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The Surface Gravity Plateau

What’s a movie director supposed to do about gravity? In The Martian, we see Matt Damon moving about on Mars with a gait more or less similar to what he would use on Earth, despite Mars’ 0.38g. Harrison Ford changes worlds but never strides in The Force Awakens. About the gravitational challenges of 1953’s Cat Women of the Moon, the less said the better. Even so, we can chalk all these problems up to the fact that both top directors and their B-film counterparts are forced to film at the bottom of a gravity well, so a certain suspension of disbelief is at least understandable.

But assuming that gravity invariably increases as planets get bigger can be misleading, as Fernando J. Ballesteros (Universitat de València) and Bartolo Luque (Universidad Politécnica de Madrid) demonstrate in a new paper in Astrobiology. We learn that some larger worlds in our own Solar System have gravity not all that different from the Earth. In fact, the surface gravities for Venus, Uranus, Neptune and Saturn weigh in at 0.91g, 0.9g, 1.14g and 1.06g respectively, although these worlds are 0.82, 14, 17 and 95 times Earth’s mass.

Bar at Takodana

Image: Walking on the planet Takodana looks more or less like walking on Earth in The Force Awakens, although the bar scene there is more interesting. Credit: Disney/Lucasfilm/Bad Robot Productions.

How do we go about making these deductions? Usefully, we have plentiful planets to work with as a result of the Kepler mission, and the fact that Kepler works with transits is likewise helpful. A transit light curve can show us how much starlight is blocked by the planet, which provides an estimate of the planet’s size, assuming we have a pretty good idea of the central star’s size.

Radial velocity measurements can then be brought to bear, a technique that supplements the transit method by adding a lower boundary to the planet’s mass. Remember that this measurement depends upon the viewing angle, as we can’t always know the orientation of a given planet’s orbit; i.e., in straight radial velocity studies, we won’t know whether we’re looking at a solar system edge-on, or from directly above (the measurement is M x sin(i), with i corresponding to the viewing angle. With transiting planets, though, we have a better read on the viewing angle because we see the planet transit across its star.

With an idea about the size of a world and a sound estimate of its mass, we can work out the planet’s surface gravity (gs = GM/R2). Ballesteros and Luque plot the surface gravity vs. mass for a range of exoplanets, folding in data from our own Solar System, where measurements are, obviously, far more precise. Three ‘regimes’ emerge from this work:

  • Rocky worlds with masses lower than Earth’s ME;
  • A ‘transition zone’ including super-Earths, Neptunes, and some Solar System planets, with masses from one to hundreds of Earth masses;
  • Gas giants, with masses above hundreds of Earth masses.

And it’s in the transition zone that things get interesting. Let me quote from the paper:

In the first regime, planetary radius grows with mass as R ~ M¼; therefore surface gravity grows as gs ~ M½ (faster than what would be expected for incompressible bodies, gs ~ M). On the other hand, for gas worlds, planetary radius remains roughly constant (i.e., gas giants with very different masses have similar sizes due to electron degeneracy), so surface gravity grows linearly with mass, gs ~ M. But in the transition zone, we find some sort of plateau where planetary radius has the fastest growth, as R ~ M½, which thereby yields a constant surface gravity roughly similar to that of Earth.

Hence the similarity in surface gravity between Venus, Uranus, Neptune, Saturn and the Earth, a non-intuitive result given the differences between these planets in structure and composition. As the number of confirmed exoplanets grows — and we saw the largest single addition to the catalog ever yesterday — we are able to understand that having five worlds with roughly the same surface gravity is a general trend. Fitting these findings in with planet formation models will be a challenge that should ultimately improve our understanding of the processes at work.

The accretion process and the competition for materials during planetary formation impose severe constraints on feasible planets. Current models of population synthesis (Mordasini et al., 2015) are designed to take this into account and can address many of the observed features. However, such models fail to explain this plateau and predict instead a noticeable increasing trend in surface gravities in this region.

