Orbits and the Cow that Jumped Over the Moon
Liza Fust, Communications Coordinator
6 minute read
You know that nursery rhyme about the cow that jumped over the moon? Have you ever thought to yourself, “Now, how could a cow jump over the moon, and whatever gave Mother Goose that idea anyway?” Well, the KMI team is here to help with that answer. But only the first part, this research does not extend to Mother Goose’s literary motivations. As the new Communications Coordinator for Kall Morris Inc, I am constantly learning about space. Needless to say, I have many questions, and as a bookworm, many of my questions start with fiction. Hence today’s topic of “whatever happened to that cow that jumped over the moon?” Adam Kall, KMI Director of Technology, helped me answer this question. So let’s jump into it.
First, some lampshading: This is a magic cow. This cow can jump in space. This cow can survive in space, and like Superman, has the ability to not burn to a crisp while traveling through the atmosphere.
We can assume the date and location of bovine-launch as that of the original publication of the nursery rhyme, which was, in its most common form, published 1765 in London in Mother Goose's Melody with the lyrics:
Hey diddle diddle,
The Cat and the Fiddle,
The Cow jump'd over the Moon,
The little dog laugh'd to see such [space]* Craft,
And the Fork ran away with the Spoon.
*my own insertion
For moon-destined launches, it is generally best to launch vertically. Cows don’t normally jump, and certainly never vertically (they need a good long run before they can hurdle), but for the sake of this investigation, we will imagine that this cow can jump like that. Already we are diverging from scientific reality, but let’s follow through with this approach. The cow will have to jump vertically with enough force to reach escape velocity or orbital velocity. Escape velocity is the force needed for the cow to escape Earth’s gravity while orbital velocity is the force needed to reach orbit.
The cow needs an escape velocity, so 11.186 km/s or almost exactly 25,000 mph. If we assume the cow takes as long to jump as I do (going from coiled muscles to feet off the ground) in 0.5 seconds, then the acceleration will be 22,352 m/s^2 or 2,280 G's. A cow weighs about 1,000 kg, so since F=ma, the force would be 22.3 million Newtons. Keep in mind none of us at KMI are bovine launch experts, but if this math is wrong, the real answer probably needs more force, not less.
A launch of that force would cause some damage to the surrounding area. Since the cow is lightweight (relatively speaking) and most of the force is going up, the damage would only be about the same as a bundle of TNT going off. Luckily, since it was common back then for cows to graze in the parks of London, the cow in question was out in a pasture and the only damage would be that the area won’t have any graze-worthy wild vegetation for a while.
Now the cow needs to fix its trajectory to get to the moo-oon (moo + moon, get it? … Okay, moving on). The cow jumps out of Earth’s atmosphere, looks up and sees the moon above it, but knows it needs to trot around the Earth to then jump to the moon. Once the cow rounds the Earth and sees the moon come over the horizon again, she jumps towards the moon which leads to a very pleasant, slow drift to the moon. Quick reminder that the moon is 238,900 miles from Earth. So since the cow “jumped,” she is going at about 25,000 mph and it will take her 55 to 75 hours to get to her destination. It is worth mentioning that for a lot of real spaceflights the rockets are not firing continuously, and so describing it as “jumping” is not that far off.
The cow also knows that of its two options to aim behind or in front of the moon, it needs to jump and cross in front of the moon in order to be looped around to come back to Earth. This is called a circumlunar free return trajectory, but whether or not the cow knows the technical term is unknown, the important thing is that the cow understands the concept. As the cow approaches the moon, she discovers that the moon is not made of cheese but sees instead that there is a man in the moon. (This visit of the cow meeting the Man in the Moon may then explain the later Mother Goose nursery rhyme about the Man in the Moon visiting Norwich, as it would only have been polite for the cow to invite the Man in the Moon for a visit in return for her unannounced appearance. I digress.)
The Man in the Moon is excited to have a visitor but knows that the cow really oughtn’t remain in space and should return to her herd, so he uses his gravity to lasso the cow just enough to send her back to Earth. The cow’s gravity and the gravity of the Man in the Moon pull against each other, slowing the cow down and speeding the Moon up somewhat. The Man in the Moon can’t keep hold for very long, the cow is going too fast, but the cow has lost some energy which was the Man in the Moon’s objective.
Having lost this speed, the cow starts falling back to Earth’s atmosphere, and though falling at a significant speed, it will still take two days. Now the reentry really wouldn’t go well for the cow since she is organic matter after all. That’s not a pretty story, even if you are a BBQ aficionado (there’s a reason the nursery rhyme doesn’t describe the return trip). So let’s pretend this is a cow from planet Krypton and, like Superman, can withstand the reentry.
Reentry accomplished, it is time to land. A lot of people like their burgers smashed, but I wouldn’t recommend this as the method for achieving that. Our magic, omnipotent, indestructible cow comes back to her green pasture at about 100 to 150mph. All things considered, like speed and weight, our cow’s landing digs a nice little ditch. Bravo cow, your space mission is accomplished. Treat yourself to some nice hay.
Let’s return to that initial question - how could a cow jump over the moon? We addressed lift off and touch down. Now, we gave the cow the ability to jump because without a massive trebuchet, the cow ain’t getting to space. That’s what rockets are for. For something as relatively light as the cow, the cow’s lift-off and touchdown had relatively little impact to the surrounding area. This is because the cow did not bring food, oxygen, a capsule, or the fuel and rockets for the subsequent jumps. By adding that weight, you compound the energy needs at the start of the process and end up with the Saturn V rocket. In the words of Michael Neufeld, “If the Saturn V blew up on or near the launch pad, it would have the force of a small nuclear weapon.” Thank goodness this was not the story of a nuclear cow. Next we went over the flight path. The jumping to reorient aside, the cow’s flight path isn’t much different than that of the Apollo 13 mission, which ended up becoming a circumlunar trajectory when an oxygen tank failed. Circumlunar trajectories utilize gravity to slingshot for an outgoing and return path that looks like a figure eight. Throughout this scientific investigation, there is a lot of suspension of disbelief that goes into telling this story, and much science was suspended from interfering with the tale.
Another element that was ignored was orbital debris. We gave the cow the ability to jump and cow’s have a natural panoramic vision, but at the speed orbital debris moves, there’s not much the cow could do to see debris coming or prevent a messy collision. Luckily, modern spacecraft don’t need superpowers or magic, they have engineers and scientists to protect them in space, tracking debris, and working on the mission of keeping space clear for all.
So what’s the moral of the story? Always consider your return trip when leaving for space and be conscientious of our shared areas, so we can all enjoy our environments, no matter how far we travel.
Recommended column to read next: To LEO and Back Again