Sir Isaac Newton probably didn't get conked on the head by a falling apple, but by many, if not most accounts, there was an apple and it did fall in his presence. Having witnessed such an event, the natural philosopher dared wonder why the apple, having suddenly become liberated from the tree, chose to accelerate toward the ground and not some other direction. As a runner starts from a standstill and accelerates in some arbitrary direction the apple accelerates from a standstill in accordance with some invisible force.
This force is gravity—an attractive force between massive bodies that diminishes according to the inverse-square law, which is a more general description of how any radiative force corresponding to a point in space becomes diluted as it is applied to an ever-larger area.
This is a very, very good description of gravity and it really only seems to fall apart at scales where quantum effects take over. Newtonian gravity has been verified in laboratory experiments and it describes our view of the universe and its many interacting bodies quite well, but there remains something of an experimental gap between laboratory precision and astronomical observation—probing the gravitational effects of large objects at very fine scales, that is.
There are even some that wonder if Newtonian gravity isn't as open and shut as it may seem and if, perhaps, Newton's formulation can be modified.
A team of astrophysicists at Stanford University think Newtonian gravity at least deserves a closer look, and have proposed a new spacecraft mission designed to probe gravitational effects as they may apply to a small chunk of matter as it travels to the very edge of the Solar System via super-lightweight space probe. The experiment, which is described in a recent paper in the journal Physical Review D, would be among the first to finely measure the effects of gravity at planetary scales, perhaps offering clues about dark matter and energy in the process.
The inverse-square law is elegant and intuitive. One might even say it's obvious. If you have some force—any force—that originates at a point and is distributed more or less equally in all directions, as you move farther and farther away, the force is distributed across larger and larger areas. The energy potential twice as far from the energy's source is spread out across an area four times as large and, thus, will have one-fourth the intensity at any given point. Just imagine the same amount of force being distributed across successively larger spheres radiating outward from the force's origin.
This is a general law, but it governs gravity as well. To get the actual strength of the gravitational field, we just need to multiply the formula above by the bodies' masses and Newton's gravitational constant—aka "Big G" or just Newton's constant.
But what if this formulation isn't all that it might seem when it comes to gravity? It's a question worthy of its own space mission, in the eyes of the Stanford group.
The proposed mission would be most closely related to the Pioneer and Voyager treks to the outer edge of the Solar System (and beyond), but instead of following the system's horizontal planet-harboring plane, the craft would travel vertically, in a perpendicular direction. This would allow the finer scale gravitational perturbations caused by the planets and Kuiper Belt to be averaged away, leaving mostly the pull of the Sun itself.
"When you want to measure this tiny deviation in the Sun's gravity, there's so many other larger effects that you have to control for," Tim Wiser, one of the paper's co-authors, told me over Skype. "Many are just the gravities of the other planets and bodies in the Solar System. The really big effect on our uncertainty is the Kuiper Belt."
The Kuiper Belt isn't so much enormously massive as it is uncharted. Accounting for its effects on a nearby craft would be difficult, but with a space probe cruising upward and above it rather than right into it, the effects could be averaged together and, thus, accounted for.
After having been rocketed into position and set on its way, the spacecraft would essentially consist of only a spherical 200 kilogram shell—as symmetrical as possible to reduce its own gravitational effects—and a small "proof mass." The idea is that this mass, as the spacecraft coasts outward through the Solar System to an eventual target distance of 100 astronomical units (AU), will only be affected by gravity.
"If gravity itself is modified, you'd expect to see that if the Sun, instead of having a 1/r2 force law, has some slightly different force law at large distances," Wiser explained.
Deviations from the expected gravitational forces can be viewed with respect to the Yukawa force. This is a generic "extra something" that can be tacked onto the inverse-square law with the effect of modifying in such a way that the gravitational constant, the strength of gravity, becomes a function of distance rather than a strict constant-constant. We know gravity feels weaker as we move away from its source because it becomes more and more watered down, but the Yukawa interaction would also mandate that, as distance increases, there's also just less gravitational force to water down in the first place.
Modified gravity theories that try to explain the apparent gravitational effects of dark matter—the "missing" 85 percent of the material universe—aren't especially popular, largely because most evidence really does suggest the presence of a large amount of extra stuff. But when it comes to dark energy, the enigmatic something that is causing the universe to expand faster and faster, wild ideas can get a bit more play for the simple reason that there should be a lot more of it to account for the universe we see today.
"The basic idea is that, very naively, we've discovered dark energy but it has a value that is much tinier than it should be," Wiser said. "So, this is a huge discrepancy than what we'd naively expect, which is based off of what we've measured it to be. One way of getting at that problem is that say that maybe dark energy is really large, but gravity doesn't feel the full effect of it somehow. Maybe, at very large scales, maybe gravity tapers off."
The Stanford proposal is very preliminary and Wiser noted that it may have to be combined with some other experiments onto one craft make the mission feasible. It's only our most primitive and basic of physics intuitions at stake.
An open-access pre-print version of the Stanford paper can be viewed at arXiv.