Hence the value of our steadily increasing exoplanet catalog as we contrast real planetary systems with the theories we apply to their formation. Thus, as Ballesteros and Luque note, watching Harrison Ford walking on the planet Takodana as if he were taking a stroll down Hollywood Boulevard is not a simple moviemaker concession to Earth’s gravity. In this case, what we’re learning about surface gravity makes such strolls plausible.

The paper is Ballesteros and Luque, “Walking on Exoplanets: Is Star Wars Right?” Astrobiology Vol. 16, No. 5 (2016). Abstract. Preprint on arXiv.

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Comments on this entry are closed.

  • Tom Mazanec May 12, 2016, 13:27

    Analog once had a science fact article on surface gravity being “quantized” in powers of 2.5

  • Ashley Baldwin May 12, 2016, 13:36

    Thanks Paul. Very thought provoking . It’s available full text as a preprint on arxiv , 26th April.

  • Alex Tolley May 12, 2016, 13:59

    The authors’ chart (Figure 1 in the paper) clearly shows that rocky exoplanets have increasing surface gravities as you would expect. The plateau only works when including gas worlds, but apart from some old SF movies, we don’t expect humans to walk on the surfaces of those worlds for obvious reasons. Luke and friends walk on Yavin, but not on the gas giant planet it orbits.

    While the chart shows a plateau, it might be arguable that chart should really be 3 separate correlations – rocky worlds, Neptunes and gas giants. IOW, that plateau is illusory.

  • Michael May 12, 2016, 14:55

    Paul slight correction needed, Venus ‘s mass is 0.82 of Earth’s, looks like a 10 factor error.

    • Paul Gilster May 12, 2016, 15:12

      A typo indeed! Thanks for spotting it. Now fixed in the text.

  • Michael May 12, 2016, 15:26

    I see the trend as real, most likely due to water and hydrogen/helium ratios been fairly constant. It just beggers belief of world’s with 10 to a 100 g’s with densities multiples that of lead!

  • Terraformer May 12, 2016, 18:16

    Well, we do at least have people who know what it is like to walk in 1/6 g. What do they say on the matter?

  • John Walker May 12, 2016, 18:16

    Expanding on this, given current thinking that the quantitative limit of “Super-earth” size may lie between 1.23 and 1.6 Earth radii, it’s easy to calculate what the surface gravity would be on a such planet if one assumes for example an Earth equivalent average density of 5.5 g/cm³. The results are 1.28 and 1.56G respectively. A far cry from the crushing force that I had dreamt of as a kid existing on the surface of some alien worlds.

    • Michael May 13, 2016, 15:14

      Self compression will skew these numbers somewhat as the density increases. The human frame can adapt to 1.5 or even 2 g, it would drive adaptions to become smaller.

  • Christopher Phoenix May 12, 2016, 19:17

    This is very interesting, Paul–I guess the universe is in line with movies for once in this case. Of course, planets like Saturn and Neptune are not habitable in any sense of the word, but this “surface gravity plateau” includes to potentially habitable super-Earths. And, I suppose that if Bespin is in the transition zone, this could explain why surface gravity seems Earth-like in Lando Calrissian’s Cloud City!

  • Ivan Vuletich May 13, 2016, 1:32

    I remember seeing a similar table of surface gravities for planets in the Solar System years ago, with the author pointing out that the only planet in the Solar System that you would have a hard time standing up on is Jupiter.

    Looks like us Earthlings are optimally designed for walking around on most planets in the galaxy!

  • John Frazer May 13, 2016, 2:57

    It speaks as if the apparent plataeu in sorts of planets, is causing the gravity to be near Earth G
    It’s a function of the mass, and your distance from the center, while standing still.
    If you move yourself upwards, to Saturn’s radius away from Earth’s center, stationary, you’ll feel less G. (too lazy now to figure it out exactly) Stand Saturn’s radius away from the center of Saturn’s mass, and you feel nearly 1G.
    In his book “Saturn Rukh” Robert Forward described a nuclear heated aerostat platform with a manned craft. Outside, it was a balmy antarctic winter day, stinky though not necessarily poisonous mix nearly Earth pressure, so not entirely intolerable.

