A question that I wanted answered

I wanted to know what kind of velocity could be obtained if an object of the size of a Nimitz sized aircraft carrier had a nuclear bomb exploded next to it (in space). Here's the question posed to the LEO AI:

 

can you calculate how much acceleration would be applied to an object of mass of 100,000 tons if an explosive of the equivalent of 1 kiloton of TNT would explode near it?

 

And the answer:

 

To calculate the acceleration, we'll need to consider the force exerted by the explosion and the mass of the object.

The force exerted by the explosion can be estimated using the TNT equivalent formula:

1 kiloton TNT = 4.184 x 10^12 Joules

Assuming the explosion is instantaneous and the object is initially at rest, we can use the impulse-momentum theorem to relate the force and the momentum of the object.

The momentum of the object is given by:

p = m * v

where p is the momentum, m is the mass, and v is the velocity.

The impulse-momentum theorem states that the impulse (force x time) equals the change in momentum.

Since the explosion is instantaneous, the time is negligible, and we can assume the force is applied for a very short time.

Let's assume the force is applied for a time of approximately 0.1 seconds (a rough estimate of the time it takes for the shockwave to reach the object).

First, we need to convert the mass of the object from tons to kilograms:

100,000 tons = 90,000,000,000 kg (approximately)

Now, let's calculate the force exerted by the explosion:

F = Δp / Δt

where F is the force, Δp is the change in momentum, and Δt is the time.

Since the object is initially at rest, the change in momentum is equal to the momentum of the object after the explosion.

The momentum of the object is:

p = m * v

where v is the velocity after the explosion.

We can estimate the velocity using the equation:

v = Δp / m

Now, let's plug in the values:

Δp = 4.184 x 10^12 J / (9.81 m/s^2) ≈ 4.26 x 10^9 kg*m/s

m = 90,000,000,000 kg

v = 4.26 x 10^9 kg*m/s / 90,000,000,000 kg ≈ 4.7 m/s

Now, let's calculate the force:

F = Δp / Δt

F = 4.26 x 10^9 kg*m/s / 0.1 s ≈ 42.6 x 10^9 N

Now, let's calculate the acceleration:

a = F / m

a = 42.6 x 10^9 N / 90,000,000,000 kg ≈ 0.0045 m/s^2

So, the acceleration applied to the object would be approximately 0.0045 m/s^2.

Note that this is a rough estimate and the actual acceleration may vary depending on various factors such as the shape and size of the object, the distance from the explosion, and the surrounding environment.

Would you like me to elaborate on any of the assumptions made in this calculation?

Comment (9:26 AM):

I stopped here.

Actually, I wanted delta-v, which would have been 4.7 m/s.  You'd need a lot of mini-nukes to get that mass moving...

I'd say a rough guesstimate of a thousand in order to get it from the far side of the moon to an Aldrin orbit for an Aldrin Cycler.

Maybe you'd want a smaller cycler or be prepared for a lot of fireworks. 

12:00 PM:

 

It looks like you might be able to optimize this based upon how much mass and delta-V you want. A bigger explosive yield would generate more velocity, and so would less mass.

 

In this case, if you wanted the whole thing sent, you're going to need maybe a thousand nukes of that size. A nuke 10 times bigger would require fewer nukes---less say 10 times less in number. Therefore, a thousand 10 kiloton nukes would move it 10 times faster. It would require only 100 nukes of that size. If the mass was 10 times less, then you'd need only 10 nukes of that size. Optimization could tell you which would give the best results.

 

The real question is what could get political approval for testing to take place. You know who would be the most upset.

 

That's why it was never done. Likely why it will never be done, unless something drastic changed. In theory, you could get to the nearest star with enough of these nukes. But it would still take a long time. You might get up to about 10% of the speed of light. A trip would take 40 years one way.

 

Here's a video I watched recently on the subject of human hibernation for space travel to distant places.