Jesse introduced me to a pretty fun game idea. The basics are this: Without looking anything up, can you arrive at a reasonable solution to a problem (within an order of magnitude)?
The questions will vary in difficulty, and you might have to make a few blind guesses for numbers. But you might know enough slightly related information to deduce a quality answer. You can use a calculator if you’d like, though paper and pen results deserve additional accolades.
Let’s look at two examples.
How does the total volume of human blood on Earth compare to the total volume of oceans on Earth?
What is the distance to the moon?
If you’d like, you can stop reading here and spend some time to try and figure out the two answers. Remember, you’re not allowed to look anything up. Otherwise, I’ll guide you through Jesse’s and my methods of calculating solutions to the first question and our attempts at the second.
Our solution to the blood problem:
First? Water. We guessed an ocean depth of 4km. We knew that the earth’s surface area was about 70% and that the diameter of the earth was about 13,000km.
The surface area of a sphere is 4 pi r^2, so the surface area of the earth is about 531 million square km. Ocean area is 70% of that or about 372m km. times depth gives us volume, 1.49b km^3
The world population is about 6750000000. We know that the average adult has about 5L of blood. That gives us a total volume of 33750000000 Liters or 0.00003375 km^3.
.00003375/1.49b = 2.26×10^-14
Or normalized: 1/44,148b
Now that we have our answer we can look up the results:
Actual volume of the ocean is 1.37b – Wow! we were crazy close.*1
Our blood estimation was pretty much right on. The world population is actually closer to 6.734b*2 but our human blood volume was perfect.*3
Actual end result
.00003367/1.37b = 2.46×10^-14
Our solution to the moon problem.
We did this one two ways. First, I remembered that it took about three days for the apollo missions to reach the moon. But we really had no idea the speed of a rocket. Jesse guessed 128,750km/h, I guessed 32,200km/h.
This gave us two results:
So we decided to try and figure it out with a different method.
If we assumed that the Earth and the Moon were of similar density then we might be able to come up with a ratio of expected gravity between Earth and the Moon. Then we could make a decent guess as to the diameter of the Moon. Knowing that, and knowing the moon appears to be about the size of a quarter at arms length – we could do some math and come up with a distance.
We know that astronauts train underwater. We guessed that a rock would take about a second to drop 3 feet in water. That’s 1/10th the acceleration of gravity on Earth. given our assumptions, this would suggest that the volume of the moon was about 1/10th that of Earth. The Volume of a sphere is 4/3pi r^3. So that means that volume depends on the cube of the radius. Unfortunately, this yields a result that suggests that the moon’s diameter is half of Earth’s. That doesn’t seem right at all. Perhaps the assumption that Earth and the Moon share a similar density is wrong.
I haven’t given up hope that there might be another way to calculate this. But I’m not sure yet what that method might be. I’m still working on it.