Considering the motion of the Earth, the solar system, and the galaxy, how fast am I moving while lying in bed asleep?
Figuring in the Earth's spin, its rotation around the sun, the suns rotation around the galaxy, and the galaxy's rotation around the center of the universe (wherever that is) how fast am I moving even while lying in bed asleep?
Well, it depends. Your latitude on Earth--that is, how close you are to the equator--and the time of year make a difference. I'll explain why. Your motion is made up of four pieces: the rotation of the Earth on its axis, the motion of the Earth around the Sun, the Sun's orbit about the center of the galaxy, and the motion of the whole galaxy.
Now, at the equator, the Earth's rotation translates into a speed of about 0.5 km/s (you can find these numbers here). But if you are at the North or South pole, the speed due to rotation is zero! If this doesn't make sense immediately, imagine a person standing on the equator. Though she's standing still, she actually covers a lot of distance as the Earth rotates--in one day, the Earth's rotation carries her a distance equal to the circumference of the Earth, about 24,000 miles. Now imaging someone standing at the North pole. The Earth's rotation doesn't carry him anywhere at all--so his velocity is zero. I assume you live somewhere in between the equator and the poles, but we'll use the speed at the equator to make things simpler.
Next, the Earth moves at about 30 km/s in its orbit around the Sun. This is a lot faster than the 0.5 km/s caused by the Earth's rotation on its axis! In fact, because it is so small compared to the other velocities we're working with, it's reasonable to ignore that 0.5 km/s for the rest of the calculation.
Now, the whole solar system is moving around the center of the galaxy at about 230 km/s. For half of the year, the Earth's motion around the sun is in the same direction as this motion about the center of the galaxy, but for the other half, it is in the opposite direction--that is, sometimes we're moving "upstream," and sometimes we're moving "downstream." When the motions are exactly aligned, the velocities combine to 230 km/s + 30 km/s = 260 km/s When they are opposite, though, we have to subtract the velocities: 230 km/s - 30 km/s = 200 km/s
So that sums up the first three kinds of motion. Finally, there is the motion of the whole galaxy, which can actually be broken down further into the motion of the galaxy in the Local Group--a cluster of about 20 galaxies--and the motion of the Local Group in an even bigger cluster, the Local Supercluster. These velocities are about 40 km/s and about 600 km/s.
Adding everything up, we get:
30 km/s + 230 km/s + 40 km/s + 600 km/s = 900 km/s
So, you're moving pretty fast as you lie in bed!
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