How much would you pay to have a robot carve your name or company logo into the Moon?

Well, if you believe a group of  students from the University of Texas, you could do so for the low low price  of $9.99 per second of doodling. Back in 2020, they submitted a proposal to NASA’s annual design competition called RASC-AL.

And not only did they win their category, ”Commercial Cislunar Space Development”, they also got an “excellence in  commercial innovation” award. Which, let’s be honest, is a bit unsettling. But this story got us thinking about  an even more nightmarish scenario.

What if someone wanted to go full  mad scientist and carve something into the Moon that was so big,  we could see it from Earth? How big would that have to be? Well, we have to make a  few assumptions and do some back-of-the-envelope math,  but SciShow has the answer. [♪ INTRO] Before we can talk about how  big something would need to be on the moon to see it, we have  to deal with human vision.

Which many of us know from  firsthand experience isn’t perfect. But “vision” can mean a  couple of different things. Like, technically, the human  eyeball is so sensitive it can perceive individual  photons as flashes of light.

But this episode isn’t about setting  up a flashing beacon on the Moon. It’s about carving an image that can be seen clearly with the naked eye from Earth. So instead, we’re actually  concerned with what scientists call visual acuity, and the  resolution of the human eye.

Resolution is the ability  to distinguish two things that are next to each other as separate entities. Think back to the classic vision chart with the large capital “E” at the top. In order to resolve the E, you  need to be able to distinguish each of those horizontal lines  as being their own thing, as well as the white spaces in-between them.

But resolution isn’t the same for everyone, or even for one person at  every single point in time. For one thing, it’s just worse in the dark, when our eyes are picking up fewer photons. And if you’re older or have a  disability, the parts of your eyes that help you do the whole “seeing”  thing can function differently.

But even so-called “average” visual  acuity is sort of… arbitrary. One definition says it’s based on seeing the difference between black  lines on a white background. Of course, the real world isn’t  so, well, black and white.

Lighting conditions and  colors change all the time. But we’ve still sort of emerged with that 20/20 “standard” optometrists are trying to get you to. But hold on.

We can’t apply  all that to the Moon just yet. I’ll tell you why after this more  terrestrial, less lunar advertisement. Thank you to JMP for  supporting this SciShow video.

JMP is a statistical analysis software that makes powerful analytics quick and accessible. For example, if you’re trying  to model when the benefits outweigh the costs in a switch to  more energy efficient transportation, the first model you use might not  give you the information you need. You could end up accidentally  overfitting your data.

Instead, you’ll need to actively  evaluate, validate, and compare different models to make sure that  you choose the best one for the job. And JMP facilitates that process.  JMP’s Model Screening platform lets you launch multiple models at  once, and evaluate their respective performances without having to  go through each one individually. They also offer a 30-day free  trial for anyone, anywhere.

You can find it at jmp.com/scishow and see the benefits of visual statistics for yourself. Angular diameter is basically the  size that something appears to be, given the fact that it’s a  certain distance away from you. It’s usually reported in units like  degrees, arcminutes, or arcseconds.

And you can calculate it using  some very basic trigonometry. If you have 20/20 vision… whether or not you need glasses to help you get there… it means you can resolve an angular diameter as low as 1 arcminute. In other words, if you’re standing  20 feet, or roughly 6 meters, away from the chart in your  doctor’s office, each horizontal segment in a capital E would  have to be about 1.8 millimeters thick for you to tell it’s  actually an E and not a smudge.

And since there are 5 segments,  black white black white black, the smallest E you can read with 20/20 vision from that distance is 5 times  1.8, or 9 millimeters tall. But you may have noticed… the Moon  is not 6 meters away from you. A 9 millimeter anything on  the lunar surface would be completely unreadable, even  to the Hubble Space Telescope.

So how tall would a lunar “E” need to be to maintain that 1 arcminute minimum? Here’s where we have to make some assumptions and deal with some more  back-of-the-envelope calculations. For one thing, we have to look  through Earth’s atmosphere, which can technically blur our view of the Moon.

We’ll ignore that for the sake of our math. But since some of you out there might be burgeoning astrophotographers, if not desperate to draw  visible memes on the Moon, it’s worth noting that  scientists do have ways to report how bad this blurring effect  will be on a particular day. Instead, we mostly have to deal  with the fact that the Moon keeps moving.

It’s never a  constant distance away from us. So if we want to figure out how big to make that “E” visible to everyone all  the time, we’d have to use the Moon’s maximum distance from Earth. Or, if we want to charge  advertisers based on distance, maybe they could just pay less if people can only read the message some of the time?

So let’s just go ahead and use the average distance of 384,000 kilometers. In which case, a capital  E that’s 5 arcminutes tall would correspond to… 560 kilometers. Which is a chunk longer than the Grand Canyon.

And if you wanted an even more complex structure… say a certain company logo…  it’d need to be even bigger. Those UT students couldn’t  possibly get the job done with their proposed fleet of two dinky rovers, with their delicate little doodling arms. But then again, that’s not what  their proposal was aiming for.

Although in the end, they were  still trying to find a way to make money off of the Moon that wasn’t your standard “mining for resources” or whatever. But hey, maybe you’re not as  opposed to this idea as we are. And for the record, I think if  an astronaut makes it all the way to the Moon and wants to stick  their finger into the regolith and draw a smiley face, or lay  down and make a dust-angel, they deserve a little treat after  all those years of training.

As of now, this is all still one big hypothetical. So in the spirit of hypotheticals,  how about we just carve this gorgeous mug up there? Even if it’s not big enough  for everyone to see back home. [♪ OUTRO]