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Background

In my setting, there is some sort of cosmic war going on between two factions. This war climaxes in one of the warring sides having the moon of their home-planet being redirected into the home-planet, basically ending all life on the planet. For more information this event takes place around the 26th-century, so very advanced military technology could be utilized here. The moon in question, has a mass of about 3.06603 × 10^25 kg (around 1.9% the mass of its primary), and a radius of 1101.64288125 kilometers (12.5% of the primary's radius).

Question

I want to know a possible way that this moon or similarly-sized astronomical object could be sent on a collision course with its primary as some form of unethical space warfare. Perhaps a high-powered gravity tractor, or a collision between the moon and some other, smaller astronomical object?

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    $\begingroup$ Any weapon that's capable of knocking a moon out of orbit should have an energy output more than capable of rendering a planet uninhabitable. $\endgroup$ – Halfthawed Mar 18 at 22:55
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    $\begingroup$ This value of mass is right? 3,06 e+25 kg is like... 5 Earths. :o and with this radius (remember your previous question) is 185x Earth gravity. $\endgroup$ – Rodolfo Penteado Mar 18 at 23:04
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    $\begingroup$ What @Halfthawed said. It would be less expensive to boil the oceans and melt the crust than to play with the moon. (And the impact will boil the oceans and melt the crust anyway, so there is nothing to be gained by employing the more expensive option.) $\endgroup$ – AlexP Mar 18 at 23:37
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You'd need to decelerate it enough that the periapsis of its orbit falls below the surface of its primary, so the specific energy requirements are going to depend on the details of its orbit (semi-major axis and eccentricity, mostly).

For best efficiency, you'll want to slow it at the apoapsis of its orbit (when it's furthest from the planet). At that point, it's moving the slowest, and velocity changes will have the biggest effect on its periapsis. This is the same sort of mechanics involved in a Hohmann transfer, so if you want to work out the exact numbers you can use the formula on that page. This does also mean that the soon-to-be victims have a bit under half of a local month to see their impending doom approaching. Whether or not that's a good thing is up to you.

Whatever the orbit is, though, for a moon that size it's going to take a lot of energy. Depending on the methods available, it might actually be easier to just apply that energy directly to the surface of the target planet and sterilize the surface of it.

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    $\begingroup$ Fall time from a large circular orbit to a comparatively small planet is about a sixth of the original orbital period, not half. Also, it's less delta-V expensive to run up to escape velocity than to deorbit if the circular orbit is more than about 4.5 times the planet's radius, so for Earth-proportion moons, a Bi-elliptic smackdown is going to be less energy-expensive than a Hohmann, if the attackers don't care how long it takes and their aim is good. But i guess, if you're throwing a planet's own moon at it, you're more concerned about making a statement than energy concerns. $\endgroup$ – notovny Mar 18 at 23:30
  • $\begingroup$ Applying enough energy to the moon to decelerate it should blast enough material free from the surface of the moon that the planet will be showered in debris. If the moon were to come down, there would be the Roche limit to consider. So I expect devastation by many smaller impacts, not one big one. $\endgroup$ – o.m. Mar 19 at 5:34

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