Science fiction stories in movies and television set on other worlds frequently present views of spectacular arrangements of moons, looming giant planets and multiple suns of the sort we do not see in our sky here on Earth. Here we have but a single large moon and a single sun with the planets visible as nothing more than bright points of light that slowly move over time against the stars. But with the discovery of extrasolar planets starting over two decades ago, we are beginning to find exoplanets whose skies are potentially much more interesting than ours and begin to resemble those of fictional worlds we have imagined for decades.

Probably one of the more interesting systems among our nearby stellar neighbors is that of TRAPPIST-1 which has seven known Earth-size exoplanets. Unlike here on Earth where the planets are mere points of light, these exoplanets would appear as distinct disks when viewed from any one of these worlds which would change in size, phase and position on time scales of a many days to just a matter of hours owing to their tight, short-period orbits. So what would some far-future human visitor see in the skies of the worlds of TRAPPIST-1?

Background

TRAPPIST-1 (also know by the 2MASS catalog designation J23062928-0502285) is a dim, ultracool dwarf star with an apparent V magnitude of just 18.8 located 39.6 light years away in the constellation of Aries. Based on the latest analysis of available data by Van Grootel et al., TRAPPIST-1 has a mass of 0.089±0.007 times that of the Sun, a radius of 0.121±0.003 times, a luminosity of 0.000522±0.000019 times and an effective surface temperature of 2511±37 K with a spectral type of M8. TRAPPIST-1 is almost as small as a star can be and still support the fusion of hydrogen in its core. And with a diameter of 168,000 kilometers, it is only slightly larger than Jupiter with a mean diameter of 139,800 kilometers (although with 93 times Jupiter’s mass, TRAPPIST-1 is about 54 times denser). The best estimate of the age of TRAPPIST-1 based on models of stellar evolution is about 7.6±2.2 billion years – older than the Sun but still only a tiny fraction of this small star’s lifetime which is likely to be a few trillion years.

TRAPPIST-1 got its name from the TRAPPIST (TRAnsiting Planets and PlanetesImals Small Telescope) survey. This star is one of about 60 ultracool dwarf stars in the southern skies whose brightness has been regularly monitored by the 0.6-meter telescope now called TRAPPIST-South located at ESO’s facility in La Silla, Chile. The purpose of the TRAPPIST survey is to look for periodic dips in the brightness of these small stars indicating the presence of transiting exoplanets. On May 2, 2016 the TRAPPIST team led by Michaël Gillon (University of Liège – Belgium) announced the discovery of three Earth-size planets orbiting TRAPPIST-1 accompanied by the dubious claim that two of them were potentially habitable (see “Habitable Planet Reality Check: TRAPPIST-1”). Using additional observations from ground-based instruments and NASA Spitzer Space Telescope, on February 22, 2017 Gillion et al. announced the discovery of a total of seven exoplanets in this system all with about the same size as the Earth. An initial assessment of this new group of exoplanets shows that three of them orbit inside reasonably conservative definitions of the habitable zone making this system a prime target for the future studies of such worlds (for a full discussion of the discovery of these worlds and an initial assessment of their potential habitability, see “Habitable Planet Reality Check: The Seven Planets of TRAPPIST-1”). Table 1 provides a summary of the orbit parameters of these seven exoplanets based on analyses by Delrez et al. and Grimm et al. using these earlier data plus new observations obtained since.

Table 1: TRAPPIST-1 Planet Orbit Properties (from Delrez et al. and Grimm et al.)

Planet Period (days) Semimajor Axis (10-3 AU) Inclination (°) Eccentricity b 1.511 11.50 +0.28/-0.25 89.56 ±0.23 0.0062 ±0.0030 c 2.422 15.76 +0.38/-0.34 89.70 ±0.18 0.0065 ±0.0019 d 4.050 22.19 +0.53/-0.48 89.89 +0.08/-0.15 0.0084 ±0.0009 e 6.099 29.16 +0.70/-0.63 89.736 +0.053/-0.066 0.0051 ±0.0006 f 9.206 38.36 +0.92/-0.84 89.719 +0.026/-0.039 0.0101 ±0.0007 g 12.354 46.7 ±1.1 89.721 +0.019/-0.026 0.0021 ±0.0006 h 18.768 67.1 +1.5/-1.3 89.796 ±0.023 0.0057 ±0.0012

