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03:51
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A: Does Earth have enough fuel to become a solar empire?

ThreoseYou need fuel only to move out of the atmosphere not to move in space, so yes probably the fuel is enough to colonize a new planet but not to move too many people from this planet, cause more people make rockets heavier which results in consuming more fuel. But technically yes if you send ships...

Actually, 20-50 people is not enough. Assuming strict control over who reproduces with who and how long they wait to have kids...the absolute bare minimum is about 80 people. More realistically, you need something more like 160. And this assumes nothing goes wrong. Ref: worldbuilding.stackexchange.com/questions/3/…
The fact that you don't need fuel to navigate in space will be a surprise to NASA. You should let them know, they've been foolishly installing navigational rockets on their satellites and space probes.
Especially the part where Their design principles are not supported by prevailing scientific theories ... It'll be fun trying to land on the moon without reaction fuel.
@SerbanTanasa If you don't care about acceleration, only delta-v, Sun already provides enough reaction fuel for you. Not the best for human cargo, but still. You can't land a solar sailboat on a rocky body without atmosphere, but that's out of scope of moving in space.
03:51
Hmm, what is it that you think the difference between delta-v and acceleration is?
@Seeds: The difference between delta-v and acceleration is that acceleration is delta-v per unit time. (So, delta-v has units of m/s, whereas acceleration has units of m/s².) So by "If you don't care about acceleration, only delta-v", Jan Dvorak means "if you don't care about how quickly you speed up and slow down, only the speed you eventually reach". Does that make sense?
There is no such thing as instantaneous change in velocity, so any change in velocity requires an acceleration. I was trying to lead @JanDvorak toward the more correct "If you don't care about the magnitude of acceleration..." And velocity is not a scalar value, it's a vector. (i.e. velocity is not speed, it is speed and direction)
Velocity is a vector, but delta-v is a scalar. It tells you (roughly speaking) how much fuel you have and how efficiently you can use it versus how heavy your spaceship is. You need 10 km/s delta-v to get to the low Earth orbit. You you have less than that, you aren't going to space today. If you have exactly that, you aren't going to space anyways, because air drag and gravity will eat up some of it. And yes, I did mean the magnitude when talking about acceleration. I do know that you need at least some of it in order to change your velocity.
Granted I have seen folks with no physics background try to make their prose sound more interesting by using terms they don't understand, like calling speed "delta-v", but in the physics I know delta-v is a synonym for acceleration. And you might rethink your statement about the sun providing "reaction fuel", unless you are making up your own definition of those words too.
I think the reference to "reaction fuel"is for a solar sail. Agree the terminology is very poor, though.
03:51
@Seeds Δv is not acceleration, it's merely a difference between two speeds, i.e. between absolute scalar values of velocities. It's actually used as more a measure of energy, whereas acceleration a = dv/dt corresponds to change in momentum. (For instance, a U-turn incurs no Δv at all, but clearly doesn't preserve momentum.)
@Seeds Nobody said there was such a thing as instantaneous change in velocity. Only that you can achieve a particular change in velocity with a small acceleration over a large time or a large acceleration over a small time. In both cases you have the same delta-v, but different acceleration, hence "not caring about acceleration, only delta-v".
As I said, in literature it isn't uncommon to see people USE Δv instead of change in speed, but in physics (rocket science) Δv is acceleration. Many people have difficulty with things like vectors, and confuse the idea of speed and velocity, even authors who understand the differences, "dumb down" their prose so as not to confuse their audience. (There is a good quote like Make your audience think they are thinking, and they will love you; make them actually think, and they will despise you)
Speed and velocity is the same thing , the only difference is when you say velocity the object has to move from the starting point constantly and in only one precise direction..... I see no difference in writing velocity 55 km/h north instead of speed 55 km/h.
@Seeds: dv and dv/dt are not the same thing. Concocting conspiracy theories about how even knowledgeable domain experts are lying in order to defend your statements is not constructive.

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