telling what we might find.

          For reasons of orbital stability, I think it would be far more likely that this system has Trojan planets instead of planetary satellites.

          • se jones

            The planets are probably all tidally locked to the star, so therefor any moons would orbital periods would be *Much* faster than the planet’s day. But the hope is, forming only ≈500Ma, there might be some moons that haven’t spiraled in yet, -or- there’s some crazy resonances that serve to pump some moons orbits *up* into some complicated “valley” of stability in the three+ body systems. The planets are already in resonant orbits, if a moon’s orbital period reaches an integral fraction of its primary’s neighboring planet’s “year”, things might evolve to be stable.

            But yeah, the whole system probably conspires to kick moons out and Trojans are more likely. Like you say, never hurts to look.

  • Herp McDerp

    Note that even though the star is *dinky,* it is gigantic in the sky of
    its planets due to proximity. For all of them, the star is bigger than
    the moon as seen from Earth (and thus bigger than Sol in Earths sky).

    A back-of-the-envelope calculation shows why this has to be. To a first approximation, stars are blackbodies as far as their radiated energy is concerned. According to the Stefan–Boltzmann law, the power radiated per unit surface area of a blackbody scales with the fourth power of the temperature. The surface temperature of TRAPPIST-1, 2550 K, is only about 44 percent of the Sun’s surface temperature, 5770 K. Since the surface brightness of a visually resolved object does not vary with its distance (which boggled be the first time I encountered the claim, but it’s true!), for a T-1 planet to get the same total amount of energy (integrated over all wavelengths) as Earth gets from the Sun the angular area of TRAPPIST-1 in the sky would have to be about 27 times the area of the Sun in our sky. That’s roughly five times the Sun’s angular diameter — a bit larger than Earth seen from Luna.

    Hmm. That doesn’t quite agree with the published figures, but (A) it’s a BOTE calculation, (B) T-1’s planets aren’t at exactly the same temperature as Earth, (C) T-1 isn’t a perfect blackbody, and (D) I may have made a mistake somewhere …

    • Herp McDerp

      tl;dr: Since TRAPPIST-1 is so much cooler than the Sun, it has to appear much bigger in the sky to keep a planet as warm as Earth is. Physics and arithmetic can tell you how much bigger.

    • publiusr

      Here is an idea for you to shoot down.

      Trappist was a Jovian type system. Parent star destroyed by some catastrophe–outgasses.

      Gas giant absorbs this and lights up after the main actors leave the stage.

      The only way the scenario from the end of “2010” can work.

      • Herp McDerp

        Okay, two problems with this:

        * What sort of catastrophe? Is there no other remnant of the parent star than some left-over gas? Why didn’t the catastrophe affect the jovian system, too?

        * It’s unnecessary: there are a lot of red dwarfs in the galaxy, more than all the other brighter stars combined — and larger objects being orbited by smaller satellites seems to be a common feature of most normal stars, brown dwarfs, planets, and even white dwarfs and neutron stars. Most of these satellites are in well-behaved, regularly spaced orbits because any satellites that weren’t in such orbits were eliminated by collisions or expulsions. (When we see planets orbiting stars in markedly non-circular orbits, the explanation that seems most likely is that they’re the left-overs of gravitational encounters that expelled other planets.)

        The end of 2010 works because the multiplying monoliths use BFM to ignite Jupiter. (IIRC, we aren’t told whether it’s hydrogen fusion or just the energy of gravitational collapse that makes Jupiter shine.)

        • publiusr

          What I was thinking of was some other object hit the main star from “below” and all the remnants have had time to move far enough away to look like unrelated objects.

          Just a guess–but those are for shooting down.

          This system is just so compact–same physics as with pulsat planets I suppose–drag from outgassing just brings everything closer in.

          That would look to leave more of a mess however, as opposed to a tightly bound jovian system build up just enough–with everything else evacuated by another passing object….

          • Herp McDerp

            That would look to leave more of a mess however, as opposed to a tightly bound jovian system …

            This system is very tightly bound. TRAPPIST-1 has about 80 times the mass of Jupiter, but its “satellite” system is nearly as compact as Jupiter’s. There’s a deep, steep gravitational potential well around the star.

            For people who like to play with planets and their orbits, I heartily recommend the “Super Planet Crash” page at http://www.stefanom.org/spc/ .

          • Herp McDerp

            Re: “Super Planet Crash” ( http://www.stefanom.org/spc/ ) … Try putting ten or twelve Earth-mass planets in orbits very close to the star. It’s almost impossible to eject any of them, because their mutual encounters don’t give them enough energy to escape the star’s gravity well.

    • se jones

      “…Since the surface brightness of a visually resolved object does not vary with its distance (which boggled…”

      Yes, which is related inversely to the old “can you start a fire with moonlight” trick question.
      I say trick because many people who should know better will refuse to admit this, even though the math don’t lie.

  • Michel Van

    Thanks for the diagrams !
    with them i realized HOW small the system is it could fit in side The Saturn Moons System !

    but there allot open question:
    Were are the gas giants of TRAPPIST-1 system ?
    How keep this planetary system stable without collition or catapult a Planet out ?

    For Surface condition on TRAPPIST-1 F, D, E
    will be troubled with Tidal heating ?
    (that if there orbit is not 100 % circular and Star gravitation knead the Planet like moon Io
    In that case the Planet F,D,E will look more like Venus instead of Earth)

    next to that there will a lot of earthquakes, if planet past each other on there Orbit

  • se jones

    Very nice work Scott!
    Your illustrations are so much cleaner and easy to interpret than the tarted up NASA stuff.

  • Rush Allen

    https://uploads.disquscdn.com/images/6e6950e5594f0ed02e225d727fce3f8537974c4d5431a2b2ad39205fc52eae22.jpg The published data indicates that the exoplanets have an inclination of essentially 90 degrees to the plane of the line of sight. But, is there any data indicating the angle of the inclination around the line sight as the hour hand of a clock? Since the star sits close to the Solar Ecliptic Plane the two stars could share the same geometric plane, though unlikely. If the clock face angle is roughly parallel to the ecliptic (~9:30 to 3:30) the Trappist-1 planets would trace seven halos over the Cup of Aquarius.