Aside from basic orbit parameters, only the planets’ radius can be readily determined from transit observations. In order to calculate the bulk density of these exoplanets (which can be used to constrain their compositions and structures), the mass must also be known. While the use of precision radial velocity measurements have been used to determine the masses of some transiting exoplanets, the dimness of TRAPPIST-1 makes this impossible with the current instruments. We will have to wait for the next generation of instruments which operate in the near infrared (where ultracool dwarfs TRAPPIST-1 are much brighter) to gather the required radial velocity data.

Fortunately, the seven exoplanets of TRAPPIST-1 form a resonance chain with orbital period ratios of about 24:15:9:6:4:3:2. These resonances amplify the effects of gravitational interactions between these exoplanets which result in measurable transit time variations(TTVs) of up to an hour or so. In their 2017 discovery paper, Gillon et al. used these TTVs to derive initial mass estimates for the inner six exoplanets but the uncertainties were fairly large. A newer analysis by Grimm et al. based on a significantly expanded transit timing data set has been able to reduce the uncertainties to a level where meaningful constraints can be set on these exoplanets’ mean density. The latest properties for the planets in the TRAPPIST-1 system based on the work of Delrez et al. and Grimm et al. are summarized below in Table 2. Also included is the amount of energy each exoplanet receives from its host star, or effective stellar flux (S eff ), compared to Earth.

Table 2: TRAPPIST-1 Planet Properties (from Delrez et al. and Grimm et al.)

Planet Radius (Earth=1) Mass (Earth=1) Density (Earth=1) S eff (Earth=1) b 1.127 ±0.028 1.02 +0.12/-0.15 0.73 ±0.09 3.9 ±0.2 c 1.100 ±0.028 1.16 +0.13/-0.14 0.88 ±0.08 2.1 ±0.1 d 0.788 ±0.020 0.30 ±0.04 0.62 +0.06/-0.07 1.04 ±0.06 e 0.915 ±0.025 0.77 ±0.08 1.02 +0.07/0.08 0.60 ±0.03 f 1.052 ±0.026 0.93 ±0.08 0.82 ±0.04 0.35 ±0.02 g 1.154 ±0.029 1.15 ±0.10 0.76 ±0.03 0.24 ±0.01 h 0.777 ±0.025 0.33 ±0.05/-0.06 0.72 +0.10/-0.12 0.14 +0.08/-0.07

While TRAPPIST-1d, e and f have S eff values which are broadly consistent with many definitions of the habitable zone, most of the exoplanets in this system seem to have mean densities less than that of Earth suggesting that they have large inventories of volatiles including water, hydrogen and helium. While the presence of water suggests that the planets of small red dwarfs can retain their volatiles despite some of the more dire predictions which have been made in recent years, too much water and the accompanying thick atmospheres would result in these worlds resembling mini-Neptunes with little chance of being habitable in the Earth-like sense. The one clear exception seems to be TRAPPIST-1e which is just a little smaller than the Earth yet retains an Earth-like bulk composition. Combined with a S eff of 0.60 times that of Earth, this exoplanet would seem to have the best prospects of being potentially habitable. With this information about the exoplanets of this system, we can begin to make predictions about the view from these worlds and how it changes over time.

The Sky of TRAPPIST-1e

In order to simplify this analysis, we will confine ourselves to assessing the view from just one of these exoplanets, namely TRAPPIST-1e. Besides being the most Earth-like of the planets in this system (at least in terms of bulk properties), it is located in the middle of the system with three inner planets (also known as “inferior planets”) and three outer planets (or “superior planets”) visible from its surface providing a fairly representative view. Another simplification made in the calculations which follow is the assumption that the orbits of these seven planets are circular. Given that their orbital eccentricities as determined by dynamical studies by Grimm et al. are all <0.01, this is a safe assumption.

