# If a cow jumped over the moon, how fast would it be going when it got back and hit earth's atmosphere? **URL:** \ **Category:** Factual Questions\ **Created:** [January 27, 2024, 4:27pm UTC](https://boards.straightdope.com/t/if-a-cow-jumped-over-the-moon-how-fast-would-it-be-going-when-it-got-back-and-hit-earths-atmosphere/996737 "2024-01-27T16:27:55Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![RickJay](https://avatars.discourse-cdn.com/v4/letter/r/bb73d2/32.png) [@RickJay](https://boards.straightdope.com/u/RickJay)\ **Post date:** [January 27, 2024, 4:27pm UTC](https://boards.straightdope.com/t/if-a-cow-jumped-over-the-moon-how-fast-would-it-be-going-when-it-got-back-and-hit-earths-atmosphere/996737/1 "2024-01-27T16:27:55Z")
According to the nursery rhyme, the cow jumped over the moon. But coming back, man, that would not be good. Let’s assume the cow’s trajectory takes it in a free return trip around the Moon, a la Apollo 13. (Apollo 8 slowed and orbited the Moon ten times.) Let’s also assume our cow is wearing a spacesuit with days of oxygen so no problem there. So I assume that at some point after departing the Moon, the cow will pass from the Moon’s gravitational influence and start accelerating towards the Earth. I cannot figure out how fast the cow will be going when it slams into the Earth’s atmosphere. I’m not smart enough. The 9.8msq/second thing is the rate of acceleration at sea level, which obviously ain’t true a hundred thousand miles out. Is anyone here smart enough to come up with a rough estimate of how fast Bessie will be going before becoming beef jerky in the upper atmosphere? ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [January 27, 2024, 4:32pm UTC](https://boards.straightdope.com/t/if-a-cow-jumped-over-the-moon-how-fast-would-it-be-going-when-it-got-back-and-hit-earths-atmosphere/996737/2 "2024-01-27T16:32:45Z")
It’s basically going to just be escape speed, about 11 km/s. ---
**Author:** ![Pardel-Lux](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pardel-lux/32/20182_2.png) [@Pardel-Lux](https://boards.straightdope.com/u/Pardel-Lux)\ **Post date:** [January 27, 2024, 4:40pm UTC](https://boards.straightdope.com/t/if-a-cow-jumped-over-the-moon-how-fast-would-it-be-going-when-it-got-back-and-hit-earths-atmosphere/996737/3 "2024-01-27T16:40:31Z")
I don’t see how the cow escapes the Moon’s gravitational pull to start falling towards Earth: If she jumps to the Moon, she stays around the Moon. That is, assuming all three bodies, Earth, Moon, and Cow are roughly spherical. ---
**Author:** ![SuntanLotion](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/suntanlotion/32/16165_2.png) [@SuntanLotion](https://boards.straightdope.com/u/SuntanLotion)\ **Post date:** [January 27, 2024, 4:41pm UTC](https://boards.straightdope.com/t/if-a-cow-jumped-over-the-moon-how-fast-would-it-be-going-when-it-got-back-and-hit-earths-atmosphere/996737/4 "2024-01-27T16:41:31Z")
Cow would need an engine to send her anywhere. She would likely just float around. ---
**Author:** ![running\_coach](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/running_coach/32/15836_2.png) [@running\_coach](https://boards.straightdope.com/u/running_coach)\ **Post date:** [January 27, 2024, 4:41pm UTC](https://boards.straightdope.com/t/if-a-cow-jumped-over-the-moon-how-fast-would-it-be-going-when-it-got-back-and-hit-earths-atmosphere/996737/5 "2024-01-27T16:41:43Z")
> [@Pardel-Lux](#): > > **I don’t see how the cow escapes the Moon’s gravitational pull to start falling towards Earth:** If she jumps to the Moon, she stays around the Moon. - Same way it escaped Earth’s gravity. ---
**Author:** ![Pardel-Lux](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pardel-lux/32/20182_2.png) [@Pardel-Lux](https://boards.straightdope.com/u/Pardel-Lux)\ **Post date:** [January 27, 2024, 4:43pm UTC](https://boards.straightdope.com/t/if-a-cow-jumped-over-the-moon-how-fast-would-it-be-going-when-it-got-back-and-hit-earths-atmosphere/996737/6 "2024-01-27T16:43:29Z")
She escaped Earth’s gravity by jumping, that is exerting a force against the surface of the Earth. She cannot do that in space. And she jumped **over** the Moon, not **to** the Moon and from there back to Earth again. > [@SuntanLotion](#): > > Cow would need an engine That does not count as jumping in my book. That is rocket science! ---
