Realistic acceleration with Laser Propulsion for intra-stellar 1 million ton cargo ship

Question

My question is about how realistic it is to imagine beamed solar energy accelerating a 1M ton or so vessel up to 600km/s or more within a few hours.

I can look up the specific energy required to displace that much mass that fast. But I am not familiar enough with the physics to know if you can concentrate a laser/maser with enough energy to to do that, or if the material on the sail similarly could withstand it.

This is for some fiction I am writing which I'm trying to keep hard-science adjacent. It involves a theoretically heavily developed inner system around the sun, making use of hundreds or thousands of solar collectors for beamed energy. The second biggest area of development is around Jupiter, with a human economy exploiting the materials there, and living on cylinders in/among the moons.

I am treating a voyage from Earth to Jupiter on a cargo ship to be ~900M km, and taking 20 to 35 days.

Theoretical cargo vessel is shaped like a wheel, with the gondolas for cargo and passengers all along the outer edges which turns slowly in flight for some artificial gravity. The inner area of the wheel may have spokes, and even a powered engine in the very center. But most of the area in the center is a large sail construct.

Could a laser/maser beam speed up a 1.25km² diameter sail to accelerate a cargo vessel realistically to a speed up above 600km/second? Or is the energy required to move 1M tons of cargo unrealistic?

Story-wise, I want to have the passengers buckle in for hard acceleration/deceleration for a few hours, after which the wheel spins up for the weeks it is being flung along its trajectory.

I am using the following equation, which I got from Isaac Arthur, as a calculation of ideal theoretical acceleration for fast travel. I assume this is more realistic to, say, light craft with fusion drives.

For 4g acceleration for six hours, theoretically,

a = 39.2 m/s², for ¼ day, t = 21,600 seconds
d = ½ x (39.2 m/s²) x 21,600 ²s
  = 9,100,000,000 m = 9.1 million kilometers
v = at = 39.2 m/s² x 21,600 x = 847 km/s

In this story, people do use fusion and fusion drives for a lot of things. But just like in our world, where I can fly across the world in 24 hours, sending cargo is just more cheaply done on a freight container that will take three weeks or more.

Edit: for the ship slowing down, either from solar relays, (if possible) or possible relays powered by the abundant fusion fuel from Jupiter and/or Saturn. Probably another set of things to work out.

Answer 1

Brace yourself.

Acceleration due to perfect reflection of light looks a bit like this:

$$\dot{V_s} = \frac{2E_b}{M_sc}$$

where $E_b$ is the energy of the incident light beam, $M_s$ is the mass of the spacecraft and $c$ is the speed of light. $\dot{V_s}$ is the change of speed of the spacecraft... if you want this in m/s², give beam energy in watts.

Given a mass of a million (presumably metric) tonnes and a required acceleration of 4G, you get a slightly eye-watering beam power of 5.9x10¹⁸ watts... that's about 10 times the solar flux that falls upon Earth, or a Kardashev rating of ~1.27. Your beam of death threatens the entire solar system, by the way. Think carefully about who controls it.

If your laser is solar powered and sits in an Earthlike-orbit, you need a total collector array 10 times bigger than the disc of the Earth if both the collector and emitters are 100% efficient. A laser with 50% efficiency is pretty gosh-darn good, and implies that your solar collector array needs to be twice as big again. Photovoltaics might be under 50%, too. You may also not get perfect 100% reflection from your sail, meaning you need more power to reach those accelerations, etc etc. Sticking your solar array in a Mercury-like orbit gives you 10x the solar flux, but you still need tens or even hundreds of millions of square kilometres of photovoltaics to power your deathray.

Anyway, on your little 1.25km² sail, that gives you a power density of about a terawatt per square metre, and you're not going to find any plausible sail material that can stand up to that sort of punishment.

I will say that lasers can theoretically be scaled up as big and crazy as you'd like, so that's one thing that you don't have to worry about, at least.

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Consider, though.

• A million tonne spacecraft is the sort of thing you might want to send to another star to start a self-sufficient colony. What do you think you're moving around that's so heavy? Is there really nowhere closer to find it? You might be better off shipping out a factory than a million tonnes of finished goods! Something that weighs a few thousand tonnes would be more than big enough for most purposes.
• A month to Jupiter is super, super fast. Consider extending that a bit. 90 days isn't that bad for living things if you've solved the shielding issues and have spin-gravity. Inert, rad-resistant, non-priority cargo can take a year or more. Slow is cheap, slow is safe.
• 1000km/s is a hell of a top speed. What happens if you hit a bit of grit on the way? How much shielding will you need? How much repairing will your sail need? If you brakes fail, who will you destroy if you hit them? How will a rescue mission catch up?
• Interplanetary spacecraft with multi-G accelerations are almost always waaaay too powerful to have in a hard-science scenario. Cut that right down, and use longer acceleration and braking phases.
• Use bigger sails. Space is big; you've got room to spread your wings.
• Use other propulsion systems. My personal favouite is the late Jordin Kare's sailbeam which is a much more efficient way to impart momentum to big spacecraft, but big fusion rockets may be safer and more plausible than your planet-sized laser array. It makes use of a magnetic sail, which is less awkward than a lightsail once you've worked out how to build them, and can be used for magnetic braking at your destination, too.

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Your laser, as originally specified, is exactly the sort of thing you'll need if you want to launch interstellar spacecraft. It seems likely to have been built by a multinational consortium or alliance for just this purpose (it is too powerful and dangerous and expensive for anything else) and is unlikely to be used for mere interplanetary jaunts. Just a thought.