# How much force would it take

to move a moon-sized body from Earth's orbit?

Background, I've been curious about science my whole life, but I've normally focused on paleontology as I loved dinosaurs growing up. I'm interested in physics but don't know enough regarding forces like gravity or physical forces to calculate things like this.

Basically I'm a nerd and a project I'm working on is quantifying in-universe feats of fictional characters, in this case Megatron from the 1980's Transformers. I know it's stupid and might not be the best application of a physics forum but I'm not sure where to look as I'm aware of my limitations regarding computations. I can memorize history and literature instantly but equations have never been a strong point.

Basically though, I'm looking to learn how powerful an explosion would need to be to move a moon-sized planetoid (Cybertron), composed of the strongest metal in the galaxy and with roughly the same gravity as Earth's, clearly out of Earth's orbit. This is mainly for me to calculate how durable said character was while being at ground zero of such an explosion and tanking it.

Again, I know it's ridiculous, but you'd be surprised how much I enjoy cataloging fictional feats and cross-referencing such things in fanboy Deadliest Warrior-style discussions. Sorry for being out of line on here if that's the case. I appreciate any and all help given.

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Simon Bridge
Homework Helper
IIRC: the moon is currently moving away from the earth. A uniform motion requires a sustained force equal but opposite the weight of the object... so the force needed would tail off over time - or you can apply a constant unbalanced force until the moon was far enough away that it's accumulated speed is at the escape velocity for that distance.

But you are thinking of something like the back-story for the program Space: 1999 ... a big explosion knocks the Moon from it's orbit, along with the Moonbase and it's residents.

For an explosion - you are thinking in terms of applying ali the energy in one go.
The energy needed to remove the Moon completely from the Earth (to infinity) is the potential energy of the Moon all applied in one place. 8x1022MJ

1MegaTonne of TNT is about 4x109 MJ so that's 2x1013MT of TNT.

Also see Phil Platts treatment, here ... the situation is more dire if you want to escape the Sun as well.

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Thank you very much for the help. One question though:

If the body in question is the size of the moon but has the same gravity as Earth, that would mean said body has an equal-ish amount of mass just denser, wouldn't it? If so, instead of the figure of 0.5 x (7.4 x 10^22 kilograms) x (12,000 m/sec)^2 for 5 x 10^30 joules given, should I not substitute Earth's mass to gain 0.5 x (5.9742 x 10^24 kilograms) x (12,000 m/sec)^2 to achieve 4.301424 × 10^32 joules ?

Or am I incorrect in my assertion on the gravity bit?

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Simon Bridge
Homework Helper
Well sure, you did not specify mass in the original question so I just used Earth and Moon as the examples.

If it had the same radius as the Moon, but the same surface gravity as the earth... then it would have 6x the mass of the moon, or 5x1023kg ... still an order of magnitude less than the mass of the Earth.

I'm getting an escape velocity (from Earth, at lunar distance) of about 400m/s [check] which will give you total kinetic energy 4x1028J ... but how much is this? Lets do some comparisons:

This is 1013 average nuclear bombs. Sounds like a lot doesn't it?

The worlds nuclear arsenal stands at something of the order of 20,000 warheads ... so the force you are asking for is the entire nuclear stockpile let off at once, repeated 50 million times.

A total conversion plant, a magic SF machine that converts matter into energy, operating at unity, would need 400,000,000 tonnes of material as fuel.
(Hmmm... looks like an iron sphere 3km across ... OK sci-fi dimensions. Still need to work out why your heavy moon is not vaporized.)