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For the purposes of this question, let's assume space travel does not involve 'shortcuts' through other dimensions (like so-called hyperspace) and that 'tractor-beam' technology exists.

Provided the mass and craft 'towing' it are not in a specific body's (planet, sun, black hole or whatnot) gravity well, is there a way to determine a limit to how much mass the spacecraft could pull unencumbered? I've heard people speculate there shouldn't be such a limit, but have a hard time reconciling the image of a ship towing something the size of Earth's moon.

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  • $\begingroup$ It depends. If your towing mechanism is a physical cable, how hard you can pull comes down to the cable strength or engine output. At some point the cable will snap or engines burn out. If you instead use gravity, so having a small mass hover over the body, your limit is probably time and overcoming normal tidal forces. You couldnt pull the moon for instance with a gravity tug that dosnt weigh millions of tons. $\endgroup$
    – ErikHall
    Dec 23, 2023 at 2:32
  • $\begingroup$ Whereabouts inside the system's gravity well are you going from? From somewhere near the orbit of Mercury would seem to be a lot tougher than circa Pluto. I take it you don't have anything the equivalent of regenerative breaking past the halfway point? $\endgroup$ Dec 23, 2023 at 2:37
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    $\begingroup$ I don't get how something can be "in" the solar system, but not in a gravity well. Can you clarify. You understand that gravity extends to infinity... what you're dealing with between two solar systems is competing gravity wells. $\endgroup$ Dec 23, 2023 at 4:34
  • $\begingroup$ Calculating 3 body sys is already above a rocket scientist pay grade 😅 $\endgroup$
    – user6760
    Dec 23, 2023 at 6:12
  • $\begingroup$ @Escapeddentalpatient. To be fair to the OP, who likely isn't a celestial mechanic, I can stand in an ocean tidal pool that's a centimeter deep and be "in the ocean." The energy expended moving through that pool would be measurable, but trivial, and entirely ignorable for the intent of most calculations - compared to standing neck-deep in an ocean and discovering walking is a problem. Worldbuilding is about simplification and I suspect this can be answered without worrying about the nefarious details. $\endgroup$
    – JBH
    Dec 23, 2023 at 17:08

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That depends entirely on how fast you want to make the trip.

If you don't need to break orbit first, an arbitrarily small impulse will set an arbitrarily large mass moving at some, possibly extremely small, speed in whatever direction you want to go. Just give it a push, wait a billion years, and it will get there. If you want to go faster, or tow a larger payload, you will need a more powerful engine on your ship, or more fuel to push longer. But if you don't care how long the trip takes, and you've already broken orbit, the Dawn probe's ion engine could move the Moon between solar systems.

So, how fast and how far do you want to go? That'll determine your mass limit.

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In addition to @KerrAvon2055's excellent answer, which I upvoted, I'd like to point out the following:

An object in motion remains in motion until acted upon by another force.

Could a ship haul a moon between stars? That depends on what forces are already acting on that moon. The forces involved with an orbit are substantial.

So, simplistically, given infinite time and access to a power source during all of that time, there really isn't a limit to the amount of mass a ship can tug between solar systems — assuming the force your ship can bring to bear can overcome all of the other forces already bearing on the object you want to move.

NOTE: let's say that moon isn't in orbit but is a rogue floating through space. It has inertia due to a velocity vector but (and I declare this) no gravity affecting it. Could a bottle rocket with an infinite burn duration move that moon in another direction and transport it between solar systems? Surprisingly, the answer really is "yes." Can it do it in a reasonable period of time? Nope. The whole of the universe might suffer heat death before that poor bottle rocket completes its task, but little by little the velocity vector of the moon would change.

So, how to figure out a practical maximum?

Some equations:

  • Velocity = initial_velocity + (acceleration * time)

  • Force = mass * acceleration

  • Force = mass * (distance / time2)

Given those relationships, you can figure out how much you can haul "unencumbered" (which I interpret to mean, "without fighting another force," like gravity). How much mass you can haul depends on the acceleration you can bring to bear, how long you can bring it to bear, and how much time you want to take in transport.

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There are a number of potential issues:

