Calculating the Energy of Antimatter Help

[Visperidia]

It is said that, " A kilogram of antimatter, annihilating with ordinary matter, can produce ten billion times the amount of energy released when a kilogram of TNT explodes." I'm attempting to figure out how much antimatter it would take to propel a ~800 kg object through space at 11 miles per second, for 20 light years.

 

I've a very limited knowledge of E=mc2 and would appreciate a simplified explanation as to how I would even go about answering this problem and which formulas I would need.

 

Thanks very much for any help

[Janus]

I'm curious as to why you want to know this, as it seems an unusual combination of values.

 

First off, the distance you travel has now effect on the energy needed if you are traveling at a constant speed. You only need energy to get up to 11 mps, and then you coast the whole way.

 

Doing a straight conversion, The energy needed is found by

 

[math]E = \frac{v^2m}{2}[/math]

 

The unit have to be in the same system (for example m is Kilograms, then V is in meters/sec)

 

11 mps is 17600 m/s, so this gives 1.24 x 10^11 joules. which works out to 0.0013 grams of Antimatter and matter combined.

 

However, it is not quite that straight forward as there is no way to convert that energy directly into velocity.

 

What you have to do is use a rocket which means that you are throwing stuff out the back in order to go forward. A percentage of the energy used is carried off by what you throw out. How much depends on some factors. A major one is how fast you throw the stuff out. The faster your exhaust gasses the more efficient your rocket.

 

Without knowing exactly what kind of exhaust speed you are going to generate with your ship, you can't really get a good answer as to what you are going to need to get up to your required speed.

 

On a side note, 11 miles per second is a really slow speed to try to travel 20 light years at. It would take you some 338182 yrs to do so.

Edited November 8, 2013 by Janus

[Visperidia]

Thank you so much! You did a really great job of making it understandable to someone who is more versed with the soft sciences, like me.

Edited November 8, 2013 by Visperidia

[Sensei]

Object in cosmic space once accelerated to 11 mps will continue going with that speed as long as particles from cosmic rays won't slow it down (or it won't be attracted by some massive object).

Collisions with them or with photons from Sun or other stars will have effect in long term.

But in short term, it's like discussing about changing path of 800 kg asteroid by cosmic rays and photons (negligible).

 

11 mps is half of speed of Earth around Sun (30 km/s)..

 

Maybe you're thinking about accelerating 11 km/s^2 for 20 years instead?

 

20 light years is distance = 20 * 365.25 * 24 * 3600 * c = ~1.89*10^14 km

not time.

Edited November 10, 2013 by Sensei