MadSci Network: Astronomy
Query:

Re: Why can't we travel faster in space ?

Area: Astronomy
Posted By: Jason Goodman, Graduate Student, Massachusetts Institute of Technology
Date: Thu Apr 10 12:56:46 1997
Message ID: 859053582.As


The short answer: a rocket's speed is limited by the fuel it can carry.

The long answer:
A rocket works by expelling gases backward at high speed. There is an equal and opposite reaction to this which pushes the rocket forward. A rocket can generate more thrust, and therefore accelerate faster, by burning fuel faster. Unfortunately, this faster fuel-burning means you run out of gas quicker. If you carry more fuel, you can run the engines longer, but since the extra fuel weighs more you need to thrust harder (and so burn more fuel) to increase your speed.

All these effects cancel out: if you work through the physics (explained in any college freshman physics textbook), you find that if a rocket starts from rest, its speed when it runs out of fuel will always be

V = Ve ln(M0/Mf)

where Ve is the speed of the exhaust leaving the back of the rocket, M0 is the starting mass of the rocket, and Mf is the final mass of the rocket after all the fuel is burned. The math isn't important: what matters is that a rocket's final speed when it runs out of fuel depends on the exhaust speed and Mf/M0, the "mass fraction". Since a rocket can't be all fuel (it needs fuel tanks, engines, a frame, astronauts, and cargo to be useful) it's very hard to make the mass fraction less than 0.1. The exhaust velocity depends mostly on the chemicals used as fuel. The best is hydrogen and oxygen, which has Ve = 4.5 km/s. That means the fastest a single-stage rocket can go is about 10 km/s, or 22,000 miles per hour. This is barely fast enough to reach Earth orbit from the ground. Practical rockets often drop parts of themselves (empty fuel tanks) as they travel, to reduce the final mass, but this doesn't help a whole lot.

Spacecraft can go faster by using other things besides chemical rockets for power. A rocket which heats the exhaust using a nuclear reactor can get Ve = 100 km/s, giving rocket top speeds of hundreds of km/s.

Sunlight exerts pressure against objects in space: a "solar sail" works by using that pressure to move around the solar system, just like a sailing ship uses wind pressure. A solar sail, like a sailing ship, never needs fuel.

Finally, a spacecraft can fly close by a planet and use the planet's gravity to speed up: this is called a "gravity slingshot".

Spacecraft like Voyagers I and I and Galileo used gravity slingshots on numerous occasions. Nuclear rockets and solar sails have been built, but never flown in space.

There's a much bigger limit on a spacecraft's speed. Einstein's theory of general relativity says that no object can travel faster than the speed of light: 300,000 km/s or 600,000,000 mph. The reasons for this are rather complex, but books explaining special relativity such as A Traveler's Guide to Spacetime require only high school physics and algebra.

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