Chapter 3: Gravity and Orbits

3.2
Gravity

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.

Stephen Hawking in Zero Gravity

Stephen Hawking: Exempt from your petty "laws".

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?

The answer can be found in Newton’s description of gravity: the amount of gravitational force is proportional to the masses of the two objects and inversely proportional to the square of the distance between them. As promised, I won’t try to help you make sense of the mathematical meaning of that sentence, but I thought I might mention that this is the first example of an ‘inverse square law’, something which we’ll see again later on.

In the meantime, the key point is that the amount of gravitational force the pen feels depends on its own weight and on the weight of the water glass (as well as the distance between them). And these two objects are, in the big scheme of things, actually quite light – certainly not as heavy as a planet or a star. So the amount of force they exert on each other is so weak that your arms aren’t sensitive enough to feel it.

Meanwhile, right below us there exists a ridiculously large and heavy thing called the Earth. And the pen and the water glass are also attracted to the Earth, but because the planet is so heavy, it pulls them with a much stronger force than the one that pulls them towards each other.

And so right away we can see two reasons why an understanding of gravity eluded us for so many thousands of years (as discussed in the previous section). The first is that gravity is invisible. We’re quite comfortable with the obvious sorts of pushes and pulls – ‘contact’ forces, as they’re called in physics. When you can see the muscles of a human being strain as he leans into something heavy like a big rock, it’s not at all surprising to see that rock start to move. But the force of gravity occurs even when the two objects involved aren’t in contact. If you jump into the air, some intangible connection between you and the planet remains, and you get pulled back down. And although Isaac Newton discovered how to calculate and use this invisible force to explain all kinds of natural phenomena, the bizarre nature of the ‘action at a distance’ always bothered him tremendously, as we’ll see when we talk about Einstein’s General Relativity.

The second reason gravity remained hidden for so long is that it is tremendously weak. You may not feel that way when you’re leaning over a balcony on the twenty-third floor and looking down, but it is. To prove it, try this simple experiment: lift up a nearby object. Choose something small – if that pen you had earlier is still around, use that. Most people won’t find this experiment very difficult to accomplish. But think about it: there is an entire planet trying to pull this pen down, and yet with the slightest effort, you’re able to pick it up and toss it around gaily.

Baby toss

Also: babies.

In fact, as I’ve already mentioned, gravity is the weakest of the four fundamental forces. The next strongest force of the four is more than a billion billion times stronger, and it is named the Weak force. How embarrassing for gravity.

But there is one important redeeming factor for this milquetoast of a force: its effects are felt even at infinite distances. That’s right – infinite. Gravity gets weaker the farther apart the two objects are (following the inverse-square law), but it never entirely disappears. If you took off in a rocket and headed straight up, then at an altitude of 100 km, the Earth would be pulling on you about 3% less than when you were on the surface. At 500 km, gravity would be 14% weaker. If you went all the way to the moon (which is about 386,000 km away), you would still feel a gravitational pull towards the Earth. This pull would be only about 0.03% of its strength back home, and even the moon’s weak gravity would be more than 600 times stronger, but you would still, technically, feel it.

If you start to think about this too hard, you might accidentally blow your own mind. Because what this means is that when we’re on our own planet, we’re feeling gravitational forces coming from the moon, from the sun, from Jupiter… and also from stars billions and billions of kilometers away, and even from distant galaxies, at distances so large that they’re beyond our imaginations.

Of course, most of these forces are very weak because of how far away those things are. If you’re standing on the Earth, the planet’s gravitational pull is 1600 times stronger than the one coming from the sun and ten thousand billion times greater than the one coming from the entire Andromeda galaxy, the closest spiral galaxy to our own.

So, everything exerts a gravitational force. If you’re standing on the moon, you don’t feel weightless (a surprisingly common misconception), but there’s a lot less force pulling you down – about one sixth of the amount of gravity on Earth. That’s why the Apollo astronauts were able to leap around on the moon even though they were in bulky space suits. If you were on the surface of the sun, which is rather big, you’d feel an enormous gravitational force for the fraction of a second before you turned into a little pile of soot.

This is yet another example of the fact that although gravity is everywhere at all times, it never attracted all that much attention from us humans.

The last thing to mention about gravity is that curious fact pointed out by Galileo: all objects, regardless of mass, accelerate due to gravity at the same rate. What this means is that if you held a hammer in one hand and a feather in the other and dropped them both at the same time, they would both hit the ground at exactly the same moment.

“No,” you say, “that’s impossible! You already told me that gravity depends on mass, and the hammer is much heavier, so a greater force of gravity must pull it down, making it fall more quickly. This is hogwash!”

Don’t throw your computer across the room in a fit of righteous fury quite yet: you’re correct. But the reason they don’t land at the same time is that the feather experiences a much greater amount of air resistance relative to its small force of gravity, and so the net result is a very small acceleration. If you could get rid of all of the air messing things up, you’d find that the feather would plummet straight downwards at the same rate as the hammer. If you don’t believe me, try putting a piece of paper on top of a big book; drop the book, and the paper will stay right on top of it as it falls. Or you can ask the Apollo 15 astronaut Dave Scott. When he was on the moon, where the atmosphere is extremely thin, he performed this exact experiment.

The reason this happens has to do with Newton’s Second Law, which, as you’ll remember, states that mass tends to decrease acceleration. So while heavier objects experience more gravity than lighter ones, they also accelerate less quickly. The two effects just cancel each other out, meaning that all objects have the same acceleration on Earth (or the moon, or in any other location) regardless of their mass.

Big Ideas:

  • All objects attract each other with an invisible gravitational force. This force is stronger when the objects are heavier and weaker when the objects are farther apart.
  • Gravity is the weakest of the four fundamental forces.
  • The gravitational field around an object extends forever in all directions.
  • In the absence of air resistance, all objects experience the same gravitational acceleration on Earth, no matter how heavy they may be.
3.2 Gravity   (from Chapter 3: Gravity and Orbits)


   

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