[ExI] Von Neumann Probes

[Ben Zaiboc]

On 25/01/2026 00:44, spike wrote:
> Ben it wouldn't need to be a speck of dust, which is quite unlikely to
> encounter in interstellar space.  But I agree with your concept for a
> different reason: the probe going at .01c would erode from encountering
> hydrogen.  It is easy enough to estimate if we want to go with Wiki's
> estimate of a trillion molecules per cubic meter, then recognize at .01c,
> you pass thru about 3 million cubic meters per second.
>
> If the frontal area of the probe is one square millimeter, it is hitting
> about 3 trillion molecules per second, and some ions, which is significant:
> accelerating the ion from the collision creates radiation.  But before we
> bother pondering radiation, estimate the drag from the 3 trillion molecules
> per second hitting the probe at .01c.
>
> spike
>
>
>
>
> OK I did some BOTECs and I estimate the cubic millimeter probe, if we assume
> a mass of about a milligram and initial velocity of .01c will decelerate
> from hitting interstellar hydrogen at about 6 m/sec^2.
>
> It is a very unsophisticated calculation however.  If anyone would try to
> check my work, I will cheerfully accept any answer within an order of
> magnitude.  
>
> Ben your point is carried however: anything that small will need to consider
> deal with the drag from the diffuse interstellar medium, as well as the
> erosion.

Don't ask me. One measly order of magnitude? Pah, my mistakes are usually much, much bigger. See below.

Ok, so we're probably talking about probes in the region of 100s of grams. Maybe pebble-sized. They should be able to withstand a few centuries or millennia of abrasion from interstellar stuff (wild guess).

So how much energy would it take to accelerate, say, a 200g object to our arbitrary speed of 0.01c?

Duck.ai is telling me:

"To calculate the energy required to accelerate an object, you can use the formula for kinetic energy: KE=1/2​mv^2. For a mass of 200 grams (0.2 kg) and a speed of 0.01c (where c is the speed of light, approximately 3×10^8 m/s), the energy needed would be about 0.0001 joules."

That seems very small to me. Is it right? (I have no mathematical intuition at all, so it could be spot-on or wildly inaccurate, I'd have no idea)

If it is right, why aren't we building small robot probes right now, and flinging them out at respectable fractions of c?

I'm very suspicious. 200g of baked beans contains 683kJ of chemical energy, according to the label. That's barely enough to keep me alive for 2 hours. Yet it could accelerate a mass of 200g to relativistic speeds?

When I do that calculation, I get 900 billion joules, so somebody's getting it badly wrong.

KE = 0.5 * 0.2 * 3,000,000^2
= about 1.3 billion small tins of beans
(as opposed to about one-thousandth of a bean)

Help me, somebody who has a clue.

Oh, hang on, I asked for more details, now it gives me (after a bunch of incomprehensible maths) 3.6 x 10^21 Joules!

So around 10 orders of magnitude bigger than my answer.

I'm fairly confident now, that to accelerate a 200g probe to 0.01c would take somewhere between 0.0001 and 3,600,000,000,000,000,000,000 Joules. Sorted :/

-- 
Ben