    If somehow the Sun’s mass were under your feet and you were 9km from the center, you’re on the surface of a sort of Neutron Star, under absurdly high G loading. Forward also wrote about life on one of those, too…

  • MikeLorrey May 13, 2016, 3:15

    Treating the top of the atmosphere of a jovian or Neptune an gas giant as the “surface” is an absurdity, sorry. The terrestrial world’s gravity scales faster than mass, but only at constant density. Low metals worlds, perhaps orbiting low metal red dwarfs (and yes I know it means anything other than H or He, such stars will still have planets, if they have any, with lower density, and lower atomic number elements) will have much lower surface gravity even at higher mass and radius. Interestingly, orbital velocity is higher with bigger world’s even if they are low gravity and density.

    • Terpi May 13, 2016, 13:15

      Which is the surface of Jupiter, in your opinion?

      • Eniac May 14, 2016, 12:46

        It is best to define surface at where the planet becomes opaque, as this is very well defined. All planets look like sharp circles. To further distinguish by what is actually at the surface, just call them “solid”, “liquid”, and “cloud” surfaces, variously.

  • Bynaus May 13, 2016, 3:28

    Like other commenters, I’d like to mention that most worlds on the “plateau” do not have a surface on which one could walk (Star Wars style). Due to internal compression, surface gravities on rocky planets will increase as G ~M^0.46 or G ~R^1.7, so on the largest rocky planet known (the exceptional BD+20594b), it will be a crushing 3.5 Ge, and a planet a the rocky/gaseous transition at 1.2 – 1.6 Earth radii will have 1.4 – 2.2 Ges of surface gravity.

    But it would seem that short of constructing huge “orbitals” to increase human living space, the solar system would set humanity up to adapt for a life (on floating surfaces) in atmospheres. That seems strange now, but think also how Earth has set up humanity to live in environments very different from the Savannah on which it evolved. In that sense, Bespin could be a better blue-print of future human living than Takodana or Tatooine (I think its fascinating to think about the kind of societies that would develop in such “floating cities”: e.g., would everybody be afraid of “falling off the edge”? Would building a house amount to securing enough material extracted from the surrounding atmosphere to expand the city by the needed area? How would trade, warfare or technology in general adopt to the fact that one could have cities at different pressure levels?). Venus would be a good point to start the process: sunlight is abundant, and nearly all that is needed for a floating colony can be retrieved from the surrounding atmosphere or (robotically) from the surface below. Later generations of atmosphere dwellers (radiating out from venusian cities?) could make use of the somewhat more challenging atmospheres of Saturn, Uranus and Neptune, where fusion from abundant 3He and D could be used to make up for the deficit in sunlight these worlds receive. In particular, Saturn provides for a ~1 Ge surface 95 times larger than the Earth, or almost ~75% of the combined area of the ~1 Ge surfaces in the solar system. Saturn could thus one day well be the future “Asia”, i.e., the region where most of humanity lives.

  • Horatio Trobinson May 13, 2016, 4:44

    Has anybody calculated how much less food needs to be transported to a destination planet like Mars? (given that much of the physical mobility of the martian astronauts will demand less calories than they would need on Earth for the same amount of work)

    • George King May 13, 2016, 11:44

      Did they — markedly — reduce the caloric intake of the Apollo astronauts while in low lunar gravity?

      I don’t know the answer. But I would think that: (a) there’s a relatively high baseline requirement for just basic metabolic processes regardless of gravity; and (b) the body still works fairly hard (vis-a-vis caloric needs) during physical activity even in a low g environment, just differently.

      The Apollo lunar experience should provide a good reference point, either way. I do remember those guys huffin’ and puffin’ while they were hopping around on the Moon.

  • Terpi May 13, 2016, 13:01

    What the paper states is that the line of nearly-atmosphereless rocky planets cannot grow forever (similarly, the line of pure-gas planets cannot decrease forever, as there is a minimum amount of gas that can be self-gravitatorily stable). In the case of pure rocky wordls, although you can design one so massive as Jupiter, it does not exist in the wild: at a given point rocky bodies reach a mass threshold which accumulates very efficiently the surrounding gas.

