Shoveling Away the Earth

Disclaimer: I’m brain-damaged.

Ridiculous question, but let’s say you took a shovel and tried to shovel away the entire planet. How long would it take to shovel it all away? Firstly, it doesn’t take an Einstein to figure out that doing this isn’t really that easy. You can’t actually shovel away all of Earth, with its hot plasma core and whatnot with a bloody shovel, but let’s oversimplify everything to an “assuming the chickens to be spherical and in a vacuum” level and assume we have a shovel that can essentially shovel away any possible substance, without breaking, disintegrating or melting. How long would it take one to shovel away all of the earth?

The capacity of an average bucket is about 8 m^3, we’re already ridiculously oversimplifying everything, might as well assume the shovel we’re using to have the same capacity. Next, what about the Earth? The circumference of the earth is approximately 4.0075 \times 10^7 m, and since the radius equals the circumference divided by 2\pi. the radius of the Earth is about 6.38 \times 10^6 m. Since the volume of a sphere is \frac{4}{3} \pi r^3, and we’re being super simplistic and assuming the Earth is a sphere, the volume of the Earth turns out to be a whopping 1.09 \times 10^{21} m^3.

Now, not considering the fact that the Earth also has fluids etc. and different materials on Earth have vastly different densities, the number of shovel strokes we’ll need to shovel away all of Earth is \frac{1.09 \times 10^{21} m^3}{8 m^3} = ~1.36 \times 10^{20} strokes. Let’s say we’re working at a rate of 1 stroke every five seconds i.e \frac{1}{5} strokes per second, then the time needed to shovel away all of Earth is about 6.8 \times 10^{20} s or about 22 thousand billion years! The current age of the universe is about 13.8 billion years so that is one heck of a lot of time.

Note: Since I gave the answer in years, I’m assuming we’re using a definition for a year based on the speed of light and not the orbital period of the Earth around the Sun since the mass of the Earth will be decreasing because of our stupid shoveling endeavor. But then again, since the equation for orbital period only takes into account the mass of the more massive body (i.e the Sun), I don’t think decreasing the mass of the earth will change its orbital period assuming the semi-major axis of its orbit remains constant. 

However, as we shovel out the mass, because momentum is always conserved, Earth will gain a very tiny velocity in the opposite direction to the direction we’re shoveling out the mass. We can sum up all these tiny gains in velocity (probably by integration) to figure out the semi-major axis of orbit and hence the orbital period every year. I have a hunch that if one begins shoveling on the equator and throws the mass shoveled directly upward, since the earth is rotating all the tiny gains in velocity will cancel out and the orbital period will not change and hence the answer will still turn out to be the one I stated above.

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s