Chapter 3: Gravity and Orbits

Critical Questions:

• What is a black hole?
• What happens near a black hole?
• How do we know they exist?
• What about wormholes?

In order to explain what black holes are like, I’d like to relate to you the following parable.

A bunch of physicists are up late one night. They’ve been at a party. Most of the guests have left by now, nobody’s noticed that the music has stopped, and the air smells only faintly of sweat and a remarkable range of mind-altering substances. Somebody is passed out on the couch, but no one seems to know who it is. During a lull in the mumbled conversation, one of them happens to look up through a skylight and see the stars. She begins to think about how far that light has travelled to reach Earth, and about why it didn’t just stay where it is. She says so, out loud. One person mumbles in agreement. Another person suggests that maybe some stars don’t allow their light to leave at all. This sparks a two-hour long discussion that includes a whole complement of theories related to this kind of dark star, with names like the no-hair theorem and the information loss paradox. Before the last of them finally falls asleep, he mutters, “Black hole. We can call it a black hole.”

To the best of my knowledge, this is not a true story. But if you learn enough about black holes, you might be tempted to think that this is how people thought up the idea.

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Critical Questions:

• What is General Relativity?
• How do we know that general relativity is correct?

Ok, if you’ve already read the previous post, we can now dive into the awesomeness of General Relativity.

I’ve already said that Isaac Newton was bothered by his own theory of gravity because it seemed to involve things affecting each other through empty space, without ever coming into contact. In fact, nobody felt comfortable with the idea of a force that acted at a distance: it seemed too much like fantasy and not enough like solid science.

The only problem was that this theory worked very, very well. It explained almost everything related to gravity, most notably the motions of all of the planets and stars in space. It was even used to successfully predict the existence of the planet Neptune based on the motions of Uranus (albeit almost 200 years later), and verified predictions are the true test of any scientific theory. But Newton wrote the following in a letter six years after publishing Principia:

“That gravity should be innate, inherent and essential to matter, so that one body may act upon another at a distance through a vacuum, without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me a great absurdity, and I believe that no man who has in philosophical matters a competent faculty of thinking, can ever fall into it. Gravity must be caused by an agent acting constantly according to certain laws; but whether this agent be material or immaterial I have left to the consideration of my reader.”

This was a daunting challenge, and one which most people judiciously ignored until Albert Einstein began working on General Relativity in 1907.

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Critical Questions:

• What can we say about General Relativity without using math?
• What does ‘relativity’ mean?

Before I even say one word about General Relativity, I feel obliged to issue a stern warning: prepare to be frustrated.

You see, most of the rest of the physics you’ll see on this site originated within one or two hundred years of Isaac Newton and the invention of calculus. This means that although there is some quite difficult mathematics behind it, most of it is based on direct observation and can be understood from a conceptual standpoint without worrying too much about the math.

But by the time Einstein came along, the field of mathematics had made some significant progress. All of the physics theories loosely called ‘Modern Physics’ (the Theories of Special and General Relativity and Quantum Mechanics being the main elements) involve lots and lots of extremely difficult math, and General Relativity is no exception. Read almost anything on the subject, and you’ll only need to encounter a few words like ‘semi-Riemannian metric’, ‘Lorentz invariance’, or ‘tensor fields’ before realizing that a true understanding of this stuff requires a small library of books, a PhD, and godlike determination.

So when it comes to modern physics, if you want to avoid the math, you’ll be limiting yourself to hearing only the consequences of the theory rather than getting satisfying arguments for why it must be true.

But with that said, the consequences are so important and yet so eye-gougingly bizarre that they deserve some mention.

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Critical Questions:

• What do the orbits of the planets really look like?
• What causes the tides?
• How do artificial satellites orbit the Earth?

Back in Section 2.9, I explained a bit about how orbits work. I said that things in space orbit other things because gravity acts as a centripetal force, resulting in circular motion that goes on forever because there is no friction to slow things down. Now I get to do the fun part: go back and explain why much of what I said then was incorrect.

First of all, no orbits are perfectly circular. Circular orbits require a very specific combination of speeds, forces, and distances, but nature doesn’t like specific requirements, preferring instead the exciting chaos of random numbers. If you take a planet and get it moving near a star, then there are a few possible outcomes depending on speed and distance. The planet may end up with a circular orbit, but that is so unlikely it’s essentially impossible.

The second option is an elliptical orbit. An ellipse is just a circle that has been flattened (a circle is actually just a special kind of ellipse, just like a square is a special kind of rectangle). The ellipse is the shape of all of the orbits we know about, including Earth’s path around the sun and the moon’s path around the Earth. And in an elliptical orbit, the thing that is being orbited doesn’t sit at the exact center of the ellipse, but is located a bit off to one side.

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Critical Questions:

• What is the difference between weight and mass?
• Why do you weigh less on the moon?
• Why does your stomach lurch when the elevator you’re in starts moving?

You might have noticed that in the last section, I used the words “mass” and “weight” interchangeably. If a certain type of physicist were reading that section, I might be in jail by now. At this point, I should placate the purists out there and be a bit more precise about all of these terms.

Imagine stepping onto a simple bathroom scale and seeing the little needle turn. You might think that the way a scale works is obvious, but let’s Think Like a Physicist here and describe this situation technically. First of all, your body is pulled downwards by the gravitational attraction between yourself and the Earth. A coiled spring inside the scale compresses, providing you with more and more upwards force the more it is compressed. The whole thing adjusts itself, with a bit of wobbling, until it stops at a point when the upwards force from the spring is exactly equal to the force of gravity pulling you down. (At that point, the net force on you is zero, so you don’t accelerate.)

We know from the previous section that objects of greater mass experience a greater force of gravity, so heavier objects will stabilize with a more tightly compressed spring and thus a higher scale reading.

That may seem like a needlessly complicated way to describe what’s happening, but it reveals an interesting truth about weight. The scale isn’t directly measuring anything about you. It measures the amount a spring compresses, which measures the amount of gravitational force acting on your body.

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Critical Questions:

• Why do things fall?

The most remarkable thing that Newton’s Law of Universal Gravitation tells us is that everything attracts everything else with a force that we call gravity.

This is not an obvious point. If you hold up two objects right now, like a pen and a glass of water, I doubt you’ll feel them pulling towards each other. You can try moving the pen back and forth a bit and you still won’t feel anything. If you let go of it, it’s not going to zip over towards the glass and stick to the side of it like a magnet. And yet the miraculous Law of Universal Gravitation tells us that the pen and the glass actually are pulling towards each other – not with the same type of force we see in magnets, but with a force that acts in much the same way. So why can’t you feel it?

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Things fall.

This is such a basic part of life that our very bodies are built to function in a world where things fall. When astronauts go up into space, they have to exercise hard to combat the effects of a lack of gravity, and when they come back to Earth, their heads are swollen and their legs are thin for a few days afterwards.[1. I am not making this up.]

We’ve been dealing with the fact that things fall since the moment the first homo sapien came up with a word (or particular tone of grunt, maybe) to describe falling. Longer than that – we’ve been dealing with it since the time when our distant evolutionary ancestors began to be able to develop a dim distinction between up and down.

We knew that things fell long before we knew that the stuff around us was made up of little bits called atoms, before we knew what stars were, even before we knew how to rub two sticks together to make fire.

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