**Author:** ![Little\_Nemo](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/little_nemo/32/3120_2.png) [@Little\_Nemo](https://boards.straightdope.com/u/Little_Nemo)\ **Post date:** [January 27, 2024, 4:47pm UTC](https://boards.straightdope.com/t/if-a-cow-jumped-over-the-moon-how-fast-would-it-be-going-when-it-got-back-and-hit-earths-atmosphere/996737/7 "2024-01-27T16:47:11Z")
This covers it: [https://what-if.xkcd.com/157/](https://what-if.xkcd.com/157/) ---
**Author:** ![running\_coach](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/running_coach/32/15836_2.png) [@running\_coach](https://boards.straightdope.com/u/running_coach)\ **Post date:** [January 27, 2024, 4:47pm UTC](https://boards.straightdope.com/t/if-a-cow-jumped-over-the-moon-how-fast-would-it-be-going-when-it-got-back-and-hit-earths-atmosphere/996737/8 "2024-01-27T16:47:12Z")
> [@Pardel-Lux](#): > > She escaped Earth’s gravity by jumping, that is exerting a force against the surface of the Earth. She cannot do that in space. And she jumped **over** the Moon, not **to** the Moon and from there back to Earth again. > > > [@SuntanLotion](#): > > > > Cow would need an engine > > That does not count as jumping in my book. That is rocket science! Since no cow could actually generate enough speed by jumping to escape Earth’s gravity _and_ would burn up before leaving the atmosphere, magic is involved. Magic solves all problems. ---
**Author:** ![wolfpup](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/wolfpup/32/10618_2.png) [@wolfpup](https://boards.straightdope.com/u/wolfpup)\ **Post date:** [January 27, 2024, 4:57pm UTC](https://boards.straightdope.com/t/if-a-cow-jumped-over-the-moon-how-fast-would-it-be-going-when-it-got-back-and-hit-earths-atmosphere/996737/9 "2024-01-27T16:57:16Z")
> [@Chronos](#): > > It’s basically going to just be escape speed, about 11 km/s. That’s my answer, too, though probably just a touch less. Since the cow has no means of propulsion in space, in order to jump over the moon she’d have to propel herself off the earth with enough speed to reach the L1 earth-moon Lagrange point, at which point the moon’s gravity takes over. L1 is around 85% of the distance to the moon, so the required speed of the jump would be fairly close to escape velocity, but not much more or Bessie would go flying past the moon and never come back. She’ll need to be traveling slow enough for the moon’s gravity to flip her around but fast enough to reach L1 again and start accelerating toward earth. From that distance, the unfortunate cow would hit the atmosphere at something fairly close to escape velocity. ---
**Author:** ![Sam\_Stone](https://avatars.discourse-cdn.com/v4/letter/s/ecccb3/32.png) [@Sam\_Stone](https://boards.straightdope.com/u/Sam_Stone)\ **Post date:** [January 27, 2024, 5:06pm UTC](https://boards.straightdope.com/t/if-a-cow-jumped-over-the-moon-how-fast-would-it-be-going-when-it-got-back-and-hit-earths-atmosphere/996737/10 "2024-01-27T17:06:22Z")
Imwas going to say ‘approximately the same as dropping a cow from an infinite height’, which would be escape velocity, or approximately 11 km/s. I just looked up the re-entry velocity for Apollo 13: 10.84 km/s. ---
**Author:** ![Pardel-Lux](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pardel-lux/32/20182_2.png) [@Pardel-Lux](https://boards.straightdope.com/u/Pardel-Lux)\ **Post date:** [January 27, 2024, 5:27pm UTC](https://boards.straightdope.com/t/if-a-cow-jumped-over-the-moon-how-fast-would-it-be-going-when-it-got-back-and-hit-earths-atmosphere/996737/11 "2024-01-27T17:27:22Z")
> [@wolfpup](#): > > She’ll need to be traveling slow enough for the moon’s gravity to flip her around but fast enough to reach L1 again and start accelerating toward earth. According to my (admittedly very vage) mental calculations this orbit would pass below the Moon’s surface, that is, the cow would crash on the Moon, not turn around the Moon. If she avoids crashing on the Moon the trajectory is no longer elliptical but hyperbolic, then she misses the Earth on her way back. As a matter of fact she misses the Earth anyway, because during the cow’s coasting in space the Earth has moved along its orbit. ---
