Travelling Through Space and Time

Hello Everybody! Let’s do a science! You may have heard that traveling near the speed of light causes time to “slow down” relative to those that are traveling at slower speeds. If you are like me, you have probably wondered how strong this effect is for different velocities. Well my new (and old) friends you are in luck. I have created an excel file, which you download here that automatically calculates this effect, called time dilation, for fractions of the speed of light. Don’t want to download it, or don’t trust me to not give you a virus, well you are still in luck, because time dilation and the possibility of manned space travel to other stars is what this post is about. First here is a chart of the time dilation effect for certain percentages of the speed of light.

Caveats and addendums: I am not a physicist. I don’t even know that much about physics. This project is part of my attempt to change that. It is certainly possible I made a mistake. If you spot one, please leave a comment. If you attempt to travel to another star system based on this post you are an idiot, and I am not responsible for any loss of finances, limbs, or life that may occur.

As you can see you need to attain a significant fraction of the speed of light for time dilation to really matter. Just how hard is it to reach these kinds of velocities? Well let’s put things in to perspective. The fastest velocity ever achieved by a human made object was attained by Helios 2, a satellite that studied the sun. Helios 2 attained a velocity, relative to the sun, of 157,078 miles per hour or 70,220 meters per second. The speed of light is 299,792,458 meters per second. Helios 2 achieved (70220/299792458) about 0.023% of the speed of light. To be fair I don’t think most space mission directors (or whatever they are called) consider maximizing velocity a priority. Space on a rocket is limited. It is better to save that space for more scientific instruments, rather than fuel. However if we want to travel to other star systems velocity is going to be extremely important. Our closest stellar neighbor, Alpha Centauri, is 4.4 light years away. To be clear light years are a measure of distance not time, no matter what Andy says. I think Dr. Sheldon Cooper said it best when he said

“I would not say that. No-one would say that, a light year is a unit of distance, not time… You see people hear the word year and they think duration. Foot-pound has the same problem, that’s a unit of work, not of weight.”

A light year is the distance light travels in a year or about 5.9 trillion miles.

I am going to be using some very large numbers so I will use scientific notation. In scientific notation you take a number times 10 to a certain power. The power that 10 is raised to determines how many decimal point you move to the right, for instance 5.67*10^4 = 56,700. 5,500,000 is equal to 5.5*10^6. If we were to send a spacecraft to Alpha Centauri at a velocity of 70220 meters per second relative to the Earth, it would take the spacecraft more than 19,000 years to reach the star (actually stars, it is a trinary star system). The problem with travelling near the speed of light is it requires a huge amount of energy. As well as the fact that the more mass you need to propel, the more energy that is required. To propel the mass of Helios 2, 370 kilograms, to Alpha Centauri in 50 years would require a minimum of 1.2*10^17 Joules or the equivalent of a 1000 megawatt (which is large by today’s standards) nuclear power plant running for 4.28 years. Keep in mind that none of these calculations take into account the time it would take to accelerate to the desired velocity. They also do not take into account the energy needed to slow down upon reaching the destination. If you actually wanted to stop at your target, it would take twice the energy. That’s why flyby missions are so much easier then orbit attaining missions.

What if you wanted to send humans on a mission of 50 years? Let’s say you wanted to send a mission of four people. A low estimate for the amount of food required for one human for one year is 500 kilograms. A low estimate of the average mass of a human is 50 kilograms. Let’s say they would require a space craft at least the mass of the space shuttles, about 60,000 kilograms. In total then we would have 500kg*4 people* 50 years+50kg*4 + 60,000kg= 160,200 kilograms. To send this mass on a  one way 50 year mission to Alpha Centauri at 8.76% of the speed of light would require a minimum of 5.6*10^19 joules or the energy from a 1000 MW nuclear power plant running for 1,852 years. If they wanted to reach 50% of the speed of light they would need 2.2*10^21 joules or 74,283 years of 1000MW nuclear power plant output. I think I have already made my point, but just for fun let’s look at what it would take to move the entire population of Earth to Alpha Centauri in 50 years. Mr. Munroe at what if xkcd looked at what it would take to get every person off the planet. He estimates that the total mass of all humans is 400 million (I assume metric) tons. Once we were all off world it would take about 1.2*10^26 joules or 4 billion years of 1000MW power plant energy to propel us to Alpha Centauri.

                I actually do think that humans will eventually travel to and maybe even colonize other star systems. I could see us building a spacecraft that could support a small population for multiple generations more or less indefinitely. However barring some huge technological breakthrough which is always possible, but should not be assumed or counted on, humans will not be travelling to another star system for a very, very long time.


Update:
I forgot to thank Yahoo Answers user debydete for telling me the equation for the energy needed to propel a given mass to a certain velocity. Thank you good sir(mam?).

Also it was recently discovered the Alpha Centauri B has a planet orbiting it, so there may actually be a good reason to someday send a mission there. Though a manned mission may not be necessary as the planet is definitely not inhabitable. The Bad Astronomer has more details.