Implications of the Rocket Equation

The rocket equation relates two ratios. A rocket makes a payload move by throwing something away in the opposite direction. The rocket equation relates the ratio of payload to the mass of the entire rocket (including fuel) to the ratio of the velocity we threw our propellant away with and the velocity we want our payload to attain. The equation can be written as

     vfinal / vexhaust = ln(mtotal/mpayload)

Here
v_final is the final velocity we attain assuming we start at 0,
v_exhaust is the exhaust velocity of our propellant,
m_total is the total mass of our rocket, and m_payload is the mass of the payload.

We've established that we need to achieve a v_final of at least 0.1 c = 3x10⁷ m/s. The Wikipedia article on specific impulses gives the highest specific impulse to a concept of VASIMR ion engines with an exhaust velocity of 10⁵m/s. If we use this in the rocket equation we have

     mtotal=106kg e(3.e7/1.e5) or about 10137kg.

So using the best rocket technology that we can currently compass, our initial rocket would weight more than the entire universe. Clearly we aren't going anywhere with convention rocket technology. If we are going to use rockets we need much higher exhaust velocity -- at least a few per cent of the speed of light.

Nuclear explosions can produce an 'exhaust' of 3-30x10⁶m/s. At the upper range this gets our velocity ratio down to just 1, so that the mass of the propellant is roughly comparable to the mass of the payload. This Orion concept goes back to the 1950's but seems unlikely to make a comeback until we are looking at launches far from Earth.  However it is the only current technology which is even in the ballpark.

The rocket equation suggests three alternatives:

1. Use nuclear explosions for our propellent,
2. Use new rocket technologies with very high exhaust velocities, e.g., photon rockets, or
3. Use non-rocket technologies where we either supply our vessel during the mission, or we extract energy/momentum from the ambient environment.