  1. The total delta v of the towing craft may be insufficient to move the total mass within its anticipated operational lifespan, or the lifespan of any entity or organisation that wants to achieve the objective. The total delta v may also be insufficient to get the combined mass from solar system A to solar system B depending on the relative velocities of the two solar systems even if the tugboat, its crew and its sponsors are truly immortal. Given the mind-boggling distances involved in interstellar travel and the likely practical limits in rocket efficiency, having 90% of a ship being fuel is not unreasonable. If you now want a ship to tow something, for example, 10 times its mass, then it will be an order of magnitude slower, since obviously a ship can't increase its fuel percentage to 900% to compensate for the extra mass.
  2. There needs to be a practical way to attach the towing craft to the object being towed. Noting that it is believed that a large number of asteroids are held together about as strongly as a loosely packed snowball, you probably need to build a sufficiently strong set of cables, or possibly even a net, to encircle the body being towed. (If the tractor beam mentioned can magically target all particles in the towed body equally then disregard this issue.)
  3. If you are towing with a single ship with a reaction-based thrust mechanism (ie a rocket) then a wide-body tow is a problem. Throwing reaction mass out the back of a rocket is how it gets its thrust, but if the reaction mass is then impacting the body being towed then it means an equal force in the opposite direction is "braking" the towed body. (Think about the idea of a boat with a propeller that it aims at its sails - while Mythbusters were able to get a tiny amount of forward motion due to various spillage effects, it gives you the idea.) If there are multiple engines on the tugboat then it can point them somewhat off to the side so that the ejected reaction mass misses the towed body, but this is wasting delta v. Worse, the wasted force is trying to crush the tugboat, and that's a lot of force when you are talking about engines to tow a moon. More is wasted the greater the angle that the engine must be offset, so the tractor beam needs to be able to tow from a distance such that the towed object is only occluding a degree or so of arc. So, if you are towing Earth's moon then you want a tractor beam with a range of about 100,000 km. Alternatively, use multiple tugboats and position them at equidistant positions around the object to be moved instead of directly in front.
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Intuition on these scales can be tricky. In the simplest way of thinking, there's no limit, but a practical limit does arise.

We're used to motion where there's lots of friction. Because of that, we're used to the idea that a small force cannot move a large object. But really, if you have a small force on a large object, it just means the acceleration is really small. So as long as you have fuel, you can accelerate said moon. No laws of physics will get in your way.

Of course, you say "no shortcuts." You specified you meant no tricks like hyperspace or wormholes, but I'd like to point out that your ship has to have some propulsive device. How that device works will matter for these extreme problems. If you can just magically produce force by pushing on the universe or some pseudoscience phrasing like that, you may just have a really long trip ahead of you. However, if you're using any form of propulsion we have ever dreamed of, you'll be using a reactionary mechanism: you push exhaust out of the back of your ship really really fast, and that force has a reactionary force on the ship which moves it forward. This should feel natural -- its how quite literally every vehicle mankind has ever created works.

In space, we are dominated by the tyranny of the Rocket Equation. Long story short, we don't just get to accelerate our payload. We also have to accelerate all of the fuel needed for the rest of the trip. This fuel mass typically accounts for the vast majority of the mass of a rocket. As it works out, these effects lead to a natural limit measured in terms of delta-V. For any rocket, they can change their velocity by so many meters per second before they run out of fuel. It doesn't matter in what direction. For any practical science fiction involving rockets, this is a key metric to be aware of.

So how much can we accelerate a body like a moon? If you have a very large rocket, we'd have to do these complicated equations. But it sounds like you want a very small rocket, and for the case where the propellant makes up a very small fraction of the payload, we can handwave away all of the exciting exponentials of the real equations and just treat this like a normal physics problem. We apply a force to a moon over a period of time, and get a change in velocity out of it.

So let's grab numbers. Let's use a SpaceX Falcon Heavy to move our moon. The Falcon Heavy fires for 154.3 seconds with a max force of 16.2 MN. For simplicity, we'll assume it achieves that force for the entire flight. The moon is $0.07346\cdot10^{24}$ kg. Using F=ma, we see that the acceleration is about $2\cdot10^{-16} m/s^2$. Multiplied by the burn time, we get a change in velocity of $3.5\cdot10^{-14} m/s$.

Congratulations, you can get to Alpha Centauri in 10,000,000,000,000,000,000,000 years! Importantly, this is less time than it takes for the predicted heat death of the universe. However, Alpha Centauri-B having an expected life of only 20,000,000,000 more years, you may be rather disappointed when you arrive.

Well, almost. On these time and speed scales, there's more to account for. The above calculations assume space is empty. It is not. There's a fine haze of hydrogen atoms called the Interstellar Medium (ISM). There's not much mass out there, a mere trillion molecules per cubic meter. But over time it adds up. Our sun is traveling through its local part of the ISM at a rate of about 25km/s. We can assume other stars have similar rates. At 25km/s and the cross sectional area of the moon is [about]7 10,000,000 km^2, so a moon traveling at roughly the same velocity as our solar system would plow through 250,000,000 km^3 of ISM every second. That's on the order of 500,000kg/s of hydrogen. This imparts 12500MN of force. (assuming non-elastic collisions -- the actual math is more complicated, but wont change the story)

Remember, our Falcon Heavy only outputted 16.4MN. So if you were burning one Falcon Heavy in the middle of the ISM, you could barely overcome the drag forces applied to your moon. 154.3 seconds later, you're out of fuel.

So practically speaking, with a small rocket, you'll have to go where the winds take you.

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It depends on how you define a spacecraft. Theoretically you can move a whole galaxy if you want to. The trick is using stars as a spaceships. It is entirely in the realm of known science to do that. The simplest way is building a Shkadov thruster. The concept is that you use the output of a star to generate thrust. Anything in the gravity well will move as well.

But that is in the realm of K2+ civilizations. Isaac Arthur made a video about it a few years ago (in fact, any question about realistic sci-fi that is about large scales can usually be answered by him).

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