Just as on Earth, the daytime view from the surface of TRAPPIST-1e will be dominated by its “sun”. But because of the very different properties of TRAPPIST-1 compared to the Sun, the system’s host star would also appear very different. For starters, TRAPPIST-1 would appear as a disk 2.21° across as viewed from Planet e compared to the average 0.53° apparent size of the Sun in Earth’s sky. Despite its much larger apparent size, the lower effective temperature of TRAPPIST-1 of 2511 K (compared to the Sun’s 5780 K) means that any given area is radiating only ~3.6% of the energy the Sun does. Even with the larger apparent size, TRAPPIST-1e would receive only 60% of the energy Earth receives from the Sun. From the point of view of TRAPPIST-1e, the Sun itself some 39.6 light years away would appear as a V magnitude 5.3 star in the constellation of Leo in the sky of TRAPPIST-1 – an insignificant star just barely visible to the unaided eye.

Based on the latest photometry, the apparent V magnitude of TRAPPIST-1 would be -20.9 as viewed from Planet e compared to the -26.7 of the Sun as viewed from the Earth. This large difference is mainly due to the much lower effective temperature of TRAPPIST-1 which radiates the majority of its energy at infrared wavelengths instead of the hotter Sun which radiates most of its energy at visible wavelengths. As a result, TRAPPIST-1 would appear 2.3 magnitudes brighter in the R band which is centered at redder wavelengths than the V band. But the difference in temperature is only part of the story. As can be seen in the comparison of the spectra of the Sun and TRAPPIST-1 below, the spectrum of the latter deviates significantly from a simple blackbody curve because of the presence of molecular absorption bands such as TiO which absorbs much light in the red end of the visible spectrum. Taking these effects into account, TRAPPIST-1 would appear only ~1.1% as bright at visible wavelengths as the Sun appears from the Earth – still too bright to safely view with the unaided eye especially when the much higher flux of invisible (but still potentially damaging) infrared light is considered. And because of its spectrum, TRAPPIST-1 would have a distinctly reddish-orange appearance with little light radiated at bluer wavelengths. Since TRAPPIST-1e (and its siblings) is expected to be a synchronous rotator which keeps the same side facing its sun, TRAPPIST-1 would appear fixed in the sky at any given location on the sunlit side of the planet and would never be visible on the perpetual night side. Climate models of such worlds suggest that circulation in the atmosphere and any oceans (if present) would help maintain habitable conditions across the planet’s surface.

Aside from differences in the appearance the sun, the sky itself would also appear very different. Here on the Earth with no clouds, hazes or other aerosols present, the sky looks distinctly blue due to Rayleigh scattering. Rayleigh scattering is caused by light bouncing off molecules of gas in the atmosphere and is significantly more efficient at bluer (i.e. shorter) wavelengths hence the blue skies on Earth. Even assuming that TRAPPIST-1e had an Earth-like atmosphere, its sky would be a different color owing to the lack of blue light in the spectrum of TRAPPIST-1. This would make the daytime sky appear only about 0.5% bright as it does on the Earth and it would have a distinctly yellow or possibly greenish-yellow appearance which would probably only be readily noticeable close to the horizon where the line of sight must pass through more of the atmosphere.

The presence of hazes would surely brighten this dark sky but the exact amount and resulting color would depend on the size and composition of the particles present in the atmosphere of TRAPPIST-1e. Water clouds, which are composed of water droplets and ice crystals typically much larger than the wavelength of light which reflect well across the visible spectrum, would appear bright reddish-orange against a very dark yellowish sky. This is in stark contrast to white clouds against a blue sky we see here on the Earth. Given the dark skies of TRAPPIST-1e assuming an Earth-like atmosphere, the other known planets in this system and even bright stars could be visible well away from the glare of the sun in daylight.

The View of the Inner Planets

The distances and apparent size of the inner planets for key events as viewed from TRAPPIST-1e are summarized below in Table 3. The synodic period is the average period of time between successive conjunctions as viewed from TRAPPIST-1e. Superior conjunction is when the inner planet is on the opposite side of the sun and would appear to be fully illuminated. Inferior conjunction occurs when the inner planet is lies between TRAPIIST-1e and its sun and all that is seen is the planet’s dark side save for a narrow crescent (if the planets do not line up precisely with respect to their sun) as well as light scattering through its atmosphere. Elongation is the angle between the planet being observed and the sun with greatest elongation being the farthest a planet appears from the sun. At this time the planet appears to be in a half illuminated phase.

