Why we don't feel the motion of the Earth

Rotating Earth

The Earth rotates once a day, but that's a speed of about 1000 mph at the equator. It also orbits the sun at about 66,000 mph, and the sun moves even faster around the center of the galaxy. The question is: why don't we feel these motions? The answer is given by Isaac Newton. Let's get an intuitive understanding of Newton's insights by noticing what we experience on a plane ride, especially the contrast between takeoff acceleration and smooth cruising at flight altitude.

Aircraft engines powering takeoff acceleration

Takoff

Within seconds at the beginning of takeoff, we feel strong effects of acceleration, even when the plane is going only 30 mph. We feel ourselves pushed back against our seatbacks. We're forbidden to use our tray tables, since anything on them will fly off and hit us. A tennis ball left in the aisle will accelerate toward the rear of the plane and make the flight attendants unhappy. If we wanted to measure the acceleration, there's a thing called an accelerometer that could do that. There's no need to look out the window to know that we're accelerating.

Cruising at altitude

Now let's imagine a smooth turbulence-free ride at cruising altitude. The plane is moving through the air at a steady speed of 550 mph. The physics couldn't feel more different! Feel our backs. There's no pressure at all against the seatbacks. Use the tray table. A cup of hot coffee will not fly off and scald us. Stand up in the aisle and drop a tennis ball. It will fall straight down to the floor. Read the accelerometer. It reads zero. Despite the high speed, the physics very much resembles what we would experience while still parked at the gate.

Relaxing at 550 mph

Can we detect the steady motion of the plane through the surrounding air? Yes, but only by looking out the window at the passing clouds. There's no such thing as a "velocimometer" that can detect steady motion without looking outside at the clouds or the ground. In other words, steady motion is detectable only relative to something else.

Now let's show how this experience demonstrates Newton's three laws. We'll take them in reverse order.

Newton's Third Law: A cannon on wheels will roll back when it fires a ball

Third Law

Newton's Third Law states that while object A exerts a force on object B, object B simultaneously exerts a force on object A of equal strength and in the opposite direction. This is illustrated by the recoil of a civil war cannon when it fires a ball and by rocket propulsion. During takoff acceleration, our backs push on the seatbacks toward the rear. Simultaneously, our seatbacks push our backs forward with equally strong force.

Second Law

The Second Law states that forces cause changes in the speed and/or the direction of motion. Our bodies accelerate during takeoff because the seatbacks push on our backs.

First Law

The First Law is a consequence of the Second Law. If there's no net force on an object, the motion doesn't change. The natural tendency of the object is to keep going straight at a constant speed. This is counterintuitive because we live in a friction-ridden world. Friction is a real force that decelerates moving things. As a result we observe moving objects slowing down and coming to rest, so we think that this is their natural tendency. In the physics classroom we can use dry ice pucks to minimize friction and demonstrate that their natural tendency is to keep going once set in motion.

On the plane ride, the First Law says that once our bodies get the steady 550 mph speed, they get to keep it. The seats don't need to push on us to keep us going, as long as we are protected from friction. This protection is provided by the cabin of the airplane. The closed environment of the cabin shelters us from wind resistance. If we jump straight up, we won't fall behind the aircraft while we are in the air; we'll go straight up and come straight down. (Trying this might bother the flight crew, so dropping the tennis ball is a safer experiment.)

Tennis ball dropped while the plane cruises at 600 mph

Cabin Earth?

The surface of the Earth is also a closed environment. Gravity acts as the "lid" to keep the atmosphere clinging to the Earth. The atmosphere rotates with the Earth just as if were a solid skin. (A rotating planet drags its atmosphere around with it, just as a spinning mixing bowl will cause the liquid inside to spin with it.) This is why a person at the equator will not experience 1000 mph winds; the air is rotating with the Earth.

So when a person on the equator jumps up, he maintains the 1000 mph speed while in the air. As in the airplance cabin, he will land on the spot from which he jumped. Similarly a hovering helicopter keeps its 1000 mph speed while in the air. This is consequence of the First Law.

Bottom line: We don't feel steady motion

All the motions of the Earth, its rotation, its orbit around the sun, its ride around the galaxy, add up to an almost entirely steady motion. There is no turbulence or potholes in space. (There's a tiny bit of centrifugal force, which I discuss in another post.) As in the plane cabin, we don't feel steady motion.

Nor can any instrument sense it except by looking out at something else such as a planet or star and measuring our motion relative to that thing. We know, for example, that the distance between Earth and the star Sirius is decreasing at a rate of 5.5 km per second. We can measure this relative motion measuring the Doppler shift of the light from that star.