How massive can a spacecraft be?

Question

Enter Iaeptus - A million man mission born on a fleet of ten thousand ship to the outer solar system. Their commander : Minevera, a brain-in-a-vat super computer. With a weight of 5 tons, a neuron density 12 times that of mortal man, and 3.4 x 10^25 synapses, it is the most powerful computational device to exist in the Solar System. Their mission: Construct the Atlas Prime, the soon to be largest Spacecraft in human history. An enormous, self propelled gravity tug and inertia thief , it will be built to modify the orbits of Trans-Neptunian and Kuiper-Belt objects.

Since bigger is better for a gravity tug, just how massive can Atlas Prime be?

Limitations

• It Must be self propelled

• It's propulsion system must be demonstratably​ possible

• the name of the drive may not contain the words "worm" or "warp"

• the mass payload must make up ~50% or more of the sum mass (if possible)

• the craft must be able to accelerate to at least 1.0 m/s^2

Given these specs, what is the upper limit on the mass of Atlas Prime?

Notes

For clarification, I am asking, given the parameters, what drive will propel the most mass, and what that most would be

Atlas prime is liable to be anything from an O'Neil cylinder to and mass of lead with a rocket strapped to it. The most important part of Atlas Prime is it being portable mass

Answer 1

It may not meet your acceleration requirements, but you should look into fusion candles. You can't get much more massive than that other than a Shkadov thruster which would we way overkill for your needs.

In general, the easiest way to build a massive gravity tractor is probably:

1. Decide how massive you want it to be.
2. Find a celestial body of approximately that mass, ideally composed primarily of a material that could also be used as reaction mass.
3. Harden against acceleration if small enough that its own gravity/cohesion will not hold it together.
4. Strap your preferred engine to the back and go. Options here include project orion, NSWR, mass driver, and ion thrusters (though it may be difficult to reach the desired acceleration with these)

But as Slarty mentions, gravity tractors are only necessary if you cannot mount an engine directly onto the target object.

Answer 2

Theoretically a spacecraft can be arbitrarily large and still accelerate at 1m/s. Consider this thought experiment: take two Saturn V rockets and link them together side by side in space. This unit would still have the same acceleration as a single Saturn V but would have twice the mass. Technical stability issues aside, this process could be repeated as many times as you want. If the payload needs to occupy at least half of the weight then assume the second and third stages of the Saturn V’s are replaced by equal masses of whatever payload is required.

A better measure for rocket performance is the change in velocity that it can achieve which is given by the rocket equation:

Change in velocity = exhaust velocity * natural log(initial mass / final mass)

The initial mass is the vehicle plus the mass of the propellant

The final mass is simply the vehicle mass

The exhaust velocity is the speed of the propelling hot gases as they leave the rocket engine

If the payload is half of the mass then this simplified to Change in velocity = exhaust velocity * 0.69 The space shuttle main engine has an exhaust velocity of 4.4 km/s in a vacuum

Ion engines have an exhaust velocity around 20-50 km/s

Fusion rockets potentially might have an exhaust velocity of the order of 100’s km/s

If you want to change the orbit of a Trans-Neptunian or Kuiper-Belt object a better bet would be to land a large ion engine on it together with a large nuclear power plant and processing facilities. Process some of the material of the body into gas and then use that gas in the ion engine powered by the nuclear plant.