Cy Davis asked, “If we were to make an exact duplicate of a waterless earth the size of let’s say a basketball… would it roll like a sphere? I don’t think so. So my question is… Was the earth ever smooth and uniform like a basketball? If so why didn’t it stay that way?”
Cy, you ask several interesting questions. Let’s look at them.
Because Earth spins once on its axis every 23.9344696 hours (and why it’s not exactly 24 hours is a subject for a separate post) centrifugal force causes it to bulge slightly at the equator and flatten slightly at the poles.
The diameter of our planet measured from North Pole to South Pole is 12,714 km, but the diameter of our planet measured across its equator is 12,756 km, a difference of 42 km (26 miles).
From these numbers you can calculate that Earth is out-of-round by about 0.3%
A regulation basketball has a diameter of a little more than nine inches (~23.5 cm). A basketball that was out-of-round by 0.3% would translate to a difference between extreme variations in diameters of less than 3/100ths of an inch (about 0.7 mm). Such a ball would absolutely roll across a hardwood floor just fine.
The extremes of Mt. Everest (8.8 km above sea level) and the Mariana Trench (10.9 km below sea level) translate into a change in diameter significantly less than the bulging of our equatorial diameter produced by Earth’s rotation.
I don’t have the equipment to make exact measurements, but I suspect that if you measured the little bumps on a basketball’s surface those bumps would be more significant than the scale height of Mt. Everest on the ball. I also suspect that a scale-sized Mariana Trench on the ball would not be as deep as the seams holding the pieces of the basketball together.
In other words, the “roughness” we observe on Earth’s surface may seem huge to us as we gaze up at mountains or down into an ocean abyss, but in terms of the overall shape of our planet these imperfections are trivial.
Our planet is at least as round and “roll-able” as basketball.
Cy’s last question was, “Was the earth ever smooth and uniform like a basketball? If so why didn’t it stay that way?”
We’ve seen that Earth is already at least as round and smooth as a basketball. Was it ever smoother than this? I really doubt it.
Depending on where you measure, Earth’s crust is only 5 to 50 km thick, and represents only a few thousandths the diameter of our planet. Our planet’s fragile, thin crust has been constantly jostled, poked, stretched, and otherwise roughed-up by forces both internal and external since our planet formed more than four and a half billion years ago.
And for a final moment of geek… Now that we’ve established that Earth is at least as round and smooth as a basketball, what would a basketball-sized Earth weigh? Earth’s mean density is 5.5 grams per cubic centimeter, and a basketball has a volume of about 6,800 cc, for a total basketball-sized Earth tipping the scales at about 37 kg, or roughly 80 pounds. (Remember, a significant portion of Earth’s interior is nickel and iron.)
Good luck making a three-pointer with that.
Maybe we should try bowling?