by Shane L. Larson
General Relativity is only the latest refinement of our ever growing understanding of gravity. Most of us become aware of gravity at a very young age. It is a playmate when we throw balls, an accomplice when we knock our unwanted food off the table, and our Nemesis as we learn to stand up and walk. All things being equal, gravity is a source of much mayhem when we are children, but hidden in the chaos we learn a few things, and we learn them deeply. When we drop things, they fall. When we jump in the air, we always come back down. It is such a pervasive part of our lives, that we seldom give it a second thought. Once you start school, you learn that gravity is a thing, and that thing keeps you on the floor, makes rain fall from the sky, and makes planets go around the Sun. Gravity is something you learn about in science class. But why is it a part of science class, when you learned about it as a toddler?
The job of a scientist (and a toddler) is to look at the world around us, take note of those “obvious” things that we don’t even give a second thought to, and ask “why is the world that way?” The answers to that question enable us to harness Nature by predicting the future. If I understand gravity, I can figure out how strong a building needs to be without tipping over (like the Leaning Tower of Pisa), I can figure out how much pressure a water tower will provide for a city, or I can figure out how big to make an airplane wing so it can fly. There is other physics to be sure in all of these, but gravity is at the heart of it all, just as we learned as children.
So how do we think about gravity? After all, it is not like an orange or a Lego brick — it’s not something tangible that you can pick up. In fact, if anything, it is totally invisible! The discovery of the invisible and how to talk about it is still one of the greatest feats of the human imagination. The first person to do this for gravity, was Isaac Newton. Fundamentally, Newton put us on the path to describing gravity using mathematics, the language of science. He first wrote down the Universal Law of Gravitation in his 1687 book, the Principia, along with all the math you needed to work with the Universal Law (read: calculus). Einstein refined and extended our understanding of gravity by writing down general relativity using a new mathematical approach: curvature and tensor calculus.
But learning how gravity works in the Cosmos from mathematics can take years of practice and patient study. Fortunately, we can develop some intuition about how gravity works by learning to draw some simple pictures.
Physicists describe the long range effect of gravity using the concept of a “force field,” or simply a “field.” As is often the case with spoken language, scientists adopt common words to mean very specific things that don’t always jive with what the rest of us think the word means. What do you think of when I say “field?” If you’re a country kid like me, you may imagine a vast expanse of rolling hillsides in eastern Oregon, stalks of wheat heavy with ripening grain rippling as the wind blows across the “field.” Others of you may imagine a late July afternoon, the hot sun shining down on the bleachers in Wrigley Field as the Cubs once again try to chalk up a win in the run to the pennant. Neither of these examples is what a scientist means by “field,” but they both have an important element to the scientific definition — big, open spaces.
An important part of understanding gravity is recognizing that no matter where you are in space, if there is a source of gravity somewhere (say a planet, or a star), then you feel the tug of that gravity. Gravity fills all of space. That simple fact leads to the concept of a “field” in physics. We are going to draw pictures of fields, but there is a robust and well understood mathematical treatment of fields that will give you the same intuition (and more) as our simple pictorial model.
So how do we draw a picture of the “gravitational field?” The rules are:
- Draw arrows to represent the “gravitational force.” Those arrows fill all of space, and point toward the source of gravity (the direction that gravity is trying to pull you); they are usually called “lines of force.”
- Big, massive objects have more gravity than small objects, so they have more arrows pointing toward them — they exert more gravitational force on their surroundings.
- The gravity any object experiences is understood by how closely packed the field lines are in the vicinity. Lots of field lines near you equates with stronger gravity in your vicinity.
The planet itself is enormous, comprised mostly of gas surrounding a small rocky core. Deep beneath the clouds the pressure and temperature soar, making Jupiter glow in the infrared, cloaked in the light of its own inner heat.
On the top of the clouds, an enormous cyclonic storm has roiled and churned for at least the last 400 years, sometimes growing to three times the size of the Earth. We call it “The Great Red Spot.”
Among Jupiter’s entourage of moons is a wild and unpredictable world with volcanoes that spew molten sulfur 500 kilometers into space. This is the most volcanically active world we know, called Io.
In 1992, Comet Shoemaker-Levy 9 strayed too close to Jupiter and was torn apart into 22 fragments. In 1994, as we watched from the relative safety of Earth, each of those 22 chunks of rock and ice pummeled into Jupiter one after another. Any one of them could have leveled our cuvilization; they burned and scarred the clouds of Jupiter, but over time even those marks faded into memory and Jupiter kept on about its business as if nothing had happened.
