So, the moon stays in orbit around the Earth, right?
Yeah, I thought so. But why? The moon’s orbit is not a straight line, which means it’s accelerated motion (using the physics definition, which is absolutely any change in speed or direction).
And in order for acceleration to happen, according to Newton’s first law of motion, a force has to happen—meaning, something has to reach out, touch the moon, and drag it into orbit around Earth.
Well, that doesn’t happen, last I checked. I mean, it’s not like we have some kind of giant cord connecting us to the moon. How crazy would that be?
So why does the moon orbit the Earth?
It all depends on the inverse square law.
Here, we see the inverse square law as it works for light. Luckily for Newton, it works the same way for light and gravity. And Newton already understood the way it works for light, since he’d worked with optics (the parts of telescopes you see through).
Basically, imagine a light source at the center of the circles diagramed here. It’s intense enough to shine on, say, one square meter of a surface one meter away—as demonstrated by the orange sphere.
But here’s the trick of it. If you make that light shine on a surface two meters away, the light will cover four square meters. And since the light didn’t get more intense, the same brightness has to spread over all four square meters.
In plain English, that means the light is getting spread out. So for each individual square meter, it’s much less intense.
Fun fact, by the way—this is why summer light is more intense than winter light. Sunlight hits the ground at more of an angle during the winter, spreading out the light.
As you can see, if you move your surface three meters away, the light will have to shine over nine square meters, making it that much weaker.
And gravity—surprise! —works in the same way.
This image is a little bit mathy, but I included it in case you wanted to see the actual numbers and calculations involved. I try my best not to go into depth about math on this blog.
Basically, as distance from a planet increases, the strength of gravity decreases. At any distance from the Earth, if you divide gravity’s strength at the surface by the square of the distance, you get gravity’s strength at that distance.
How did Newton figure this out, anyway?
Part of it, he just assumed—and got lucky. Philosophers, mathematicians, and astronomers before him had tried to figure out the universe by assuming things, such as the idea that the Earth was the center of the universe.
That’s one paradigm that shackled astronomy’s progress for quite some time.
Newton wondered if the force that kept the moon in orbit was the same as the force that caused apples to fall from trees. The only question was whether that force extended farther than the mountaintops.
Newton assumed that it did—and from his work with optics, he assumed that the inverse square law would work to explain it.
In other words, he guessed that gravity decreases with the square of the distance.
But Newton was different from past astronomers, in that assumptions weren’t enough for him.
Like Kepler before him, who was the first to apply mathematics to astronomy and get the right answers, Newton actually calculated what the gravitational force would be at the moon’s distance if he was right.
He knew the size of the Earth, and he knew the rate at which object’s fall. So he was able to calculate the strength of gravity at Earth’s surface.
From that, he took the distance to the moon and figured out how strong gravity would be that far out.
He calculated that the moon should fall toward the Earth at 0.0027 m/s2. But would that be enough to hold the moon in orbit?
Newton then calculated the moon’s acceleration. He knew its distance from Earth and how long it took to complete an orbit (its orbital period), so he was able to figure out the rate at which the moon was actually accelerating toward the Earth.
And lo and behold, it came out to be 0.0027 m/s2.
What does this mean? The moon is indeed held in Earth’s gravity according to the inverse square law.
But that’s not all Newton figured out. Naturally, if Earth exerted a gravitational force on the moon, then—according to his third law—the moon has to exert a gravitational force on the Earth.
And those forces are equal.
Wait a second, what? Since when are those forces equal? I mean, the Earth doesn’t orbit the moon…and they sure don’t orbit each other.
Or do they?
As it turns out, the moon actually does tug the Earth around a bit. It’s not enough to make the Earth orbit the moon, but the Earth does move.
Imagine how far this idea is from the classical astronomers’ original idea of Earth…had anyone told them, over a thousand years ago, that the Earth moved at all, they would have laughed in modern astronomers’ faces.
But now we know that not only does the Earth orbit the sun, instead of the other way around, the moon actually tugs a bit on the Earth. And so do all the other planets.
Yes, I’m serious.
That’s the concept of universal mutual gravitation. In fact, not only does every planet in the solar system tug a little bit on every other planet in the solar system, every object in the universe tugs a bit on every other object in the universe.
I know that idea is way insane…but it’s true.
Are you wondering how that can possibly be true, when Earth doesn’t get bounced about the universe as everything that’s out there exerts a gravitational tug?
Well, just remember the inverse square law. By the time we get outside Pluto’s orbit (and the orbits of the Kuiper Belt and the Oort Cloud, which I’ll write about much later), even the sun’s gravity isn’t enough to hold anything in.
So how could the gravity of a star 4.2 light-years away—so far away it takes light 4.2 years to reach us—even noticeably touch our solar system?
Gravity exists all throughout the universe, and there’s no set distance where it suddenly stops. It fades and fades and fades until it doesn’t make a difference at all.
But what is gravity?
Well, astronomers wouldn’t figure that out until Einstein came along. We’ll get into that a few posts from now.