The Physics Philes, lesson 70: Gravity. It’s the Law!
This is an exciting day. Today is the day we start discussing gravity, and I’m mad excited about it. No, not the film. The real deal! It’s the most important force in the universe! It holds stars together and it holds the moon in orbit and it keeps slapstick comedy hilarious. (You know, because of all the falling.) It bends spacetime, for crying out loud! This is cool stuff. There is a lot to talk about, but we have to walk before we can run. Let’s begin!
As you probably know (because you’re super smart), gravity is one of the four forces found in nature, and it’s the one that we humans first started studying extensively. It was Isaac Newton who realized that the force that caused things to fall to the ground was the same force that kept the moon from doing the same thing. He published his law of gravitation in 1687. It states that:
Every particle of matter in the universe attracts every other particle with a force that is directly proportional to the product of the masses of the particles and inversely proportional to the square of the distance between them.
OK, this is one of the few times that I think seeing the equation makes a concept more clear.
In this equation, the F is the magnitude of the force on either particle, the “m”s are the particle masses, and the r is the distance between the particles.
But what is G? G is the gravitational constant, and it must be measured. Sir Henry Cavendish did just that in 1798. He used this thing called a torsion balance. It’s a rigid rod shaped like an inverted T that is supported by a thin quartz fiber. It has two small spheres mounted on the ends of the horizontal arms of the inverted T. These are mass m_1.
When we bring two large spheres (mass m_2) into close proximity with the small spheres, the attractive gravitational force between the spheres cause the T to twist. Kind of like this (as seen from the top):
As you might expect, the actual movement and force measured in this experiment are incredibly tiny. What you have to do is shine a light on a mirror that is mounted on the top of the T. The reflected beam strikes a scale and we can measure how the light moves along that scale as the T twists. Kind of clever, really. Measured to three significant figures, the gravitational constant is:
It’s important not to get G and g mixed up. Lowercase g is the acceleration due to gravity that relies on location and mass. The uppercase G is the gravitational constant and it’s universal. It doesn’t matter where in the universe a particle is; the gravitational constant acts on that particle in the same way.
Now here is where it gets weird.
Gravitational forces form an action-reaction pair, á la Newton’s third law of motion. Even when the masses are different, the magnitude of the gravitational force exerted on each body is the same. So whenever you fall down, the Earth also falls up to meet you! You just don’t notice because the Earth is so much more massive than you are that its acceleration is tiny.
How bananas is that?
So far we’ve been talking about particles, but if an object has spherically symmetric mass distributions, we can treat it as a particle. Which is super handy when dealing with super cool space stuff, like planets.
For example, say we modeled Earth as a spherically symmetric body. The force it exerts on another particle can be written like this:
But this only works if you’re outside the Earth. What happens when you go inside. Weird things, man. But they make sense when you think about it.
You see, the gravitational force decreases as you go inside the Earth. How could this be? Well, as you dig your way into the Earth’s center – not something I suggest you do in real life, by the way – some of the Earth’s mass is on either side of you and pulls in opposite directions. Exactly at the center of the Earth, the gravitational force is nothing. You’d be effectively weightless. (You’d also be dead, but that’s another thing entirely.)
In addition to all the other things it does, gravity explains why big celestial bodies are spheres. Each particle is gravitationally drawn to one another, so they want to minimize the distance between them. When there is enough mass, the body forms a sphere. That’s why planets and stars are round, but asteroids can be kind of potato-shaped.
Gravity is a force that acts at a distance. All forces that act at a distance are said to have fields. That means that one body sets up a disturbance at all points in space and the force that acts on the second body at a particular point is a response to the first body’s field. In this section we won’t be dealing a lot with fields. Just a little FYI from me to you.
That’s a lot to take in, so we’ll leave it hear for now. Tune in next week for MOAR GRAVITY.
Featured image credit: Wikipedia