Each of these wonders, each of these strange and wonderful things we have discovered at Jupiter, are a consequence of Jupiter’s enormous gravity.
Let’s draw the picture of Jupiter’s gravitational field. The number of field lines is related to the mass of the planet. Suppose we drew 10 lines to represent the gravity of the Earth. Jupiter is 318 times more massive than Earth, so we should draw 3180 lines to represent the gravitational field of Jupiter! That’s too many to easily see, so let’s just think about Jupiter’s own gravity, and decide it can be represented by 8 lines.
The gravitational field fills all of space, so no matter where you are, you feel the tug of Jupiter pulling on you, from wherever you are, directly toward Jupiter. Far from the planet, the lines are more widely spaced, so gravity is weaker than it is down close to the planet where the lines are closer together.
Now, let’s conduct a gedanken experiment — a thought experiment — together. This is a time honored method in theoretical physics to try and understand how the world works. The basic idea is this:
(0) Suppose you have some aspect of Nature you are trying to understand; in this case, the “field description” of gravity.
(1) Imagine a situation to which the law of physics should apply. This could be a situation that could legitimately be addressed in the laboratory with an experiment, given enough time and money, or it could be a physical situation that we can’t recreate but might encounter in Nature. This second case is the one we would like to consider, as it involves the gravitational field of an entire planet.
(2) Apply the law of physics to your situation, and examine all the possible outcomes that would result if you could actually do the experiment for real.
(3) Lastly, you examine the consequences of your gedanken experiment by asking legitimate questions and answering them. Do the predicted outcomes make sense? Do any of the outcomes violate the laws of physics? Are there observational consequences that we might be able to see that would confirm our gedanken experiment?
For our thought experiment, let’s imagine we had the ability to simply squeeze Jupiter and make it smaller. We don’t want to take any mass away, or add any mass to it, we simply want to squeeze it into a smaller, denser ball of stuff, and ask what happens to the gravitational field.
If we follow our rules for drawing fields: (1) The number of field lines won’t change, because the mass of Jupiter doesn’t change. (2) The field lines fill all of space. When we squeeze Jupiter smaller, the field lines in the picture already fill space far away from Jupiter, so we just need to extend down toward the new, smaller Jupiter.
Now we examine the consequences of our experiment. Far away from Jupiter, nothing has changed. The same number and spacing of field lines are present with the big or the small Jupiter. If you’re an astronaut, drifting aimlessly in orbit around Jupiter, nothing noticeable happens. But in close, things are a bit different. In the case of the big Jupiter, if we hovered over the clouds we felt some pretty strong gravity. If we compare that to the case of hovering over the clouds of the new small Jupiter, we feel even stronger gravity! How do we know this? Because near the new small Jupiter, the field lines are closer together.
So what do we conclude from this? The “surface gravity” of an astronomical body depends on the compactness (or, more properly, the density) of the planet/star/thing in question. Far away from the astronomical body, the gravitational field depends only on the total mass of the object.
Can we observe these effects for real, somewhere in the Cosmos? Yes!
When a star like the Sun reaches the end of its life, it does not explode. Instead, it shrinks to a husk of its former self, a shriveled skeleton known as a white dwarf. White dwarfs are about the size of Earth, but have the same mass as the Sun. We observe atoms moving in their atmospheres, just over the surface and find that the surface gravity is a staggering 10,000 times greater than the surface gravity of the Sun. By a similar token, many white dwarfs orbit companion stars, and some have been observed to have planets (perhaps long ago, and we just didn’t realize it), all of which are far from the white dwarf but careen happily along their orbits as if they were orbiting an ordinary, Sun-like star.
These observations agree handily with our gedanken experiment. We used our pictorial model to deduce that if you squeeze an object smaller without changing its mass, the surface gravity changes, but the gravity far away does not!
The Cosmos, and our brains, have not let us down. We’ll put these ideas to the test again, as we delve into the development of General Relativity and encounter even stranger and denser objects — black holes.
This post is part of an ongoing series written for the General Relativity Centennial, celebrating 100 years of gravity (1915-2015). You can find the first post in the series, with links to the successive posts in this series here: http://wp.me/p19G0g-ru