**Author:** ![Sam\_Stone](https://avatars.discourse-cdn.com/v4/letter/s/ecccb3/32.png) [@Sam\_Stone](https://boards.straightdope.com/u/Sam_Stone)\ **Post date:** [January 27, 2024, 5:29pm UTC](https://boards.straightdope.com/t/if-a-cow-jumped-over-the-moon-how-fast-would-it-be-going-when-it-got-back-and-hit-earths-atmosphere/996737/12 "2024-01-27T17:29:08Z")
Why can’t the cow travel on a free return trajectory? ---
**Author:** ![Pardel-Lux](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pardel-lux/32/20182_2.png) [@Pardel-Lux](https://boards.straightdope.com/u/Pardel-Lux)\ **Post date:** [January 27, 2024, 5:31pm UTC](https://boards.straightdope.com/t/if-a-cow-jumped-over-the-moon-how-fast-would-it-be-going-when-it-got-back-and-hit-earths-atmosphere/996737/13 "2024-01-27T17:31:34Z")
Because she would have to use a trajectory that is so close to the Moon’s centre of mass that it would run below the surface of the Moon at the turning point, so the cow would crash against the Moon. And then she would no longer be spherical! ---
**Author:** ![xtenkfarpl](https://avatars.discourse-cdn.com/v4/letter/x/c2a13f/32.png) [@xtenkfarpl](https://boards.straightdope.com/u/xtenkfarpl)\ **Post date:** [January 27, 2024, 5:36pm UTC](https://boards.straightdope.com/t/if-a-cow-jumped-over-the-moon-how-fast-would-it-be-going-when-it-got-back-and-hit-earths-atmosphere/996737/14 "2024-01-27T17:36:30Z")
> [@running\_coach](#): > > Since no cow could actually generate enough speed by jumping to escape Earth’s gravity _and_ would burn up before leaving the atmosphere, magic is involved. Magic solves all problems. Or if you prefer a pseudo-scientific approach: perhaps the cow has managed to figure out an extra, previously unsuspected, term to Einstein’s tensor gravity equation? Better than ending up as steaks, I guess. By the way how does the cow breath in space? It’s probably telekinesis…? ---
**Author:** ![wolfpup](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/wolfpup/32/10618_2.png) [@wolfpup](https://boards.straightdope.com/u/wolfpup)\ **Post date:** [January 27, 2024, 5:51pm UTC](https://boards.straightdope.com/t/if-a-cow-jumped-over-the-moon-how-fast-would-it-be-going-when-it-got-back-and-hit-earths-atmosphere/996737/15 "2024-01-27T17:51:47Z")
> [@Pardel-Lux](#): > > Because she would have to use a trajectory that is so close to the Moon’s centre of mass that it would run below the surface of the Moon at the turning point, so the cow would crash against the Moon. I could be wrong but I believe that the Apollo missions flew to the moon on a free-return (ballistic) trajectory as a safety precaution, most notably Apollo 13 which made use of it (and so did the Soviet Luna 3 mission). For sure you can’t get into orbit around the earth or any other body through purely ballistic means from the surface without crashing back into it, but I don’t believe this applies to a ballistic trajectory where a spacecraft or cow departs a large body like earth and is deflected back by the gravity of a smaller body like the moon. > **[Free-return trajectory](https://en.wikipedia.org/wiki/Free-return_trajectory)** > > In orbital mechanics, a free-return trajectory is a trajectory of a spacecraft traveling away from a primary body (for example, the Earth) where gravity due to a secondary body (for example, the Moon) causes the spacecraft to return to the primary body without propulsion (hence the term free). > Many free-return trajectories are designed to intersect the atmosphere; however, periodic versions exist which pass the moon and Earth at constant periapsis, which have been proposed for cyclers. > The firs... ---
