ACCELERATING A SPACESHIP TO 1/100 SPEED OF LIGHT

Science Fiction movies show spaceships cruising at some fraction of the speed of light with the passengers in suspended animation. They land on some distant star system in a few centuries and all is well. Hmm. At .01c (1/100 the speed of light) it would take 100 years to go a single light year, and 400 years to go 4 light-years, which is the distance to Alpha Centauri, the nearest star system to earth. It is what it is, so let's see how much energy it takes to bring just a 1000kg object to .01c. Remember that a real spaceship with passengers would weigh millions of kg.

So a 1000kg object is about the same weight as a Fiat500 - with no passengers. So we're going to get this beauty up to .01c or 3x10⁶ m/sec.

After accelerating, the final velocity will be
v = .01c = 3x10⁶ m/sec.

Let's say that we will allow one year to accelerate to .01c. There are 31,558,000 seconds in a year, so acceleration will be:
a = 3x10⁶ m/sec / 31,558,000sec = .95 m/sec², which is about .1G.

Now for some high-school physics formulas assuming constant acceleration:
velocity at a given t: v = at.
distance at a given t: d = 1/2at².
Work (or Energy) is defined as Force x distance and Force = mass x acceleration. So:
E = F * d = m * a * d.
So let's plug in some values:
After 1 year, distance traveled is d = 1/2at² = 1/2 * .95 * 31,436,000² = 4.69 x10¹⁴ m
E = m * a * d = 1000 * .95 * 4.69 x10¹⁴ = 4.45 x10¹⁷joules = .44 EJ (ekajoules)
So, our little 1000kg Fiat ship would burn .445 / 365 = .0012 EJ daily.

Just for context, the energy production for the entire world in 2019 was 619EJ (1 ekajoule = 10¹⁸ joules). This is equivalent to 1.7EJ/day. This means that our ship would consume .07% of the earth's entire energy production per day. A more realistic ship weighing a million kg would consume 70% of the earth's entire energy output per day. Probably will need to improve the technology before any of that is possible.