    This threshold seems to be more or less one Earth’s mass. Note that Uranus and Neptune rocky nuclei are around 1 Earth’s mass. If you have in Neptune upper atmosphere a floating city as the Cloud City in Bespin, you will feel 1g. And if you can go down until the rocky nucleus of Neptune (supposing your technology makes possible to support the atmospheric presure) you will find there also 1g, and probably all the way along.

    In short, Kripton, a walkable rocky world with a surface gravity of 30g and respirable atmosphere, do not exist. Rocky worlds with atmospheres densities suitables for human beings (as those of Star Wars) will not have crunching gravities.

    This plateau is not an artifact, the figure is a good way to quickly classify newly discovered planets in three straightforward categories without the need of calculating equilibrium equations of different components, as usually is done.

    • Michael May 16, 2016, 3:00

      ‘And if you can go down until the rocky nucleus of Neptune (supposing your technology makes possible to support the atmospheric presure) you will find there also 1g, and probably all the way along.’

      The gravity should increase towards the core and reach a peak and then drop off again.

      • Terpi May 16, 2016, 12:26

        Wrong. Think on the Gauss theoreme. For gravity only matters the mass under you. If you are over the rocky core and it has only 1 Earth’s mass, you will feel 1g, no matter if over you there are 10 Earth’s masses or 100. For example, on Earth if you dig and go deeper and deeper, gravity becomes smaller and smaller, until you reach the center where gravity is 0.

        • Bynaus May 16, 2016, 15:31

          No, Michael is right. You are right too with the Gauss theoreme, but don’t forget about density! In fact, if you were to dig inside the Earth, you would find the gravity to increase down to the core-mantle boundary, because the density of the layers you are digging through is lower than the one of the whole Earth. The core contains about 30% of the Earth’s mass and has about 45% of its radius, so the surface gravity on the core is ~1.5 Ge. The same should be true for Neptune if its core has a density that is higher than the one of the bulk planet.

          • Bynaus May 17, 2016, 7:46

            I just realized that the core has ~54% of the Earth’s radius (the core-mantle boundary is at a depth of 2880 km, not 2880 km from the center…), therefore, the gravity at its surface will be only slightly in excess of 1 Ge, not 1.5 Ge, as stated above.

      • Terpi May 16, 2016, 16:49

        Sorry, I see the point. The nucleus can have the same mass than Earth, but not the same density! So the gravity in its surface will be bigger (but how much…?).

    • Brett Bellmore May 16, 2016, 5:28

      I predict we will soon locate a Mesklin analog, the universe in my experience having a sense of irony.

  • Horatio Trobinson May 13, 2016, 13:36

    @GeorgeKing

    Thanks for your reply George. You are very right that base metabolism, (especially the brain, by cubic centimetre) consumes a large part of our energies, and some ‘fuel’ is also needed to initiate ‘combustion’ (in rocketry terms)

    But even if the difference between energy per human needed on Earth and energy needed on Mars is about 20% less, I think the cost of sending food would be something to look into very carefully, it could translate into a significant difference of volume in spaceship room (and different foodstuffs have different proportions of nutrients and calories, and different human bodies have different needs, and different metabolisms)

    Most likely this difference will only be noticeable for crews with a number of astronauts bigger than 4,. I don’t know what’s the crew size of projected flights to Mars but 5 or 6 seems to be about right for such distance.

    The Apollo mission had a crew of three, only two landed, and it lasted for 8 days and 3 hours. The scale of a trip to Mars vastly amplifies these, probably previously neglected differences.

    • Alex Tolley May 13, 2016, 15:26

      Metabolic requirements will depend a lot on temperature and activity. The Apollo astronauts used a lot of energy because of the difficulty of moving in a n inflated, stiff spacesuit. Working in a shirtsleeves environment would change this. Temperature is important, as cold will require increased metabolism to stay warm. If Mars habitats are cool to cold, this would offset any gains from lower gravity. Daily activity is also important. Physical work requires a lot more caloric intake than relative inactivity at a desk. However, to keep bones strong, Martian inhabitants might need to maintain an exercise regime to ensure that they can safely return to Earth after a long period.

