In one section of the book, they try to calculate the energy that it takes to get a 10-kg spaceship up to one tenth the speed of light. Yes, this is a reletivistic speed, but at the same time it is barely at that level and the lorentz transform at that level comes out to be very close to one, so we'll keep it simple. Your basic equation for energy is E = (1/2)mv². I will crank through the algebra...
E = (1/2) * (10 kg) * (3.00 * 10^7)²
E = 5 * (9.00 * 10^14)
E = 4.5 * 10^15 Joules
So far, the book was right on that. However, then they decided to convert to Kilowatts. According to my physics book and a couple online sources, 1 KW = 3.6 * 10^6 J. Thus, we convert.
(4.5*10^15 J) = (4.5*10^15 J)/(3.6 * 10^6 J/KW) = 1.25 * 10^9 KW
Now, in the book, it says that it would take 12.5 million Kilowatts to move that spaceship that fast. That's 12,500,000 KW, right? But I just calculated it to be 1,250,000,000 KW, right?
Or did I make a mistake somewhere?
If it's right, someone who's good at math confirm it for me. If I'm wrong and the book is right, tell me so I don't make a fool out of myself when I e-mail the authors of the book
Edit: Hahaha, I went back through and I found out that the 12.5 KW wasn't referring to the spaceship, but rather to a powerplant's energy output. Because my pride got to me, I will give y'all the section of the book I was checking up on. It's from the book "The Revised and Expanded Answers Book" avaliable on www.answersingenesis.com.
Pages 147-148
Apendix
Feasibility of Inter-Stellar Travel
The Following calculations are given for the benefit of the more technically minded.
1. for a spacecraft to acquire a speed of c/10, the kinetic energy needed is given accurately enough by the non-relativistic formula of ½mv². For a very small unmanned spacecraft of 10 kg, this is ½ x 10kg x (3 x 10^7 m/s)² = 4.5 x 10^15 J. The largest hydroelectric power station in the world, Itaipu, jointly run by Brazil and Paraguay, has an output of 12.6 million kilowatts. The total energy generated by the 18 turbines in four days equals the kinetic energy of a 10 kg spacecraft moving with a speed of c/10.
For a manned spacecraft weighing several tons, the energy requirements would greatly exceed the world's daily electricity consumption. For the city-sized spacecraft in Independence Day, the energy requirements would be staggering. And when the spacecraft slowed again, it would need to use up almost this amount of energy in braking.
If the spacecraft had to accelerate to c/10, slow down and speed up many times, the energy needed would be many times greater.
It would probably be impossible for enough fuel to be carried without some sort of antimatter drive. If perfect annihilation -- complete conversion of matter to energy (E = mc²) -- were possible, 1 ton of antimater could annihilate 1 ton of ordinary mater to produce: 2000 kg x (3 x 10^8 m/s)², or 1.8 x 10^20 J. And this is the absolute maximum amount of energy that could be produced from a given mass of fuel. A real spacecraft could be nowhere near this efficient.
2. The kinetic energy of a speck of dust with a mass of just .1 gram impacting at a tenth the speed of light, calculated from the spacecraft's reference frame, is ½mv², or ½ x 10^-4 kg x (3 x 10^7 m/s)² = 4.5 x 10^10 J.
The combustion energy of TNT is 4520 kJ/kg, or 4.52 x 10^9 J/ton. So, 4.5 x 10^10 J is equivalent to 9.95 tons of TNT. Therefore, the impact energy of a 0.1 g object hitting a spacecraft traveling at c/10 would be the equivalent to an explosion of about 10 tons of TNT.
