# What would it take for the moon to crash into Earth? **URL:** \ **Category:** Factual Questions\ **Created:** [December 7, 2003, 7:49pm UTC](https://boards.straightdope.com/t/what-would-it-take-for-the-moon-to-crash-into-earth/217597 "2003-12-07T19:49:20Z")\ **Posts on this page:** 5\ **Page:** 2
**Author:** ![Achernar](https://avatars.discourse-cdn.com/v4/letter/a/e274bd/32.png) [@Achernar](https://boards.straightdope.com/u/Achernar)\ **Post date:** [December 11, 2003, 8:17am UTC](https://boards.straightdope.com/t/what-would-it-take-for-the-moon-to-crash-into-earth/217597/21 "2003-12-11T08:17:50Z")
Okay, so my very first number was approximately right. 🙂 I don’t know if you’ve noticed, Chronos, but it’s not a trivial amount of matter you’re kicking up - it’s about one-third the mass of the moon. And the energy you’re putting in is about half the total binding energy of the moon. I think that this will affect the answer - because as the mass of the moon decreases so will its escape speed - but probably not by an order of magnitude. ---
**Author:** ![Achernar](https://avatars.discourse-cdn.com/v4/letter/a/e274bd/32.png) [@Achernar](https://boards.straightdope.com/u/Achernar)\ **Post date:** [December 12, 2003, 12:34am UTC](https://boards.straightdope.com/t/what-would-it-take-for-the-moon-to-crash-into-earth/217597/22 "2003-12-12T00:34:38Z")
Okay, I worked it out. If we kick up a bit of mass dm at a time, and we assume that the moon maintains a uniform density so that r is proportional to m[sup]1/3[/sup], then v[sub]esc[/sub] = am[sup]1/3[/sup], where a = m[sub]0[/sub][sup]1/6/sup[sup]1/2[/sup] = 5.671e-5 [mks]. The momentum of the particle is v[sub]esc[/sub]dm, and so the rest of the moon slows by an amount dv = v[sub]esc[/sub]dm/m = am[sup]-2/3[/sup]dm. Integrating gives Delta-v = 3a(m[sub]1[/sub][sup]1/3[/sup] - m[sub]0[/sub][sup]1/3[/sup]) = 3Delta-v[sub]esc[/sub]. Meanwhile, the energy spent is dE = v[sub]esc[/sub][sup]2[/sup]/2 dm, and similar integration gives E = 3/10 Delta(mv[sub]esc[/sub][sup]2[/sup]). For the problem in this thread, Delta-v = 812.7 m/s, from which you can get v[sub]esc,final[/sub] and so on. m[sub]final[/sub] = 5.111e22 kg, and E = 5.649e28 J. So, you’d wind up with 70% of the moon, but you’d get it to Earth, darn it! ---
**Author:** ![Ficer67](https://avatars.discourse-cdn.com/v4/letter/f/c57346/32.png) [@Ficer67](https://boards.straightdope.com/u/Ficer67)\ **Post date:** [December 12, 2003, 2:51am UTC](https://boards.straightdope.com/t/what-would-it-take-for-the-moon-to-crash-into-earth/217597/23 "2003-12-12T02:51:09Z")
Would it have to be a nuclear bomb? Couldn’t it be a meteor? And, is an impact absolutely necessary? Couldn’t someon slingshot a large asteroid around the moon so that the asteroid takes energy away from the moon? ---
**Author:** ![digs](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/digs/32/14889_2.png) [@digs](https://boards.straightdope.com/u/digs)\ **Post date:** [December 12, 2003, 5:39am UTC](https://boards.straightdope.com/t/what-would-it-take-for-the-moon-to-crash-into-earth/217597/24 "2003-12-12T05:39:07Z")
Wouldn’t a 2020’s-Style Death Ray be a lot more efficient than a 1920’s -Style? ---
**Author:** ![Major\_Feelgud](https://avatars.discourse-cdn.com/v4/letter/m/3be4f8/32.png) [@Major\_Feelgud](https://boards.straightdope.com/u/Major_Feelgud)\ **Post date:** [December 12, 2003, 9:24am UTC](https://boards.straightdope.com/t/what-would-it-take-for-the-moon-to-crash-into-earth/217597/25 "2003-12-12T09:24:23Z")
Just in case you’re worried about the moon crashing into Earth, it’s actually flying away into space. [Previous page](https://boards.straightdope.com/t/what-would-it-take-for-the-moon-to-crash-into-earth/217597.md?page=1)