Gravity, Pt. 1

We’ve already talked – a bit – about the possible role air pressure might play in planetary colonisation. I didn’t do much more than dip my toe into what is by any standards a vast topic. You could loosely summarise it as ‘human beings function best at 1 standard atmosphere’ – surprise, surprise! However, there is also some flexibility – presumably, our pre-human ancestors did encounter big hills and mountains often enough for evolution to factor it in. Human settlements can and do exist at altitudes as high as ~5000 metres.

Gravity, however, is potentially a very different problem. It’s something that will be a fundamental property of any planet. It’s also something that isn’t amenable to human influence, short of some kind of completely-incomprehensible, borderline-magic type technology. But, irritatingly, it’s something that will have major health implications for any putative human society. So it can’t be ignored. One can imagine taking supplements to deal with chemical deficiencies in the local soil, one can imagine pressurised houses to deal with air pressure differences, one can imagine vaccines or perhaps genetic engineering to cope with local diseases – but you can’t really do anything about the surface gravity! (By the way, if you think I’m being absurdly glib in dismissing the other issues, you’re dead right! All of these would be major undertakings just by themselves…)

Now, a note before we go any further. Most of this series of articles will be me commiting the physicist’s cardinal error – speculating outside one’s own field! So, any errors you see in the medicine and the biology are most definitely not my sources’ fault, they are a consequence of my own faulty comprehension. (Incidentally, if we do have any biologists or doctors in the audience, I would be very interested in their views on this topic.)

First off, let’s start with a brief – and it will be brief! – overview of what gravity is from a physics perspective.

Gravity: The Annoying Physics Bit

Right, let’s get this bit out of the way first. Here is a quick and rather cursory overview of gravity in physics.

Physically, gravity is the force exerted between two given masses when they are separated by a given distance. Strictly, the distance in question is actually the one between the centres of the masses rather than the surfaces[1]. (This is a subtle distinction, and one that caused me a lot of confusion in my first year of pre-GCSE Physics. At the time, I knew that doubling the distance quaters the force exerted, so what happens if you move from 1 metre above the surface of the Earth to 2 metres?! [2]) The variation in gravity with mass and distance is described by Newton’s well-known and well-loved equation[3]:

Basically, gravity increases linearly with mass – twice as much mass means twice as much weight. But it falls off with the square of the distance, so if you move twice as far away, your weight falls by four (and three times distance means one ninth the weight, and four times distance means one sixteenth, etc.). Big G here is the Gravitational Constant, the value that sets the proportionality in SI units. This number, incidentally, never ever changes, anywhere (numerically, it’s about 6.67 x 10^-11 – small!).

The relevance of this? A human being stood on the surface of a different planet will experience a different weight to the one he or she would have on Earth. To illustrate the point, here is a quick table of surface gravities for several solar system objects. Note that I’ve scaled this so that 1.0 = Earth’s surface gravity:

Planet Gravity
Mercury 0.38
Venus 0.90
Earth 1.0
Moon 0.17
Mars 0.38
Ceres 0.03
Jupiter 2.53 (equatorial cloudtops value)
Saturn 1.07 (equatorial cloudtops value)
Uranus 0.89 (equatorial cloudtops value)
Neptune 1.14 (equatorial cloudtops value)
Pluto 0.07

(I’ve noted in several noteworthy non-planets in itallics; also note that gravities for gas giants are for the cloudtops at their equator. This caveat is important – Jupiter and Saturn spin fast enough to be quite appreciably non-spherical, which muddles things all by itself, and also gas giants aren’t solid, so you have to be careful about what you pick for the ‘surface’.)

As you can see, perhaps surprisingly, we actually live on a planet with a relatively high surface gravity, at least by solar system standards.

Now, g – Earth’s surface gravity – is not absolutely constant across the planet’s surface. There are some slight variations here and there. First off, the Earth rotates. This means it bulges a bit at the equator, and is a bit ‘thinner’ pole to pole. In fact, measured across the equator, the Earth is just under 43 km ‘fatter’ than it is when measured pole-to-pole. So, if you stand at the north pole, you’re about 21.5 km (43/2, as diameter = 2 x radius) closer to the centre of mass – so that will mean you experience a slightly heavier gravity than at the equator.

But there’s a further complication. Because the Earth is spinning, the rotation sets up what feels like a sort of outward force, often called ‘centrifugal acceleration’ [4]. This counterbalances the gravity a little bit, pushing you outwards a little bit as the Earth tries to pull you in. So you really do feel very, very slightly lighter at the equator than at the poles.

In addition to these effects – rotation and the bulge – the Earth also supplies different altitudes. At the top of a tall mountain, you’ll be farther from the centre of mass than at the bottom, and thus will feel a (minutely) lower gravity. And some of the biggest mountains on Earth – the Himalayas – are near the equator.

So, add all of these effects up, and you can find the maximum range of gravities that we might experience here on Earth. This is important, biologically, as it presumably puts some limits on evolution. Evolution is a conservative process – it doesn’t build in features that aren’t needed (like adaptation to gravity values that we never encounter here on Earth).

So, what is the planet’s gravity range?

Well, an object at sea level at the equator will weight about 0.5% less than it would at the poles. The top of Mount Everest can reduce the apparent weight by a further 0.28%. So, using that as a limiting case, it turns out that we have no more than an absolute maximum variation of 0.78% in gravity anywhere across the Earth.

The biological relevance of this? Well, there’s simply no reason for evolution to have built in any capacity to deal with a gravtiy regime outside of this 0.78%. And this is ominous for potential colonists – what are the odds of another planet agreeing with Earth to within 0.78%? Not very high, I can tell you right now. And what are the odds of such a planet being in a convenient star’s biozone and having water and an oxygen-nitrogen atmosphere as well? The latter ones are unquantifiable right now, but I suspect they’re not very high!

This is all looking a bit ominous, isn’t it?

[1] The centre of mass is effectively a sort of average position of all the matter in a given body. If the body is more or less spherical, and at least vaguely uniform in density, then the CoM will also be somewhere in the vicinity of the geometrical centre. If the body is spectacularly not-spherical, or very uneven in density, or – horror of horrors! – both, then the maths gets entertaining. (Something called ‘Guass’s Theorem’ comes into play at this point. In my undergraduate physics course, we spent a lot of our time calculating descriptions of the gravities for hypothetical structures like flat, infinite planes or hollow shells or demented toroids and so on. Frequently, I got these spectacularly wrong. To this day, you can still make twitch and look nervous by saying something like ‘Given a mass of M and assuming Gauss’s Theorem…’)

[2] Answer: not much. In more detail, the radius of the Earth averages 6,378,000 metres, so if you add 1 metre in altitude, you’ve changed from 6,378,001m to 6,378,002m. You haven’t doubled your distance from the centre of mass – in fact you’ve not even changed it by as much as 1%. Hence you don’t notice any change in gravity if you climb on top of a table. When 14-year old me finally understood this, it led to one of those wonderful ‘lightbulb goes on’ moments – wonderful if rather belated!

[3] Relativity complicates this picture, and one day quantum gravity will muddle it even more. However, these are not really relevant to our discussion here. In the energy/pressure/momentum/temperature regime where human beings can live, the differences between relativistic and Newtonian gravity are only just barely detectable, even with the most sensitive instruments.

[4] I’m not going to get drawn on the whole centripetal force and rotating frames of reference thing. If you want to go that far into depth with it, try here for starters.


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