How Much Energy to Move a Moon-Sized Planetoid from Earth's Orbit?

[IustitiaPrime]

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.

 

[Simon Bridge]

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.

 

[IustitiaPrime]

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?

 

[Simon Bridge]

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? Let's 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.)

Did you read the article?

For comparison the energy output of the Sun is 5x10²⁶J ... so you need about 100x the total solar output in energy... all at once in a single explosion.

 

[pmacias]

I understand the curiosity and fascination with quantifying fictional feats and applying scientific principles to them. However, it is important to keep in mind that these are fictional scenarios and may not always align with real-world physics.

In terms of moving a moon-sized body from Earth's orbit, it would require an immense amount of force. The force needed would depend on the mass of the moon-sized body, the distance it needs to be moved, and the gravitational pull of Earth.

To calculate this force, we would need to use the equation F = G(m1m2)/r^2, where F is the force, G is the gravitational constant, m1 and m2 are the masses of the two bodies, and r is the distance between them.

In this case, the mass of Cybertron would be the mass of the moon-sized body and the mass of Earth would be the mass of the Earth. The distance between them would be the distance from Earth's orbit to the new orbit of Cybertron.

Without knowing the exact values for these variables, it is difficult to give an exact answer. However, we can estimate that it would require an explosion with a tremendous amount of energy, possibly in the range of billions or even trillions of joules.

Keep in mind that this is just a rough estimate and may not accurately reflect the fictional scenario. Additionally, there may be other factors at play, such as the strength and composition of the metal in Cybertron, that could affect the calculation.

In conclusion, while it is interesting to apply scientific principles to fictional scenarios, it is important to remember that they may not always align with real-world physics. It is best to approach these calculations with a sense of curiosity rather than trying to find exact answers.