      • George King May 13, 2016, 21:19

        Yep, an intriguing question with a lot of potential variables. And, as Horatio points out, an important question bearing on how much food needs to be brought and/or grown on site.

        I found this piece that reflects that NASA had 2500 calorie meals during Gemini as against a 3000 calorie baseline, due to expected reduced caloric needs in those microgravity missions in tight quarters.

        http://airandspace.si.edu/exhibitions/apollo-to-the-moon/online/astronaut-life/food-in-space.cfm

        They upped that to 2800 for Apollo. On a quick scan, the article does not appear to reflect that that amount was any different for non-landing missions, command module pilots vs. lunar module expedition crews, etc., etc. Nor does the article reflect whether they perhaps simply learned during Gemini that 2500 wasn’t quite enough. Although that, again, was a much more cramped spacecraft setting than Apollo, even in LEO.

        And all those Gemini and Apollo missions of course were comparatively short duration missions where the body likely lifted off accustomed to a higher caloric intake, whether specifically needed or not on one day or another.

        Gosh, I sure would want the ability to pig out on pizza and beer every now and then and have a snack occasionally. Some days my base training diet doesn’t leave me wanting more; other days you would like a bit more.

        No doubt all things that NASA has studied and is studying — including probably the physiological and psychological benefits of breaks from being on a strict number of calories per day ad infinitum on a long mission.

        • Alex Tolley May 14, 2016, 8:58

          Bear in mind that sending food is a mass issue that impacts fuel/propellant requirements. You can get a lot more calories for each kilo of mass by:
          1. high calorie, fat rich foods.
          2. Drying the food before shipment and using local water for rehydration.

          However there is a morale issue with dried food. It is relatively tasteless when rehydrated. Tim Peake tried food prepared by top British chef Heston Blumenthal and was very impressed compared to Anasazi/Esa food. This was the subject of a documentary on the BBC recently.

          My take home is that food should be as tasty and nutritious as possible for the crew, rather than MRE quality. While highly motivated people will tolerate much, when we start to ship out more professionals as part of a work assignment, quality meals will be important to ease tensions on the flight and staying on the base. This is also accepted practice at Antarctic bases where chefs rather than cooks are now employed. Food is important.
          Using the water in those meals as part of the propellant in an electric spacecraft then makes sense, and is [a small part of ] the rationale for the Spacecoach idea my colleague Brian McConnell & I proposed.

  • DJ Kaplan May 13, 2016, 19:40

    Is there an unspoken conclusion that simply because we have a handful of planets that appear to have approximately the same gravity, therefore other planets in the galaxy will have similar conditions?

    It’s a nice thought-experiment, but I wouldn’t want to follow it too far.

  • Harry R Ray May 17, 2016, 16:30

    Interesting that the movie analogy was brought up. The only movie that I know of where this issue was even addressed was “John Carter” although they actually OVERDID it a bit(the first scenes with Carter ON Mars were HILARIOUS!)as he pretty much transformed into Superman, which, of course is NOT the reality of the situation on Mars. Conversely, a relatively NEW exoplanet has piqued my imagination. K2-3d(which Andrew LePage gave the THUMBS DOWN on in his ongoing “Habitable Planets Reality Check” serioes last year. What has CHANGED SINCE THEN is that it’s MASS has been determined via radial velocity(it was TRICKY, because the planet’s ORBITAL PERIOD was almost identical to the star’s rotation period, so a LOT of measurements were needed), and it is a WHOPPING 11.1 Earths, making it the first POTENTIALLY(but probably NOT) habitable MEGA-EARTH(notice that I did NOT say “most probably not” because the SEVERAL Earth gravities of this planet MAY ACTUALLY PREVENT this planet from become a Mega-Venus via the runnaway greenhouse effect)! If an intellegent bipedal K2-3d native were able to transport to Earth via a Thern medallion, that native would become the “John Carter” of Earth!