“I wouldn’t know a spacetime continuum or a warp core breach if they got into bed with me.” -

Patrick Stewart

It’s the end of the week once again, and so it’s time for another Ask Ethan segment! There have been scores of good questions to choose from that were submitted this month alone (and you can submit yours here), but this week’s comes from our reader garbulky, who asks:

Why does gravity decrease the further away you are from the object? I’ve read that it does decrease with distance squared but not why it does this.

This question seems *so simple*, and yet the answer — to the limits of our understanding — is nothing short of profound.

Physics, and science in general, doesn’t normally address the question of *why* when it comes to natural phenomena; it normally sticks to *how*. You give me an overarching theory, such as a set of laws, and physical objects with specific properties, such as a set of particles, and science tells you *how* those objects behave according to the predictions of that theory. Gravity is no exception.

For centuries, Newtonian gravitation was the most successful theory describing forces on the largest scales, saying that every object in the Universe that has a mass exerts an attractive force on every *other* object in the Universe with a mass, and that the magnitude of that force is proportional to the mass of both objects and inversely proportional to the distance between them. That’s what Newton’s law of universal gravitation says, and what it tells us is — in principle — how any system of particles will behave under the influence of gravity.

Can we say something intelligent about *why* gravity works this way, though? Let’s think about our own neighborhood for a minute.

The Sun, the largest mass in our Solar System, is orbited in circles and ellipses by practically every known object, from planets to asteroids and (most) comets. There’s something special about circles and ellipses that we don’t normally think about as special: they’re **stable,** **closed orbits**, meaning that these objects return to the same point they started at after what we call a year.

That alone, mathematically, tells you something incredibly interesting. You see, all forces are *vectors*, meaning they have magnitudes and directions. In the case of our Solar System, the direction of the force on each object is (to an excellent approximation) towards the center of the Sun. Want something to go around the Sun in a closed orbit? Guess what.

**You only have two options**! One is to have a force that obeys an inverse-square law (like gravity does), and the other is to have a force that increases linearly with distance (like a spring does), and there’s a theorem that proves those are the only two possibilities!

So it could have gotten stronger or weaker as the distance increased, but only in one particular way, or we wouldn’t have stable, closed orbits.

And since those are the types of orbits required to have stable, moderate temperatures necessary for life, we sure did luck out that these are the laws governing our Universe!

Now there are *some* forces where the force increases as your distance from the object increases: the strong force is a great example! And there’s even an example of a type of force that has no direction and is *constant* everywhere: that’s what dark energy is, permeating all of space equally!

The thing is, though, saying that gravity is an inverse-distance-squared force is an incomplete story. In fact, the very fact that we have an orbit in our Solar System that very clearly *isn’t* closed is how we wound up replacing Newtonian gravity with our modern theory of gravity: General Relativity!

*precesses*, or

*doesn’t*close on itself, that was our first major hint that something was not quite complete about Newton’s theory of gravity. It took about half a century to solve this problem and replace Newtonian gravity with Einstein’s General Relativity, and one of the things we realized from that is that gravity isn’t

*exactly*following an inverse-square law, but that’s only a great approximation when the involved distances are large and masses (and energies) are small.

We’ve come up with a whole host of predictions that have been borne out by experiment and observation, including the gravitational bending of light, the different orbital mechanics of systems with large masses and small distances, gravitational redshift, and many, many others.

But the greatest advance that’s related to this question of the strength of gravity is the knowledge that *all* orbiting bodies **do not** technically obey an inverse-squared force law.

All orbits under General Relativity come from forces that behave ever so slightly *stronger* than inverse-square laws, and this means that they will eventually decay over long enough timescales. The innermost planets will have their orbits decay first, followed by progressively outer worlds, because the distance is larger. Eventually, in the absence of all other phenomena, everything would spiral into the gravitational source at the center of all orbital systems.

For an object like Earth that orbited an imaginary, infinitely-long-lived Sun, it would take something like 10^{150} years for the orbit to decay, but it means that a true stable, closed orbit is a phantasm, something that doesn’t really exist in this Universe!

At least, in a Universe governed by General Relativity, which is the best law of nature we have to describe gravity. In the weak-field limit (an approximation) — when masses are small and distances are large — this can be shown to reduce to Newtonian gravity, which is where the inverse-square-law-with-distance comes from!

But **why** do we have General Relativity as the theory that governs gravitation in this Universe, with the particular details that it has? I can’t say for certain; no one can.

Which means I have to resort to the standard cop-out answer: the force of gravity is this way because the laws of nature cause it to be. We can imagine a Universe where those laws are different, but this is the one we’ve got, and we don’t fully understand *why* the laws are this way any deeper than that. We can observe phenomena, infer the laws, test them in new and spectacular ways, and maybe someday we’ll understand *why* the laws are this way. In the meantime, this is the best answer we’ve got!