Stop the World I Want to Get Off!
Around the Earth in 24 hours
Now that we know how to estimate the circumference of a circle from its radius we can go back to what we really want to know, if we travel around the earth in 24 hours, how far do we go and how fast? Okay, get out your calculators (or you pencils and paper)….
The Earth is about 12,750 km in diameter. We’ll round that up to 13,000 km and multiply by 3 to get the circumference as 39,000 km. It takes you 24 hours to travel that distance. So we divide by 24 hours to get just over 1,600 kph (1,000 mph)! That’s faster than the speed of sound! It’s a good thing the Earth also drags the atmosphere along with it, too.
Actually, that’s the speed at the equator. We’re pretty far north compared to the equator so it turns out we’ “only” travelling about 1,200 kph (760 mph). That works out to be about 1 km every 3 seconds. Quick question: how fast would you be travelling if you were standing at the North Pole? At the South Pole?
Around the Sun in 365 (and 1/4) Days
Now let’s repeat our estimate for our annual trip around the Sun. The distance to the sun is 150 million kilometers. So the trip around the Sun is almost 900 million kilometers. Let’s estimate the year as 360 days just because we can do the math easier:
900,000,000 km / 360 days = 2,500,000 km/day.
Okay, there’s 24 hours in a day, so since we’re estimating, 2,400,000 km/day is pretty close and it divides by 24 easily, so we’ll just “round” down a little to get 100,000 kph. Yep, you read that correctly, 100,000 kilometer every hour. That works out to almost 28 kps (kilometers per second).
Around the Galaxy in 250 Million Years (More or Less)
You might have thought we were done. Heh, heh. The Sun is not sitting still, it’s orbiting the galactic center. It takes a very long time to go around. People have not been around on Earth long enough to have witnessed a single full orbit, but we can still measure the distance to the galactic center and how fast we’re moving. The distance to the center of our galaxy is about 28,000 light-years. That makes the diameter of our orbit about 56,000 light-years. Since it takes 250,000,000 years to cover “onlhy” 56,000 light-years, that sounds pretty slow compared to all the other speeds. Get your calculator and you find that works out to 0.000672 light-years per year. But…
A light-year is the distance traveled by light1 in one year. And light travels fast. 300,000 kps (that’s kilometers per second) fast. It takes light a bit over one second to get to the moon. In that same second it goes around the earth 7-1/2 times.2 And there are a lot of seconds in a year: (60 sec/min) x (60 min/hour) x (24 hour/day) x (365 days/year) gives 31,536,000 seconds/year. The official definition of a light-year is a little different and it works out to be 9,460,730,472,580,800 meters.3 Call it 9.5 trillion kilometers.
Okay, at the risk of being boring, we do the math again, and just get out your calculator:
(9,500,000,000,000 km/ly) x (3 x 56,000 ly) / (250,000,000 year) = 6,384,000,000 km/year
Convert it to kps and we get just over 200 kps!
Stop!
Okay, so we’re spinning around the Earth at a “mere” 1200 kph taking a whole 3-seconds to travel one kilometer. Then the Earth is whipping around the Sun at nearly 28 kilometers every second. And if that wasn’t enough, the whole Solar System is whizzing around the galactic center at over 200 kilometers every second. Whew, that’s fast. But wait! Our galaxy isn’t sitting still. We’re currently on a collision course with M31, the Andromeda galaxy speeding toward one another at about 130 kps4. And our entire local group of galaxies is heading in the general direction of galaxies in the constellation Virgo at a speed of about 5,000 kps!.5
Footnotes
1 Technically, its the distance traveled by light in a vacuum. That may sound picky, but light slows down when it has to travel through matter, even the air. It can slow down a lot in certain types of naturally occuring crystals and glasses. In fact, your eyes depend on this effect in order to focus! Light coming in at an angle to a medium where its speed changes results in the light bending. The same thing happens to water waves when, for example, the cross from a deep to a shallow area (or vice-versa). Also, while we talk about “light,” the speed really applies to any form of electromagnetic radiation, including things like radio and X-rays.
2 The numbers I used here are not consisten with our earlier estimate of the size of the earth but used the slightly more accurate number of 40,000 km for the radius.
3 http://en.wikipedia.org/wiki/Light_year. The IAU uses 365.25 days/year for their calculation and a more exact speed of light number.
4 See http://www.cita.utoronto.ca/~dubinski/tails/node11.html.