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If Earth stopped suddenly, you would fly off into space. Maybe.

September 28, 2007

It was a Thursday. I remember it clearly. A crisp fall breeze, some leaves scattered below the trees and around my feet as I walked through the park. Then I was flying in outer space.

OK. It will never happen, but on this particular day, the hand of G-d came down, and stopped the earth from rotating. He didn’t slow it down, wobble it, or let it go. He just stopped it, dead.

Earth Stops Rotation

Would we fly off into space? Doubtful. Would we have the wildest ride into the upper atmosphere? Probably!

You see, the earth’s equator is about 40,000 km in circumference. Given a 24 hour day, this is a relative speed of about 1666.6667 km/h. While this is impressively fast, it’s just not enough to launch us into outerspace for 2 reasons.

  1. Escape velocity of the earth’s gravity is 40,000km per HOUR! We’re only doing that per day.
  2. We wouldn’t have enough momentum to overcome the drag of our bodies in the earth’s atmosphere.

We need to consider the launch vector. Even if we were going a zillion kilometers per hour, we wouldn’t be launched straight up. We’d be launched sideways! Most likely you would end up smacking into a tree at mach 1.357.

But, let’s say that you were standing on a pier in Nova Scotia, looking at the ocean. You would not run into anything when you get launched Eastward. Because you would start off flying at a remarkable speed, there’s a chance here that you would gain *some* altitude. We need to consider the following if we’re going to see how high off the ground you’d go:

  • Initially, gravity would “appear” to have no effect on your direction of travel.
  • As you moved at great speed, the earth’s horizon would appear to fall away from you. In this respect, you would gain altitude. This won’t be the case for our experiment though, we’re just not going fast enough.
  • Because you have more mass and kinetic energy than the air around you, your body could potentially become an airfoil as it flies through the air, providing additional lift.

Wow, let’s just pretend for now that you’re in vacuo (no atmosphere to create drag or lift on your body). Obviously, earth’s gravity is eventually going to win. Let’s also pretend that this pier you’re standing on is 10 meters high off the ocean. How far are you going to fly until you make splashdown?

Vertical motion at 10 metres height is sqrt( (2)(10m) /(9.8m/s2) )=1.42857 seconds.

Therefore, with us moving at 462.962972 metres per second (wow), we will travel 661.375 metres before we hit the water. That sucks.

Drag effect. Oh man, don’t ask me to do that…. way too many variables. First off, we’re not just talking induced drag (from creating lift) or parasitic drag (ie. skin friction, form drag), but also, because we are flying faster than the speed of sound, we’d need to calculate Wave Drag. What a drag.

Suffice to say, you’d die. And it was such a nice day….

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One Comment leave one →
  1. brown permalink
    April 19, 2011 2:01 am

    was thinking about this just theother day and came across this post by chance much giggling thank you for crunching the numbers i couldnt be bothered šŸ™‚

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