Table 3: Key Events for Inner Planets as Viewed from TRAPPIST-1e

Planet b c d Synodic Period (days) 1.419 4.017 12.055 Distance at Superior Conjunction (106 km) 6.08 6.72 7.68 Apparent Size at Superior Conjunction (arc min) 8.1 7.2 4.5 Distance at Greatest Elongation (106 km) 4.01 3.67 2.83 Greatest Elongation Angle 23.2° 32.7° 49.6° Apparent Size at Greatest Elongation (arc min) 12.3 13.1 12.2 Distance at Inferior Conjunction (106 km) 2.64 2.00 1.04 Apparent Size at Inferior Conjunction (arc min) 18.7 24.0 33.1

As can be seen from Table 3, the synodic periods for the inner planets are in the 1.4 to 12 day range so that they move quickly and through all phases in a short period of time compared to the inner planets of our solar system or even the Moon. These planets would also appear as distinct disks during all parts of their orbits even to the unaided eye. The illustration below shows the apparent sizes and phases during key events compared to the Moon as viewed from the Earth.

While transits of the inner planets of our solar system across the face of the Sun are comparatively rare given their mutual inclinations and the large sizes of their orbits, that will probably not be the case with the inner planets of TRAPPIST-1. While we do not know the mutual inclinations of the planets in the TRAPPIST-1 system, we have measured their inclinations with respect to the plane of the sky as viewed from the Earth based on an analysis of their transits. This shows that the inclinations have an RMS scatter of <0.1°. Since it seems improbable that the orbits of all seven of these planets are actually highly inclined to each other yet still line up by chance to produce transits as viewed from the Earth, it is likely that the actual mutual inclinations of these planets is probably also on the order of 0.1° guaranteeing that the inner planets would produce transits (or maybe more precisely, eclipses) as viewed from TRAPPIST-1e once every synodic period. But unlike the Moon which covers the entire disk of the Sun during a total eclipse as viewed from the Earth, the inner planets of TRAPPIST-1 would only cover a fraction of the huge 2.21° disk of the host star as viewed from Planet e.

In addition to relative sizes and phases, apparent brightness is another important parameter in describing the appearance of these exoplanets. In order to perform this calculation, we would need to know how much light they reflect as a function of the angle between the line of sight and sun-planet line or the phase function. Unfortunately we do not have such information at this time and it may be quite a while before we do. But considering that these worlds are likely to be volatile-rich, they are bound to be shrouded in highly reflective clouds. For the purposes of estimating the apparent magnitude of these exoplanets, I have adopted the phase function of Venus derived by Hilton. The phase function of cloud-shrouded Venus would provide at least some idea of how bright these exoplanets could appear and how it changes over time. A plot of the V magnitude as a function of elongation is shown in the plot below.

As these plots show, TRAPPIST-1b and c would be at their peak V magnitude of -7.5 and -6.6 respectively at superior conjunction. The disk of TRAPPIST-1b, while small, would be comparatively bright because of its proximity to TRAPPIST-1. Because of the interplay between the phase function and how the distance changes over time, TRAPPIST-1d would start out comparatively dim after coming out of superior conjunction and slowly brighten over time. It would reach its peak V magnitude of -5.9 about 13 hours before inferior conjunction (or 13 hours after) when it is about 30% illuminated. While much dimmer than the -12.7 V magnitude of a typical full Moon seen from the Earth (not to mention smaller), these exoplanets would still be readily apparent in the dark sky of TRAPPIST-1e especially after they move out of the glare of the host star.

The View of the Outer Planets

The distances and apparent size of the outer planets as viewed from TRAPPIST-1e are summarized below in Table 4. For this class of planets, there are different set of key events that mark their passage across the sky. Conjunction is when the planet being observed is appears to be on the far side of the sun. Quadrature is when the angle between the line of sight and the planet-sun line is 90°. It is at this time that the phase angle is at a maximum resulting in a slightly gibbous phase whose magnitude depends on the orbit sizes of the observer’s planet and the planet being observed. Opposition is when the planets line up on the same side of the host star they orbit. It is at this time that the distance to the planet being observed is at a minimum and it appears its largest.

