Rockets and momentum (short version)

Compare these two rocket engines. First, the mighty F1,

five of which powered the giant Saturn 5 moon rocket,

On the other hand, the Deep Space 1 ion engine is just a small portion of this tiny spacecraft:

Which do you think gave its payload a larger final speed?







           Well?  Guess!

The answer is .... the tiny ion engine, which accelerated its payload to 7,800 m/s. The F1 could only reach a speed of 7,500 m/s. How is that possible? You need to know how rockets work to understand ....

Rockets and Momentum

So far, in all the examples of momentum you have seen, the mass has been constant. That simplifies the calculations ....

But what if the mass of an object changes as it moves? Then the derivative of momentum becomes more complicated ...

But we'll have to deal with this complication if we want to understand how rockets work.

Now, the two rocket engines took two different approaches to pushing their payloads forward.



                 Saturn F1            DS1 ion engine
---------------------------------------------------------

maximize        rate of fuel           speed of exhaust
                consumption 


fuel usage       2,450 kg/s              0.000 002 kg/s
 (dM/dt)


exhaust speed    2,600 m/s          43,000 m/s
  (u)


thrust       6,400,000 N                 0.09 N


duration of
  thrust             3 minutes         440 days
 
----------------------------------------------------------

Thrust -- how hard does the engine push?

The Saturn rocket had much greater thrust than the DS1, by a factor of about 100,000,000! The Saturn could lift itself, plus a heavy payload, off the ground.

The DS1 couldn't lift sheet of paper off the ground, and so had to hitch a ride on a conventional chemical rocket.

What is the final speed of the rocket?



Rocket    initial mass     final mass      exhaust speed
            (kg)             (kg)            (m/s)
---------------------------------------------------------

Saturn      436,000          26,600          2,600


DS1             489.5           408         43,000
---------------------------------------------------------

For more details, you can read these sets of lecture notes:

Longer version of this lecture, with specific examples
Rockets and momentum (old Physics 311 lecture notes)
Detailed comparison of Saturn F1 engine vs. Deep Space 1 ion engine (more old Physics 311 lecture notes)
Picture of the F1 engine
Calculating the final speed of a Saturn V rocket
A history of the Soviet N-1 rocket , the ill-fated competitor of the Saturn.
The Deep Space 1 mission used an ion engine.
The European SMART-1 spacecraft also uses an ion engine (and is still alive in Jan 2005)
FAQ about ion engines
Richard Hofer works on ion engines for NASA.
Everything you wanted to know about rocket propellents, but were afraid to ask.
The Basics of Space Flight from JPL (who ought to know).
The Encyclopedia Astronautica is chock full of information on rockets of all kinds.