**Author:** ![Stranger\_On\_A\_Train](https://avatars.discourse-cdn.com/v4/letter/s/13edae/32.png) [@Stranger\_On\_A\_Train](https://boards.straightdope.com/u/Stranger_On_A_Train)\ **Post date:** [January 27, 2024, 6:52pm UTC](https://boards.straightdope.com/t/if-a-cow-jumped-over-the-moon-how-fast-would-it-be-going-when-it-got-back-and-hit-earths-atmosphere/996737/16 "2024-01-27T18:52:38Z")
> [@wolfpup](#): > > I could be wrong but I believe that the Apollo missions flew to the moon on a free-return (ballistic) trajectory as a safety precaution, most notably Apollo 13 which made use of it (and so did the Soviet Luna 3 mission). Although the earlier Apollo missions used a free-return trajectory (for cislunar mission often referred to as a “figure eight” trajectory), Apollo 12 and on did not in order to reduce transit time, instead using a slightly faster hybrid trajectory requiring small injection and return burns by the Service Module SPS engine. This is why Apollo 13 had to perform correction buns with the Lunar Module descent engine (unlike the Ron Howard film, multiple times) to align the return trajectory. 11.1 km/sec is about the minimum speed for a circumlunar lunar free-return although if the cow is very patient and well trained in celestial mechanics there are low energy transfers that might come in slightly slower. Stranger ---
**Author:** ![Cervaise](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/cervaise/32/16693_2.png) [@Cervaise](https://boards.straightdope.com/u/Cervaise)\ **Post date:** [January 27, 2024, 6:54pm UTC](https://boards.straightdope.com/t/if-a-cow-jumped-over-the-moon-how-fast-would-it-be-going-when-it-got-back-and-hit-earths-atmosphere/996737/17 "2024-01-27T18:54:16Z")
I just want to say I very much enjoy the references to a spherical cow. Carry on. ---
**Author:** ![wolfpup](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/wolfpup/32/10618_2.png) [@wolfpup](https://boards.straightdope.com/u/wolfpup)\ **Post date:** [January 27, 2024, 6:58pm UTC](https://boards.straightdope.com/t/if-a-cow-jumped-over-the-moon-how-fast-would-it-be-going-when-it-got-back-and-hit-earths-atmosphere/996737/18 "2024-01-27T18:58:21Z")
Thanks, I appreciate the clarification. ---
**Author:** ![Bear\_Nenno](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bear_nenno/32/3358_2.png) [@Bear\_Nenno](https://boards.straightdope.com/u/Bear_Nenno)\ **Post date:** [January 27, 2024, 7:02pm UTC](https://boards.straightdope.com/t/if-a-cow-jumped-over-the-moon-how-fast-would-it-be-going-when-it-got-back-and-hit-earths-atmosphere/996737/19 "2024-01-27T19:02:30Z")
> [@Pardel-Lux](#): > > I don’t see how the cow escapes the Moon’s gravitational pull to start falling towards Earth: If she jumps to the Moon, she stays around the Moon. That is incorrect. She would need to slow down at the moon in order to stay in orbit around the moon. Otherwise, she’s headed back to the Earth, or shooting off away from everything depending on how she approached the moon. To accurately answer the OP, we need to know a lot more information. An elliptical orbit going around the moon and back to Earth could result in a wide variety of velocities. There is a lower and upper bound, sure, but there’s a huge gap in the middle. The result is the same, no matter what, though. The cow doesn’t survive. ---
**Author:** ![Stranger\_On\_A\_Train](https://avatars.discourse-cdn.com/v4/letter/s/13edae/32.png) [@Stranger\_On\_A\_Train](https://boards.straightdope.com/u/Stranger_On_A_Train)\ **Post date:** [January 27, 2024, 7:16pm UTC](https://boards.straightdope.com/t/if-a-cow-jumped-over-the-moon-how-fast-would-it-be-going-when-it-got-back-and-hit-earths-atmosphere/996737/20 "2024-01-27T19:16:41Z")
> [@Bear\_Nenno](#): > > An elliptical orbit going around the moon and back to Earth could result in a wide variety of velocities. If the characteristic energy C3 of the cow is negative, i.e. the cow is not on an Earth escape trajectory, the return speed of the cow can’t be more than 11.2 km/s, and a trajectory returning from beyond the Moon can’t be much less. Of course, the cow could go into a heliocentric orbit that just happens to pass by the Moon and which eventually comes back to intercept the Earth, and could have a speed up to just under 42.1 km/s but that would be an extraordinarily patient cow. Stranger [Next page](https://boards.straightdope.com/t/if-a-cow-jumped-over-the-moon-how-fast-would-it-be-going-when-it-got-back-and-hit-earths-atmosphere/996737.md?page=2)