Table 4: Key Events for Outer Planets as Viewed from TRAPPIST-1e

Planet f g h Synodic Period (days) 18.071 12.046 9.035 Distance at Conjunction (106 km) 10.10 11.35 13.59 Apparent Size at Conjunction (arc min) 6.5 4.5 2.5 Distance at Quadrature (106 km) 3.73 5.46 8.13 Phase Angle at Quadrature 49.5° 38.6° 28.2° Apparent Size at Quadrature (arc min) 17.6 9.3 4.2 Distance at Opposition (106 km) 1.38 2.63 4.87 Apparent Size at Opposition (arc min) 47.8 19.2 7.0

As can be seen in Table 4, the synodic periods of the outer planets in the 9 to 18-day range so that they would appear to move and change more slowly than TRAPPIST-1b and c as viewed from Planet e. TRAPPIST-1f would display the most pronounced gibbous phase at quadrature because its orbit is only 32% larger than Planet e. This world at opposition would swell to have an apparent size half again as big as the Moon as viewed from Earth – the largest any planet would appear from the point of view of TRAPPIST-1e. Despite its small apparent size compared to the other exoplanets in this system, even TRAPPIST-1h (the smallest and most distantly orbit planet in this system) would appear as a small disk during all parts of its orbit as viewed from Planet e. The illustration below shows the apparent size and phases for the outer planets during key events compared to the Moon as viewed from the Earth.

As was done with the inner planets, the brightness of the outer planets can be estimated assuming a Venus-like phase function. As can be seen in the plot below, the changes in brightness from conjunction through opposition are much simpler than they are for the inner planets with a minimum V magnitude experienced some time after conjunction and a peak brightness reached at opposition (a behavior which would be mirrored after opposition as the planets approach conjunction once more). While at opposition TRAPPIST-1f would appear larger than the Moon does in our sky and would be the brightest object visible in the sky (after TRAPPIST-1), the peak V magnitude of -8.7 is still four magnitudes dimmer than a typical full Moon see here on Earth. Despite the comparative dimness, these three outer planets would likely be visible in the clear dark skies of TRAPPIST-1e even in daylight, assuming it had an Earth-like atmosphere.

Putting It All Together

Much of the previous discussion has centered on the appearance of the exoplanets in the TRAPPIST-1 system from the position of Planet e. But what would an observer on the surface of TRAPPIST-1e actually be able to see? The answer to this question is entirely dependent on the location of the observer on Planet e. Since it is likely to be a synchronous rotator, the position of the sun in the sky of TRAPPIST-1e would appear to remain almost constant with only tiny variations due to the planet’s slightly eccentric orbit and any librations (i.e. swinging motion) it might experience as a result periodic variations in its orbit as well as of tidal interactions with the other bodies in this tightly packed system.

From the point of view of an observer located on the equator at the center of the daylit hemisphere, TRAPPIST-1 would appear directly overhead. With the observer facing south, the inner or inferior planets would appear to come out from behind the sun at superior conjunction and move to the left until they reached greatest elongation. As a result, these three planet would always appear high in the sky with TRAPPIST-1d sinking to an elevation angle of 40° before reversing direction. After greatest elongation, the inner planets would then appear to move to the right at an ever faster angular rate and increase in apparent size. At inferior conjunction, each of the inner planets would produce eclipses as they pass between TRAPPIST-1 and Planet e. The inner planets would then continue moving to the right until they once again reached greatest elongation when they would reverse direction and slowly move back towards superior conjunction.

From this same location on the daylit side, the outer planets would rise to the left of the south-facing observer on the eastern horizon when the planets were at quadrature. These worlds would not be visible from this location between opposition (when they are their largest and brightest) through quadrature. The outer planets would continue to rise and move at a slowing rate as they approached the sun and conjunction. During this time they would appear to be getting smaller and dimmer over time. After conjunction, the outer planets would reverse the process and set to the right on the western horizon at the next quadrature.

