iStockphoto / hiloi
A bunch of amateur and professional physicists just served up a reminder that dudes rock by calculating the necessary trajectory and force required for a male astronaut on the moon to pee and send that pee into orbit.
The question was posed on the popular subreddit ‘TheDidTheMath’ where people often request obscure calculations and the Internet’s most accomplished neckbeards set about solving the complex problems. In this instance, a user by the name of ‘Thamior290‘ asked “At what angle would you have to pee to send the pee into orbit on the moon?” They added “If it’s not possible, what would the minimum acceleration due to gravity have to be to send pee into orbit at 45 degrees be?”
Angle And Force Needed For An Astronaut To Pee Off The Moon
There are several answers here that bring us to the answer. The first answer astutely points out that it isn’t about the angle, it’s all about the velocity because the moon still has a considerable amount gravity. ‘Hikke_Pakke’ writes:
“The moon’s gravity is abouth 1/6 of Earth’s. That it still a noticable amount of gravity. You can look up the “hammer and feather” drop of Apollo 15 to see the effect yourself.”
“The question here is not of angle, but velocity. Orbiting means that you go fast enough that your trajectory constantly misses the ground. Meaning that the ground curves away faster than you lose altitude. The proper launch trajectory will help in getting to orbit, but a single kick (or squirt) will not get you to orbit. It will just give you an arc.”
“EXCEPT if you were to pee at 1.6 km/s, which orbital velocity in low Moon orbit. In that case, if you were to pee directly ahead, 0 degrees elevation, the pee would impact your behind at 1.6 km/s, some 118 minutes later. This of course makes the assumption of no gravitational anomalies, lunar rotation or other real world problems.”
“Someone more in tune with fluid dynamics can expand the effects of a water stream that fast impacting human flesh…”
For the curious, here is the Apollo 15 Hammer-Feather Drop:
Another user named ‘TrustmeImAnEngineer‘ points out that at those speeds the pee would literally turn the astronaut into a rocket on the moon. They responded to say “It’d actually also make you into a rocket using urine as a reaction mass. Based upon experiments I’ve personally conducted while standing alone in the middle of nowhere, an unimpeded urine stream will flow about 3-4 feet when starting 3 feet about the ground on a parallel vector. Using time = sqrt(2*distance/acceleration), we can calculate that it traveled that distance over about .43 seconds. That works out to something like 2.5 m/s exit velocity.”
Another person, Salex_01, chimed in with the only feasible way it could happen. They said “The only viable solution is to shoot at 0° and hope that there is no rock in the way. Anything else would make the orbit go through the ground at some point.”
Basically, since it is a closed orbit it will always come back to the point of origin at some point. So the astronaut peeing on the moon would need to be peeing perfectly parallel at 0° or, at some point, it would hit the ground.
Now that we’ve established it’s not actually possible, someone ran the calculations of what is required. User Tyler_w_1226 writes:
“If you’re standing at the highest point on the moon so that your launch angle can be 0 degrees (the only way a launch with no extra energy added later on can lead to orbit is possible):
v=sqrt(GM/r)
Where: G = 6.67×10-11 m3 m3/kg*s3 M = 7.35X1022 kg R = 1.740X106 m
Therefore to make it orbit the urine would have to travel at 1678.5 meter per second.
Or 3754.7 mph
Or 6042.6 KPH
I’d like to see someone pee that fast”
This is eerily reminiscent of the legendary scene in Silicon Valley where the group of coders get sidetracked running ‘d— jerk calculations,’ a scene that lives in infamy. Because we are, after all, looking at what it would take for an astronaut to pee off the moon and send that urine into orbit.
This was for anyone out there who needed a reminder that dudes rock.