Fuel: Here's the Math

If you want to calculate the energy required to accelerate your spaceship to a particular speed, here’s how. 

First, you need to calculate a numerical value called gamma (). Gamma depends on how fast something is going. You calculate it with the following equation:

        

Once you have gamma, you can figure out how much energy you need with this equation:

        

where m0 is the rest mass of the object.

Using this equation, you can calculate the energy required to accelerate your 1000-kilogram spaceship to 0.99 times the speed of light. First, you need to calculate  by plugging the appropriate values into the equation. Note that the speed of light is approximately 300 000 kilometers per second, or 3 x 108 meters per second.

           

Then you use  to compute the required energy. 

           

That’s 550 million million million joules (J) —about five times the total energy used in the United States in one year. Named after British physicist James P. Joule, a joule (rhymes with “pool”) is a unit that measures energy or work. That’s what it takes to accelerate your spaceship to 0.99 times the speed of light.

 

 


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