# Accelerating a massive spaceship

How much wattage would you need to accelerate a four petaton spaceship by 1g for a year? This should be about enough to reach near light speed, which is perfect for interstellar cruising, but I'm wondering how feasible this timeframe is given that it would obviously require a lot of energy (not sure how much but it's definitely a lot), and I want to keep my antimatter generators realistic, within a few grams to a kilogram per day per generator.

I suppose, put simply, how much wattage would I need to accelerate this massive spacecraft and do I need to adjust my timeframe for reaching top speed? Or as a secondary possible solution, would it still be scientifically plausible if I increased the output of my antimatter generators further than this?

EDIT: Okay, I made a mistake in my question and said petatons instead of teratons (this ship's mass would be somewhere around 5.5e15 kg). Using this new weight and assuming it takes either 10 or 100 years to reach full speed instead of 1, how much will the power requirements be reduced? Could you use the gravity assist of large planets to reduce the power consumption any further?

• This question depends heavily on how effective your engines are. You can't just put "how much wattage" is required, because the "wattage" required between different engines producing different amounts of thrust are very different. As a story point, you can have your futuristic engines produce as much thrust as you need (eg: they are as efficient as you need them to be). – Aify Oct 11 '16 at 4:02
• wattage per year? Watt is already work per unit of time. Per year or per second, it's the same. – Mołot Oct 11 '16 at 6:25
• @Mołot but power does have some odd units that people actually use: J/s, kW-hr, MW-hr, etc. – PipperChip Oct 11 '16 at 6:55
• @PipperChip So? I was just addressing first paragraph. It doesn't matter if acceleration is meant to stay at 1g for a year or for 5 minutes. Power needed is exactly the same. – Mołot Oct 11 '16 at 8:01
• 5E15 kg, or 5E12 tonnes, at 1E9 tonnes per cubic km of water, you have equivalent mass to 5500 cubic km of water. That's a pretty big ship. Whatever are you doing? – puppetsock Jul 31 '19 at 21:16

# The Physics

Well, wattage is simply a measure of power. Power is the amount of energy per unit of time. Even better, you can use the concept of work to figure out how much energy you need to put out over the course of the year.

In variables: $$W=Fd = \Delta KE$$ where W is work or energy put out by the force, F is the force (in Newtons), and d is the distance (in meters), and $$\Delta KE$$ is the change in kinetic energy.

and $$P = W/s$$ where P is power, W is the work done, and s is the time (in seconds)

We know a spaceship is going to accelerate by 1 g for about a 1 year. That'll put you really close to the speed of light, so we'll just approximate it as c. (Yes, you'll never actually reach the speed of light, but let's just say you'll get "close enough.") Doing some math I can tell you that this spaceship will accumulate about $$1.798*10^{35} J$$ from its anti-matter reactors. Divide this by the seconds in a year and you get a whopping $$5.701 *10^{27} W$$!

Using Einsteins famous equation, this means you would need about $$2.01 *10^{18} kg$$ to be converted to pure energy. That's about 40% the atmosphere of earth converted into pure kinetic energy in total. This corresponds to burning about 69 times the total biomass of earth every day!

Sure, you can pick up astroids, comets, and other such things and such along the way and likely make no one angry, but this is a lot of mass! This is also assuming that there are no inefficiencies in your engine, which would otherwise increase the mass needed significantly!

# Burn a Kilo a Day

Taking a kilo of matter in every day sounds "reasonable" for an interstellar craft, but this only yields $$8.988 * 10^{16} J$$ every day.

This takes you $$5.477 * 10^{15} YEARS$$ to get up to speed.

# In Conclusion

I suggest only taking things you cannot live without. The mass of your spaceship increases the energy needed significantly. The alternative is to take 69 copies of every living thing on earth and feed them into the ship's engines, every day!

I guess you could collect asteroids or comets and use those... I mean, life isn't rare or anything. The hulking maw of death that is this ship wouldn't be noticed, I'm sure. Besides, I hear life is a renewable resource.

• Eesh. That's uhhh... gonna be a problem. Okay, I made a mistake in my question and said petatons instead of teratons (this ship's mass would be somewhere around 5.5e15 kg). Using this new weight and assuming it takes either 10 or 100 years to reach full speed instead of 1, how much will the power requirements be reduced? Could you use the gravity assist of large planets to reduce the power consumption any further? – Z.Schroeder Oct 11 '16 at 4:50
• Looks like you calculated this from the "outside" reference frame. Not bad, because "ridiculously huge" is a good answer, but it might be worth noting that from the inside time flows at different rate and your results may not be exact. (+1 from me anyway) – Mołot Oct 11 '16 at 8:03
• @Z.Schroder: Teratons instead of petatons cuts the power by a factor of a thousand, taking 100 years instead of 1 cuts it by a factor of 100. So you now only need 5.477 * 10^10 years to get up to speed. You can use gravity assists to gain some speed, but only in places where there are any giant planets, and once you're outside a solar system, there are none handy. Using the solar system's planets might knock off a few tens of years but the impact on 10^10 years is trivial. You need much more power, and a much lighter ship. – John Dallman Oct 11 '16 at 12:19
• @Mołot True, and I've not really accounted for any kind of relativity at all, but my gut tells me those adjustments just make going anywhere near this fast only a worse prospect. – PipperChip Oct 11 '16 at 19:29
• @Z.Schroeder Science is pretty unforgiving, and I'm sad to report that John Dallman's comment hit the nail on the head. Lighten the load, or burn a lot in you antimatter reactors. – PipperChip Oct 11 '16 at 19:32