The system’s resonance chain with an orbital period ratio of about 24:15:9:6:4:3:2 means that there will be repeating configurations of planets visible in the sky with a cycle whose length is 24 times that of the orbital period of TRAPPIST-1b (i.e. 36.3 days). This is especially true of TRAPPIST-1d and g whose 12½-day synodic periods are within about 13 minutes of each other – comparable to the TTVs experienced by these planets. This means that TRAPPIST-1d might be observed during greatest elongation, for example, only when Planet g is going through quadrature, depending on the phasing of the orbits and how it may change over time. The resonances could result in other cycles such as triple eclipses (or triple superior conjunctions) of the inner planets taking place every 12.08 days as viewed from TRAPPIST-1e. The periodic changes we observe on Earth as TTVs would probably cause interesting variations of these cycles of planet configurations on time scales of months to years and more. But much more data about the dynamics of the TRAPPIST-1 system will be required to work out with any certainty what those cycles would be over time.

The view from the opposite side of TRAPPIST-1e at the center of the night hemisphere on the equator would be very different. The inner planets would never be visible from this point along with the system’s host star, TRAPPIST-1. At locations with a longitude of about 40° from the center of the night side, an observer would see TRAPPIST-1d peek above the horizon at greatest elongation before setting again. As the observer moved closer to the terminator, the inner planets would appear one by one. The outer planets would appear to rise in the east at quadrature but continue to grow and brighten as they head towards opposition when they would be visible directly overhead. They would then continue towards the western horizon and set at quadrature.

The only location on TRAPPIST-1e where its sister planets could be observed throughout their entire orbits would be at the poles on the terminator. TRAPPIST-1 itself would appear on the horizon as a perpetual setting sun with a deeper red color than it would normally have when viewed high in the sky. The inner three planets would hug the horizon as they move back and forth around TRAPPIST-1. The three outer planets would slowly circle around the horizon (clockwise as viewed from the north pole) with a period equal to their synodic periods. At opposition they would appear on the horizon directly opposite of TRAPPIST-1. Being so close to the horizon, the maximum sizes that are reached at opposition which would appear even larger due to the Moon illusion (where the Moon appears larger close to the horizon compared to when it is high in the sky).

While the view from the surface of TRAPPIST-1e would be starkly different from our skies here on the Earth, it is still only a hint of what is possible among the trillions of exoplanets (and tens of trillions of large moons) that exist in our galaxy alone. As astronomers continue to find new exoplanets, we will undoubtedly discover more spectacular views that could rival those of even fictional worlds.

Follow Drew Ex Machina on Facebook.

Related Reading

“A Sky with Quadruple Suns”, Drew Ex Machina, March 7, 2015 [Post]

“Habitable Planet Reality Check: The Seven Planets of TRAPPIST-1”, Drew Ex Machina, February 25, 2017 [Post]

General References

L.Delrez et al., “Early 2017 observations of TRAPPIST-1 with Spitzer”, Monthly Notices of the Royal Astronomical Society, Vol. 475, No. 3, pp.3577-3597, April 2018

Michaël Gillon et al., “Temperate Earth-sized Planets Transiting a Nearby Ultracool Dwarf Star”, Nature, Vol. 533, pp. 221-224, May 12, 2016

Michaël Gillon et al., “Seven temperate terrestrial planets around the nearby ultracool dwarf star TRAPPIST-1”, Nature, Vol 542., pp. 456-460, February 23, 2017

Simon L. Grimm et al., “The Nature of the TRAPPIST-1 Exoplanets”, arXiv 1802.01377 (in press for publication in Astronomy & Astrophysics), February 5, 2018 [Preprint]

James L. Hilton, “Improving the Visual Magnitudes of the Planets in The Astronomical Almanac. I. Mercury and Venus”, The Astronomical Journal, Vol. 129, No. 6, pp. 2902-2906, June 2005

Jack T. O’Malley-James and L. Kaltenegger, ”UV Surface Habitability of the TRAPPIST-1 System”, Monthly Notices of the Royal Astronomical Society: Letters, Vol. 469, No. 1, pp.L26-L30, July 2017

Valérie Van Grootel et al., “Stellar Parameters for TRAPPIST-1”, The Astrophysical Journal, Vol. 853, No. 1, ID 30, January 2018